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NISTIR 7839

Examination of Downsampling Strategies for Converting

1000 ppi Fingerprint Imagery to 500 ppi

Shahram Orandi

John M. Libert

John D. Grantham

Margaret Lepley

Bruce Bandini

Kenneth Ko

Lindsay M. Petersen

Stephen S. Wood

Stephen G. Harvey

  

http://dx.doi.org/10.6028/NIST.IR.7839

   
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NISTIR 7839

Examination of Downsampling Strategies for Converting

1000 ppi Fingerprint Imagery to 500 ppi  

   Shahram Orandi  

John M. Libert

Kenneth Ko

Stephen S. Wood

Stephen G. Harvey

Information Access Division ‐ Image Group  

Information Technology Laboratories

John D. Grantham

Systems Plus, Inc.

Margaret Lepley

Lindsay M. Petersen

MITRE Corporation

Bruce Bandini

Booz Allen Hamilton, Inc.

http://dx.doi.org/10.6028/NIST.IR.7839

January 2013

U.S. Department of Commerce  

Rebecca Blank, Acting Secretary

National Institute of Standards and Technology  

Patrick D. Gallagher, Under Secretary of Commerce for Standards and Technology and Director
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ACKNOWLEDGEMENTS

The authors wish to give special thanks to the Federal Bureau of Investigation for all their support throughout this study.

The authors also give thanks to Vincent M. Stanford who provided early guidance on the creation and utilization of non‐square filtering

strategies in signal shaping which was used as a basis in the creation of the Gaussian filter utilized in this study.

In addition we are grateful for all the guidance, support and coordination provided by Michael D. Garris, whose help made this study possible.

DISCLAIMER

Specific hardware and software products identified in this report were used in order to perform evaluations. In no case does identification of

any commercial product imply endorsement by the National Institute of Standards and Technology, nor does it imply that the products and

equipment identified are necessarily the best available for the purpose.

ABSTRACT

The Federal Bureau of Investigation (FBI) is increasing the sample rate at which it acquires and stores fingerprint imagery, and to

accommodate the higher sample rate is replacing Wavelet Scalar Quantization (WSQ) with JPEG2000 as its standard compression algorithm.

Currently the bulk of fingerprint data in operations is captured, processed and stored at 500 ppi (pixels per inch) using the WSQ compressed

digital format. With the transition to 1000 ppi, some systems will unavoidably contain an overlap between 500 ppi and 1000 ppi operational

pathways.  This overlap may be a result of legacy infrastructure limitations, or some other financial or logistical reason.  Additionally, there will

still be a need to compare newly collected 1000 ppi images against legacy 500 ppi images, for both one‐to‐one and one‐to‐many scenarios.   To

create a bridge between legacy and modern data there needs to be a pathway for interoperability putting legacy and modern data on equal

footing by converting one of the images to the same resolution as the other.  Downsampling of the higher resolution 1000 ppi imagery to 500

ppi provides this pathway.  The study compares several computational methods for downsampling of modern fingerprint images from 1000

ppi to 500 ppi. These treatments include pixel averaging, decimation, transcoding directly from the JPEG2000 codestream, Gaussian filtering

and spectral truncation. Fidelity of downsampled 1000 ppi images relative to corresponding prints scanned natively at 500 ppi is evaluated via

scoring by expert fingerprint examiners, an automated machine matcher, RMS differences and correlation of spectra.   Gaussian low‐pass

filtering (σ = 0.8475, r = 4) combined with decimation emerged as the optimal downsampling strategy with respect to image fidelity when

gauged by several different ranking strategies. Transcode methods involving selective decoding of JPEG2000 images so as to discard the

highest resolution decomposition level yielded 500 ppi images that were not of optimal quality but were processed at considerably higher

speed due to greater computational efficiency of such transcode algorithms making these methods attractive in a tradeoff between image

fidelity vs. sheer computational throughput.
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EXECUTIVE SUMMARY

The criminal justice community has traditionally exchanged and stored fingerprint imagery data at 500 pixels per inch1(ppi) or 19.7 pixels per

millimeter (ppmm).  The Wavelet Scalar Quantization (WSQ) fingerprint image compression algorithm is currently the standard for the lossy

compression of 500 ppi fingerprint imagery and the WSQ Gray‐Scale Fingerprint Image Compression Specification [WSQ] provides guidance

based on an International Association for Identification (IAI) study [FITZPATRICK] to establish the acceptable amount of fidelity loss due to

lossy compression in order for a WSQ encoder and decoder to meet FBI certifications. These certifications are designed to ensure adherence

to the WSQ specification and thereby to ensure fidelity and admissibility in courts of law for images that have been processed by such

encoders and decoders.   

Modern biometric systems are now trending towards the capture, transfer and storage of fingerprint images at 1000 ppi or 39.4 ppmm which

offers many benefits, notably greater fidelity and better representation of Level 3 features. The ANSI/NIST ITL [ANSI/NIST‐ITL 1‐2011] and ISO

19794 [ISO/IEC 15948:2004] standards require 1000 ppi image compression using the JPEG2000 algorithm rather than WSQ.  The reason for

this is due to design factors in the WSQ compression format that optimize it specifically for 500 ppi and making it unsuitable for supporting the

finer detail present in 1000 ppi fingerprint imagery.     

With the transition to 1000 ppi, some systems will unavoidably contain an overlap between 500 ppi and 1000 ppi operational pathways.  This

overlap may be a result of legacy infrastructure limitations, or some other financial or logistical reason.  Additionally, there will still be a need

to compare newly collected 1000 ppi images against legacy 500 ppi images, for both one‐to‐one and one‐to‐many scenarios.   To create a

bridge between legacy and modern data there needs to be a pathway for interoperability putting legacy and modern data on equal footing by

converting one of the images to the same resolution as the other.   Downsampling of the higher resolution 1000 ppi imagery to 500 ppi

provides this pathway.  Many well established computational methods exist for the downsampling of images.   

The following study addresses the need for interoperability between the legacy 500 ppi data and modern 1000 ppi data by comparing several

computational methods (treatments) for downsampling of modern fingerprint images from 1000 ppi to 500 ppi to allow for interoperability

with legacy 500 ppi imagery. These treatments included pixel averaging, decimation, transcoding, Gaussian filtering and spectral truncation,

which are measured using various techniques and the data analyzed to identify an optimal strategy.

To gauge the effectiveness of the downsampling methods several different fidelity measures were employed for each treatment including

expert examiner assessment or machine matcher score assessment.   The results of these fidelity measures were then fused using various

techniques to provide an overall measures of how well the treatments worked.   In order to provide a basis of measure for the downsampling

treatments, a control set of native 500 ppi imagery that did not require any downsampling were utilized in the study in addition to the

downsampled 1000 ppi images.

The experiment showed that the native 500 ppi control set of images yielded the best results versus 1000 ppi images that have been

downsampled to 500ppi.    Following the native 500 ppi control case were the Gaussian treatment cases.    

The Gaussian treatment (σ  = 0.8475, r = 4) emerged as the optimal downsampling strategy when gauged by several different ranking

strategies including Ordinal Rank Summation (optimistic decimation), Mean Rank Summation (optimistic decimation) and Expert Examiner

Winner‐Take‐All (which fuses optimistic and conservative decimation strategies).   Where the Gaussian treatment (σ = 0.8475, r = 4) was not

identified as optimal (following the control case), it was identified as second best (or tied as such) and was not a radical compromise in terms

of the fidelity measures that failed to identify it as the best/top candidate.

Looking deeper into the various individual measures did uncover some surprises.   In the case of expert examiner fidelity assessment, the

downsampled images yielded better subjective quality than the native 500 ppi control case which indicates that some signal noise reduction

may result in a positive impact in the perception of image quality by expert examiners.

With respect to objective examiner assessments of the images where the examiner was asked to make an identification decision between a

downsampled image and the native 500 ppi version of that image, a statistically significant difference could not be established.  This reinforces

findings from NISTIR‐7778 [NISTIR7778] that showed expert examiners could nearly universally detect degradation in fingerprint ridge

structure as a result of lossy compression, but this effect did not appear to measurably impact their ability to conduct their identification tasks.   

                                                                    

1 Resolution values for fingerprint imagery are specified in pixels per inch (ppi) throughout this document.    This is based on widely used

specification guidelines for such imagery and is accepted as common nomenclature within the industry. SI units for these will be presented

only once.
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This is analogous to operating a motor vehicle with a "dirty windshield", where the driver's ability and experience mitigates any effect from

occlusions large or small in their field of view.

An examination of automated (machine) matching of the downsampled images to a native 500 ppi gallery of fingerprint images showed that

the 500 ppi native control case again outperformed all downsampling treatments, followed by several Gaussian treatments including (σ  =

1.2730, r = 5, Odd‐Even) using the optimistic decimation strategies and (σ = 1.1879, r = 5, Even‐Odd) using the conservative decimation strategy.   

Based on the results of this study however, it appears that a strategy that optimized performance of the research matcher via very large

Gaussian filters yielded a degradation in subjective fidelity assessment of the image by expert examiners.  While the images favored by the

matcher were not the worst in terms of expert examiner assessments, they did rank far lower by examiners.  While it is possible to re‐apply

Gaussian filtering to an image, it is not possible to undo signal loss as a result of Gaussian filtering therefore a potential strategy to favor both

the expert examiners as well as the matcher may involve applying one pass of Gaussian filtering in the downsampling process to provide some

signal noise cleanup, and then later a second pass for some additional noise filtering just prior to processing of fingerprints for machine

matching.

Examination of system throughput however points to Transcoded A and Transcoded B as the optimal solution in terms of operational

efficiency and lower resource demands by eliminating several processing steps in the downsampling pathway.  The elimination of processing

steps by operating on the wavelet data directly helped avoid some of the intermediate steps needed for traditional downsampling and avoid

the associated throughput penalty for these intermediate steps.  Cursory studies show that these methods may be up to 10 times faster than

the more computationally intensive Gaussian methods.

Finally, with regard to Gaussian filter sizes, it was shown that the automated matching favors Gaussian cases with larger sigma & radius values

while other fidelity measures favor smaller sigma & radius value indicating that cases that are optimized for automated matching specifically

may not be optimal for other fidelity measures including expert human perception.
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VERSION HISTORY

Date Activity

12/31/2012 Released final version 1.0

   

   

	 	
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Table of Contents

1. Introduction and Investigative Goals .......................................................................................................................... 19

1.1. Background............................................................................................................................................................ 19

1.2. Key Drivers and Mandates .................................................................................................................................... 20

2. Materials.........................................................................................................................................................................21

2.1. Dataset....................................................................................................................................................................21

2.2. Fingerprint Examiners ........................................................................................................................................... 23

2.3. Equipment.............................................................................................................................................................. 23

3. Methods ........................................................................................................................................................................ 25

3.1. Downsampling Treatments .................................................................................................................................. 25

3.1.1. Decimation...........................................................................................................................................................................25

3.1.2. Averaging .............................................................................................................................................................................26

3.1.3. Transcoding..........................................................................................................................................................................26

3.1.4. Gaussian Filtering with Decimation .....................................................................................................................................27

3.1.5. Spectral Truncation..............................................................................................................................................................28

3.2. Metrics ................................................................................................................................................................... 32

3.2.1. Expert Examiners .................................................................................................................................................................32

3.2.2. Automated Matching...........................................................................................................................................................34

3.2.3. Spectral Image Validation/Verification Metric (SIVV).......................................................................................................... 36

4. Analysis..........................................................................................................................................................................39

4.1. Normality Test .......................................................................................................................................................39

4.2. Analysis Algorithm.................................................................................................................................................39

4.3. Hypothesis Testing.................................................................................................................................................41

4.3.1. Friedman’s Procedure..........................................................................................................................................................41

4.3.2. Wilcoxon Signed Rank Test ..................................................................................................................................................42

5. Results ...........................................................................................................................................................................45

5.1. Investigative Goal 1: Expert Examiner Quality Assessment ................................................................................45

5.1.1. Investigative Analysis 1 ........................................................................................................................................................45

5.1.2. Investigative Result 1 ...........................................................................................................................................................47

5.2. Investigative Goal 2: Expert Examiner Identification Assessment .....................................................................48

5.2.1. Investigative Analysis 2 ........................................................................................................................................................48

5.2.2. Investigative Result 2 ...........................................................................................................................................................49

5.3. Investigative Goal 3: Automated Matching Assessment ....................................................................................50

5.3.1. Investigative Analysis 3 ........................................................................................................................................................50

5.3.2. Investigative Result 3 ...........................................................................................................................................................52

5.4. Investigative Goal 4: Signal Analysis and Assessment......................................................................................... 53

5.4.1. Investigative Analysis 4 ........................................................................................................................................................53

5.4.2. Investigative Result 4 ...........................................................................................................................................................59

5.5. Investigate Goal 5:  Optimal Strategy Determination .........................................................................................60

5.5.1. Clustered Rank Summation Analysis....................................................................................................................................60

5.5.2. Ordinal Rank Summation Analysis .......................................................................................................................................62

5.5.3. Mean Rank Summation Analysis..........................................................................................................................................64

5.5.4. Mean Rank Summation Analysis for Expert Examiner Winner‐Take‐All..............................................................................66

5.6. Uncertainty Measurement....................................................................................................................................66

5.6.1. Expert Examiner Subjective Assessment Uncertainty.......................................................................................................... 66
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5.6.2. Automated Matching Assessment Uncertainty ................................................................................................................... 68

5.6.3. Signal Analysis and Assessment...........................................................................................................................................69

5.6.4. Normalized Score Comparative Analysis.............................................................................................................................. 71

5.7. Other Considerations .............................................................................................................................................71

6. Conclusions ................................................................................................................................................................... 73

7. Discussions and Future Work....................................................................................................................................... 75

Publications and Reports ................................................................................................................................................. 77

Standards..........................................................................................................................................................................78

Appendix A. ‐ Dataset Makeup ...........................................................................................................................................79

Demographic Make‐up of Ink Card Scan Datasets............................................................................................................................... 79

Appendix B. ‐ Equipment Used for Study........................................................................................................................... 81

Appendix C. ‐ Gaussian filter code......................................................................................................................................83
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LIST OF TABLES

Table 1 ‐ Abbreviations.............................................................................................................................................................................17

Table 2 ‐ Typical Use Cases that May Require Transcoding ...................................................................................................................21

Table 3 ‐ Treatments Applied to Test Images ........................................................................................................................................ 22

Table 4 ‐ Comparison Methods .............................................................................................................................................................. 22

Table 5 ‐ Decimation Pathways .............................................................................................................................................................. 25

Table 6 ‐ Gaussian Filter Parameters Selected for This Study...............................................................................................................28

Table 7 ‐ Identification Decision Coding................................................................................................................................................. 32

Table 8 ‐ Sorted Examiner Response Code Classification..................................................................................................................... 32

Table 9 ‐ Observation Codes for Image Degradation of Downsampling Treatments ......................................................................... 33

Table 10 ‐ Sorted Examiner Response Code Classification.................................................................................................................... 33

Table 11 ‐ Block Design Example............................................................................................................................................................. 41

Table 12 ‐ Expert Examiner Quality Data Analysis, Stage One (Sub‐treatment Pare‐Down, Adjusted α = 0.0167).............................45

Table 13 ‐ Expert Examiner Quality Data Analysis, Stage Two (Optimistic Decimation Pare‐Down, Adjusted α = 0.0018) ...............46

Table 14 ‐ Expert Examiner Quality Data Analysis, Stage Three (Conservative Decimation Pare‐Down, Adjusted α = 0.0018)........47

Table 15 ‐ Expert Examiner Match Data Analysis, Stage One (Sub‐treatment Pare‐Down, Adjusted α = 0.0167)..............................48

Table 16 ‐ Expert Examiner Match Data Analysis, Stage Two (Optimistic Decimation Pare‐Down, Adjusted α = 0.0018)................49

Table 17 ‐ Automated Matching Data Analysis, Stage One (Sub‐treatment Pare‐Down, Adjusted α = 0.0167).................................50

Table 18 ‐ Automated Matching Data Analysis, Stage Two (Optimistic Decimation Pare‐Down, Adjusted α = 0.0018).....................51

Table 19 ‐ Automated Matching Data Analysis, Stage Three (Conservative Decimation Pare‐Down, Adjusted α = 0.0018)............. 52

Table 20 ‐ Frequency Spectrum Correlation Analysis, Stage One (Sub‐treatment Pare‐Down, Adjusted α = 0.0167)....................... 53

Table 21 ‐ Frequency Spectrum Correlation Analysis, Stage Two (Optimistic Decimation Pare‐Down, Adjusted α = 0.0018) ..........54

Table 22 ‐ Frequency Spectrum Correlation Analysis, Stage Three (Conservative Decimation Pare‐Down, Adjusted α = 0.0018)...55

Table 23 ‐ Root Mean Square Difference Analysis, Stage One (Sub‐treatment Pare‐Down, Adjusted α = 0.0167)............................56

Table 24 ‐ Root Mean Square Difference Analysis, Stage Two (Optimistic Decimation Pare‐Down, Adjusted α = 0.0018).............. 57

Table 25 ‐ Root Mean Square Difference Analysis, Stage Three (Conservative Decimation Pare‐Down, Adjusted α = 0.0018) .......58

Table 26 ‐ Clustered Rank Summation Using Optimistic Decimation Strategy....................................................................................60

Table 27 ‐ Clustered Rank Summation Using Conservative Decimation Strategy ............................................................................... 61

Table 28 ‐ Ordinal Rank Summation Using Optimistic Decimation Strategy .......................................................................................62

Table 29 ‐ Ordinal Rank Summation Using Conservative Decimation Strategy...................................................................................63

Table 30 ‐ Mean Rank Summation Using Optimistic Decimation Strategy ..........................................................................................64

Table 31 ‐ Mean Rank Summation Using Conservative Decimation Strategy ......................................................................................65

Table 32 ‐ Expert Examiner Winner‐Take‐All Mean Rank Analysis........................................................................................................66

Table 33 ‐ Classifier Score Assignments .................................................................................................................................................67

Table 34 ‐ Generalized Comparison of Resource Requirements by Treatment................................................................................... 72

Table 35 ‐ Summary of Findings.............................................................................................................................................................. 73

Table 36 ‐ Ink Card Scan Data classification by Impression Type..........................................................................................................79

Table 37 ‐ Ink Card Scan Pattern Classification for Single Finger Images by Impression Type............................................................79

Table 38 ‐ Ink Card Scan Pattern Classification for Single Finger Images by Finger (Females)...........................................................79

Table 39 ‐ Ink Card Scan Pattern Classification for Single Finger Images by Finger (Males)...............................................................80

Table 40 ‐ Gender Breakdown for Data .................................................................................................................................................80

Table 41 ‐ Age Breakdown for Data........................................................................................................................................................80

Table 42 ‐ Other Metadata: Height and Weight ....................................................................................................................................80

Table 43 ‐ Other Metadata: Eye Color....................................................................................................................................................80
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LIST OF FIGURES

Figure 1 ‐ Decimation............................................................................................................................................................................... 25

Figure 2 ‐ Example of Undesirable Result with Decimation.................................................................................................................. 25

Figure 3 ‐ Pixel Averaging Strategy ........................................................................................................................................................26

Figure 4 ‐ Comparison of the Transcoded A and Transcoded B Methods............................................................................................ 27

Figure 5 ‐ Example of an inked, rolled fingerprint impression digitized at a sample rate of 1000 ppi................................................29

Figure 6 ‐ The DFT of the grayscale image depicted in Figure 5 displayed as an image. The inscribed rectangle marks the portion

of the spectrum to be extracted for construction of the 500 ppi image. (Note that the four quadrants of the spectrum have

been translated diagonally so as to center the zero‐frequency term, and the values have been scaled by the log function to

enable display of the spectrum otherwise overwhelmed by the high magnitude of the DC value.).........................................30

Figure 7 ‐ The extracted portion of the DFT exhibited in Figure 6 to be inverted to form the 500 ppi downsampled image shown

in Figure 8........................................................................................................................................................................................30

Figure 8 ‐ The 500 ppi image formed from inverting the truncated spectrum (Figure 7) of the fingerprint originally sampled at

1000 ppi. ...........................................................................................................................................................................................31

Figure 9 ‐ Split‐Screen Presentation of Image Pairs ..............................................................................................................................34

Figure 10  ‐  NIST SIVV metric applied to a 500 ppi image having undergone 1‐cycle of WSQ encoding/decoding and a

corresponding 1000 ppi fingerprint encoded/decoded using JPEG2000, downsampled to 500 ppi, and encoded and

decoded with WSQ. ........................................................................................................................................................................36

Figure 11 ‐ Normal Fit Histogram, Frequency Spectrum Correlation, Decimation (Odd‐Odd) Case....................................................39

Figure 12 ‐ Q‐Q Normality Plot, Frequency Spectrum Correlation, Decimation (Odd‐Odd) Case........................................................39

Figure 13 – Multi‐Stage Analysis Overview ............................................................................................................................................40

Figure 14 ‐ Expert Examiner Subjective Assessment 95 % Confidence Intervals for Mean Rank, Mean and Median using Bootstrap

Analysis............................................................................................................................................................................................67

Figure 15  ‐  Automated Matching Assessment 95 % Confidence Intervals for Mean Rank, Mean and Median using Bootstrap

Analysis............................................................................................................................................................................................68

Figure 16  ‐  Frequency Spectrum Correlation Analysis 95 % Confidence Intervals for Mean Rank, Mean and Median using

Bootstrap Analysis ..........................................................................................................................................................................69

Figure 17 ‐ Root Mean Square Difference Analysis 95 % Confidence Intervals for Mean Rank, Mean and Median using Bootstrap

Analysis............................................................................................................................................................................................70

Figure 18 ‐ Normalized Score Comparative Analysis ..............................................................................................................................71

Figure 19 ‐ Average Processing Time(s) by Treatment Class ................................................................................................................ 72

Figure 20 ‐ Median Processing Time(s) by Treatment Class ................................................................................................................. 72

   
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TERMS AND DEFINITIONS

The abbreviations and acronyms of Table 1 are used in many parts of this document.

Table 1 ‐ Abbreviations

ANSI American National Standards Institute

ANSI/NIST ITL ANSI/NIST‐ITL 1‐2011, NIST Special Publication 500‐290: Data Format for the Interchange of

Fingerprint, Facial & Other Biometric Information

bpp Bits per pixel

FBI Federal Bureau of Investigation

IAFIS Integrated Automated Fingerprint Identification System

IAI International Association for Identification

JPEG Joint Photographic Experts Group ‐ ISO/IEC committee developing standards for image compression

NBIS NIST Biometric Image Software

NGI Next Generation Identification

NIST National Institute of Standards and Technology

ppi Pixels per inch

ppmm Pixels per millimeter  

WSQ The Wavelet Scalar Quantization algorithm for compression of fingerprint imagery

KEYWORDS

500 ppi; 1000 ppi; fingerprint imagery; downsampling; fingerprint compression; transcoding
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1. Introduction and Investigative Goals

In partnership with the FBI, NIST launched an investigation, starting in November 2011, on the use of various downsampling strategies for

converting 1000 ppi (39.4 ppmm) grayscale fingerprint images at 8 bpp to 500 ppi (19.7 ppmm).  The 1000 ppi images were compressed with

JPEG2000 [JPEG2K] per guidance provided in [MTR], and the 500 ppi were compressed with WSQ per FBI specifications.  The methods were

studied according to their impact on image quality and the ultimate utility of those images for machine based matching.    This study

encompassed the following objectives for downsampling comparison:

1. Expert Examiner Subjective Assessment:  Investigate expert examiner opinion to gauge perceived degradation of 1000 ppi images

as a result of downsampling to 500 ppi, compared to same image scanned natively at 500 ppi.

2. Expert Examiner Objective Assessment:  Investigate impact on an expert examiner’s ability to successfully make an ident/non‐ident

decision.

3. Automated Matching Assessment:    Investigate effects on an automatic matcher by comparing match scores for pairs of

downsampled 1000 ppi images versus native 500 ppi images.

4. Signal Analysis and Assessment:  Investigate the effects of various downsampling strategies using various signal analysis methods.

5. Optimal Strategy Determination: Given the collected data, determine an optimal downsampling strategy for 1000 ppi fingerprint

data.

1.1. Background

The criminal justice community has traditionally exchanged and stored fingerprint imagery data at 500 ppi, yet modern biometric systems are

trending towards the transfer and storage of images at 1000 ppi.    Transitioning to 1000 ppi images offers many benefits, notably greater

fidelity to the original sample and better representation of Level 3 features.    Both are favorable since they may increase probability of

establishing a match/non‐match by expert examiners or automated fingerprint matchers.

However, the transition to 1000 ppi systems will also unavoidably contain an overlap between 500 ppi and 1000 ppi operational pathways.  

Some stakeholders may simply continue to operate at 500 ppi due to technical, financial or logistical reasons.  Additionally, there will still be a

need to compare newly collected 1000 ppi images against legacy 500 ppi images, for both one‐to‐one and one‐to‐many scenarios.

There are two possible methods of interoperability between 500 ppi and 1000 ppi.   The first method involves the downsampling (also known

as subsampling) of 1000 ppi images to create a smaller 500 ppi image, while the second method would take a 500 ppi image and upsample it

to 1000 ppi.  The process of downsampling involves discarding data while upsampling would lead to the introduction of new data.   Discarding

data is more generally accepted for biometric data processing rather than the introduction of new data (through upsampling).   The focus of

this study is on the more generally acceptable practice of downsampling from 1000 ppi to 500 ppi to create a common ground for

interoperability.

There are many recognized methods for downsampling of image data, each with their own set of advantages and disadvantages.   This study

focuses on four such methods: pixel averaging, decimation, transcoding, Gaussian filtering and spectral truncation.   These methods are

described in greater detail in section 3.1.

   
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1.2. Key Drivers and Mandates

NIST has an established expertise in evaluating biometric systems and standards, and has been assigned by the USA PATRIOT Act (Public Law

107‐56) the responsibility for developing and certifying biometric technology standards. NIST has been supporting biometric standards and

evaluation activities for over forty years, starting with fingerprint analysis which began in 1965.

In modernizing its environment as part of the Next Generation Identification (NGI) initiative, the FBI seeks to expand its ability to exchange

fingerprints at 1000 ppi.  As part of a broader effort to enhance fingerprint system capacity, identification, and verification, this upgrade will

help the FBI meet its mandate to:

‐ Protect the United States from terrorist attacks, foreign intelligence operations and espionage

‐ Support Federal, state, local and international partners in their efforts to reduce crime and violence

‐ Upgrade technology to support the FBI's missions

Toward meeting these goals, the FBI seeks to guide the development of next generation friction ridge systems towards operation at 1000 ppi

while at the same time ensuring interoperability with legacy 500 ppi systems, as well as maintaining fidelity and admissibility in courts of law.

The MITRE Corporation has developed an informative guidance that is widely recognized as the de facto standard guidance for utilizing

JPEG2000 for the compression of 1000 ppi fingerprint imagery in MTR‐04B0000022 [MTR].  This document provides a compression profile for

1000 ppi fingerprint imagery using JPEG2000 as well as guidance for two downsampling strategies that can be used to convert 1000 ppi

JPEG2000 imagery to 500 ppi.

In support of the FBI, the National Institute of Standards and Technology (NIST) conducted a study to compare several downsampling

strategies including the current de facto standard guidance [MTR] and measure the impact of the various strategies on operational and

subjective criteria, and to formulate a basis with which normative downsampling guidance can be built.  
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2. Materials

2.1. Dataset

A total of 2039 images were selected for this study from an updated version of the NIST Special Database 27A (SD‐27A) [SD27]. The SD‐27A

data set contains images that have been captured and stored in lossless JPEG‐2000 format.  Therefore these images have not been degraded

in any way by lossy compression algorithms along their processing path and maintain complete fidelity to the original sample as recorded by

the capture device.  These images were selected from multiple subjects and were captured natively, referred to as “Native Scans”, at 1000 ppi

and 500 ppi without repositioning the original fingerprint card on the scanner platen, resulting in scanned images with approximately the

same image content at multiple resolutions.  The flatbed optical scanner used to capture these images was an Epson Perfection 4990 Photo

scanner and was part of an FBI Appendix F certified commercially available solution.  A thorough description of the data set used in this study

can be found in Appendix A.    

This set of 2039 1000 ppi fingerprint images was processed and stored in the lossy JPEG‐2000 format per the guidance in [MTR].  The set was

then subjected to 28 different downsampling treatments plus one Control Case (see Table 3).  The rationale for converting the source images

to the lossy JPEG‐2000 format per the [MTR] guidance is because this case most closely resembles the operational Use Case of concern where

a 1000 ppi image has been captured and stored at origination point per [MTR], and later needs to be processed for a legacy pathway.   Other

operational Use Cases exist such as a 1000 ppi scanner capturing an image at the collection station, saving it in uncompressed format, and

then immediately downsampling it to 500 ppi at the collection station prior to processing at the site.  These other Use Cases are considered

outside the scope and were not examined since the study focus is on 1000 ppi images already stored in JPEG‐2000 format.  A full list of these

Use Cases is provided below in Table 2.

Table 2 ‐ Typical Use Cases that May Require Transcoding

Source Format Destination Format Notes

Lossless 1000 ppi Lossless 500 ppi Not examined in this study.

Not an anticipated operational Use Case.   

Lossless 1000 ppi WSQ lossy 500 ppi Not examined in this study.

Useful for example for backwards compatibility where a 1000 ppi‐

only scanner would capture, downsample and provide images to a

500 ppi application/processing layer.

JPEG‐2000 Lossy 1000 ppi Lossless 500 ppi Not examined in this study.  

Useful for example with on‐site processing of 1000 ppi images in

biometric systems that can only vectorize fingerprint images at 500

ppi and there is a desire to maintain operational benefit from the 500

ppi image without incurring any further degradation due to re‐

compression at 500 ppi after downsampling.

JPEG‐2000 Lossy 1000 ppi WSQ lossy 500 ppi The focus of this study.  

Expected operational Use Case where fingerprints compressed

according to [MTR] would be downsampled and submitted through a

pathway designed for production WSQ 500 ppi imagery.

Of the 28 downsampling treatments, 24 required decimation for geometric dimension correction after processing (see Section 5.7).   Rather

than selecting a particular method of decimation, all four possible combinations of decimation were applied to those 24 cases, creating 96 sub‐

treatments for the cases requiring decimation.  All downsampling treatments included WSQ compression2 as a final output step. Each case

was then paired with fingerprint images originally scanned at 500 ppi and WSQ compressed, referred to as “Native 500 ppi Scans”. The

Control Case contained two copies of the same 500 ppi native scan image which were both compressed with WSQ.

   

                                                                     2 R = 0.55 used as the WSQ compression rate control parameter.   
NISTIR 7839 ‐ Examination of Downsampling Strategies for Converting 1000 ppi Fingerprint Imagery to 500 ppi

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Table 3 ‐ Treatments Applied to Test Images

Treatment Number Treatment Name Decimation Sub‐treatment(s)

1 Native 500 ppi (Control Case) None ‐  ‐  ‐ 

2 Averaging None  ‐  ‐  ‐ 

3 Decimation Even‐Even Even‐Odd Odd‐Even Odd‐Odd

4 NIST Spectral Truncation None  ‐  ‐  ‐ 

5 Transcoded A None ‐  ‐  ‐ 

6 Transcoded B None  ‐  ‐  ‐ 

7 Gaussian σ = 0.3369, r = 2 Even‐Even Even‐Odd Odd‐Even Odd‐Odd

8 Gaussian σ = 0.4220, r = 2 Even‐Even Even‐Odd Odd‐Even Odd‐Odd

9 Gaussian σ = 0.5071, r = 3 Even‐Even Even‐Odd Odd‐Even Odd‐Odd

10 Gaussian σ = 0.5642, r = 3 Even‐Even Even‐Odd Odd‐Even Odd‐Odd

11 Gaussian σ = 0.5922, r = 3 Even‐Even Even‐Odd Odd‐Even Odd‐Odd

12 Gaussian σ = 0.6773, r = 3 Even‐Even Even‐Odd Odd‐Even Odd‐Odd

13 Gaussian σ = 0.7624, r = 3 Even‐Even Even‐Odd Odd‐Even Odd‐Odd

14 Gaussian σ = 0.8475, r = 4 Even‐Even Even‐Odd Odd‐Even Odd‐Odd

15 Gaussian σ = 0.9326, r = 4 Even‐Even Even‐Odd Odd‐Even Odd‐Odd

16 Gaussian σ = 1.0177, r = 4 Even‐Even Even‐Odd Odd‐Even Odd‐Odd

17 Gaussian σ = 1.1028, r = 4 Even‐Even Even‐Odd Odd‐Even Odd‐Odd

18 Gaussian σ = 1.1879, r = 5 Even‐Even Even‐Odd Odd‐Even Odd‐Odd

19 Gaussian σ = 1.2730, r = 5 Even‐Even Even‐Odd Odd‐Even Odd‐Odd

20 Gaussian σ = 1.3581, r = 5 Even‐Even Even‐Odd Odd‐Even Odd‐Odd

21 Gaussian σ = 1.4432, r = 5 Even‐Even Even‐Odd Odd‐Even Odd‐Odd

22 Gaussian σ = 1.5283, r = 6 Even‐Even Even‐Odd Odd‐Even Odd‐Odd

23 Gaussian σ = 1.6134, r = 6 Even‐Even Even‐Odd Odd‐Even Odd‐Odd

24 Gaussian σ = 1.6985, r = 6 Even‐Even Even‐Odd Odd‐Even Odd‐Odd

25 Gaussian σ = 1.7836, r = 6 Even‐Even Even‐Odd Odd‐Even Odd‐Odd

26 Gaussian σ = 1.8687, r = 7 Even‐Even Even‐Odd Odd‐Even Odd‐Odd

27 Gaussian σ = 1.9538, r = 7 Even‐Even Even‐Odd Odd‐Even Odd‐Odd

28 Gaussian σ = 2.0389, r = 7 Even‐Even Even‐Odd Odd‐Even Odd‐Odd

29 Gaussian σ = 2.1240, r = 7 Even‐Even Even‐Odd Odd‐Even Odd‐Odd

The image pairs (consisting of a native and downsampled image) from each treatment were then assessed using 4 different comparison

methods to measure degradation as the result of the various treatments.   These methods are listed below in Table 4 and are explained in

detail in Section 3.1.   Note that not all treatments utilized the same number of images.   The automated matcher testing method utilized the

full set of 2039 images, while the other methods utilized a subset of 200 images.   This is because anecdotal evidence suggests the automated

matcher behaves in a less predictable way for match score distribution as compared to the other metrics, thus requiring more images to

enhance statistical analysis of the resulting distribution.  The 200 sets of images selected for the other tests utilized the same set of 200 for all

the comparison methods (there was no reselection per method) to allow for apples‐to‐apples comparison of the treatments.

Table 4 ‐ Comparison Methods

Comparison Number Comparison Method Number of Image Pairs Used

1 Automated Matcher testing 2039

2 SIVV RMSD measurement 200

3 SIVV Correlation analysis 200

4 Latent Examiner analysis 200
NISTIR 7839 ‐ Examination of Downsampling Strategies for Converting 1000 ppi Fingerprint Imagery to 500 ppi

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2.2. Fingerprint Examiners

This study utilized 15 paid professional fingerprint examiners to look at fingerprint image pairs in their professional capacity and to render their

professional judgment much as they do in their normal professional activities.   

There was no attempt to evaluate the examiner’s accuracy or proficiency for this study.   There was also no attempt to identify or maintain the

identity of the individual examiners utilized in this study.  

The examiners had anywhere from three years to well over thirty years of experience in fingerprint examination.    The examiners were

recruited from various federal, state, local and commercial entities from across the United States.

A pre‐requisite for examiners being selected to participate in this study was that they be trained latent‐print‐examiners (LPEs).    This

requirement ensures that the examiners have received the most rigorous training possible. All 15 examiners participating in this study have

earned the IAI’s latent examiner certification (and are referred to as certified latent print examiners or CLPEs).  Selection of examiners for this

study was not meant to bias the results by utilizing latent‐only examiners and all of the examiners selected for this study perform 10‐print case

work in addition to latent case work as part of their regular professional duties.  While not the case in this study, it should be noted that some

of the LPE’s or CLPE’s working with larger agencies may be assigned latent only case work with almost no 10‐print case work.

The study provided three examiner workstations.   The examiners were paid professionals and were allowed to work on the study according

to their ability and timing.   Each examiner looked at a random subset of the image pairs in the study and no one examiner observed all image

pairs.  No examiner looked at the same image pair more than once.  Overall, each image pair was examined by exactly three examiners, but

the selection of which three examiners viewed a given pair was done at random.

2.3. Equipment

The equipment used for the expert fingerprint examiner portion of this study consisted of the following (equipment used for other metrics is

described in Appendix B):  

1 x Commodity Router: The router provides connectivity among the three workstations and NAS device, as well as providing remote access to

the workstations and NAS for administration.  

3 x Commodity Workstations: The workstations are configured with 8 GB RAM, 300 GB HD, 64‐bit operating system, FIXT3 software and data.   

3 x 24 inch Monitors: The IPS‐panel monitors are connected via DVI‐D and calibrated (see below) for optimal accuracy and consistency.  The

monitors were operated at their native resolution of 1920x1200, yielding a dpi measurement of approximately 94.3ppi.  The zoom functionality

in software allowed the examiners to zoom in and out of the image, and view them in the range of approximately 10x to 50x given these

specific monitors.

1 x Network Attached Storage (NAS): The NAS contains master copies of the FIXT software and data, as well as iterative copies of each

stations logs/results (saved at the end of each session).  

1 x Monitor Calibration Device: The monitors were calibrated using a system consisting of a colorimeter paired with proprietary software

designed specifically for use with the colorimeter and for the purpose of monitor calibration. The colorimeter is a sensor which provides an

accurate measurement of colors as they actually appear on the monitor screen. During the calibration process, the colorimeter is physically

attached to the monitor while the software displays a series of solid colors on the screen. The colorimeter measures the actual color values

displayed on the monitor and then provides these measurements to the software. The software uses these measurements to calculate the

difference between the color values as they are displayed on the monitor against the true color values within the software. The software then

applies configuration changes to the system in order to correct the color values displayed by the monitor, ensuring accurate color

reproduction. Due to the fact that each monitor, even of the same model, performs slightly differently in terms of the accuracy of color

reproduction, this process was completed independently on each of the three FIXT workstations.  

                                                                     3 The FIXT image comparison software was developed for NISTIR‐7778 [NISTIR7778] and has been reused in this study. More information on

FIXT can be found in the methodology section of NISTIR‐7778.
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NISTIR 7839 ‐ Examination of Downsampling Strategies for Converting 1000 ppi Fingerprint Imagery to 500 ppi

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3. Methods  

3.1. Downsampling Treatments

3.1.1. Decimation  

This treatment utilizes an algorithm that eliminates entire rows and columns, resulting in an image that is half the resolution of the original.  

Specifically, the row and column removal strategy can be one of four possible combinations as shown below in Table 5.  With odd‐sized images

(where there are an odd number of rows and/or columns), and a decimation strategy that eliminates odd rows and/or columns, the algorithm

copies over the last odd row and/or column as a special condition.

The algorithm utilizes the most common image coordinate system, with the origin, (0, 0), placed at the upper‐left corner of the image to

determine whether a row or column is even or odd.  The first row and column, with a coordinate value of 0, are considered even, and the

second row and column with the coordinate value of 1 is considered odd. As such, a decimation strategy that retains even numbered rows and

columns would retain rows and columns numbered 0, 2, 4, 6, 8, and so on in the new image resulting from the decimation process. A visual

example of decimation strategy 1 from Table 5 is shown in Figure 1 below.

Table 5 ‐ Decimation Pathways

Decimation Strategy Removal Process

1 Retain Even Columns, and Even Rows

2 Retain Even Columns, and Odd Rows

3 Retain Odd Columns, and Even Rows

4 Retain Odd Columns, and Odd Rows

Figure 1 ‐ Decimation

While decimation provides a simple and fast method of downsampling an image, the filter can be unpredictable in that it does not deal with

frequency information in an elegant fashion and in certain cases, it can effectively fold high frequency image information into the lower

frequency ranges.  An example of such an undesirable effect is an image that consists of alternating white and black lines of one pixel in height

and N pixels in width (Figure 2).  In this extreme example, removal of odd rows and columns results in an image that is half of the resolution of

the original but completely solid black.  In effect, the high frequency pattern has been replaced with a lower frequency pattern.

Figure 2 ‐ Example of Undesirable Result with Decimation
NISTIR 7839 ‐ Examination of Downsampling Strategies for Converting 1000 ppi Fingerprint Imagery to 500 ppi

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It is expected that each of the four methods should perform equally as the others when applied to the fingerprint imagery selected for this

study as the random nature of the data set was not expected to have dominance or bias towards odd or even decimation strategies.  While no

bias is expected in the data, for the purposes of completeness, all four decimation strategies from Table 5 were examined in this study.   

3.1.2. Averaging

This treatment utilizes an algorithm that derives an intensity value for a single pixel value by summing the four neighboring pixels’ intensity

values and dividing the result by four to obtain an average intensity value representative of the four neighboring pixels.  This averaged value

will then replace the four adjacent pixels as one new pixel with the average as its intensity value.  The result of this operation is an image that

is one half the resolution of the original image.  With odd‐sized images (odd number of rows or columns), the algorithm simply copied over the

last odd row and/or column as a special condition.

Figure 3 ‐ Pixel Averaging Strategy

3.1.3. Transcoding

Transcoding typically refers to the act of making a change in the representation of compressed data by operating on the compressed data

without going through a cycle of decompression and recompression.   

Wavelet based compression algorithms such as JPEG2000 and WSQ generate a data stream of wavelet coefficients that represents both

location and frequency information for discrete components that can be reassembled to create a representation of the original image upon

decompression.   The information the wavelet streams contain as well as the organization of the stream allows for operations on the stream

that can effectively extract/filter a portion of the stream containing a desired portion of the spatial frequency spectrum.    In particular, a

wavelet transform contains a decimated low‐pass filtered4 version of the image which provides a representation of the image at half‐

resolution, as well as additional high‐pass information necessary for a full resolution reconstruction.

For the purposes of this study, we utilized guidance provided by [MTR] that describes two transcoding strategies.  The first method, referred

to as Transcoded A operates by filtering an image compressed using guidance in [MTR] to decompress the low‐pass 500 ppi portion of the

frequency spectrum.    Implementation of this method amounts to specifying to the JPEG2000 decoder that the highest resolution

decomposition layer of the codestream is to be discarded.  A parameter in the command line of the CODEC is all that is required to yield a 500

ppi image upon decoding the JPEG2000 codestream. The resulting 500 ppi decompressed image is then recompressed using WSQ.  While this

may not follow the literal definition of transcoding (where the image is operated on as a compressed stream rather than going through a

decompression cycle), it does utilize aspects of the compression stream to filter frequency information resulting in an image downsampled to

500 ppi.

The second method referred to as Transcoded B operates in the more traditional sense of transcoding in that the compressed stream is

operated on without fully decompressing the stream.  The wavelet stream is filtered for the desired frequency and spatial information and

                                                                     4 Both JPEG2000 and WSQ use a low‐pass filter using 9 coefficients decimated in an even‐even fashion.  The low‐pass filter with approximate

kernel weights of (0.03, ‐0.02, ‐0.08, 0.27, 0.60, 0.27, ‐0.08, ‐0.02, 0.03) in a single dimension is applied both horizontally and vertically.  At the

edges of the image where the kernel extends outside the image region, the kernel is instead reflected back from the border to reuse image

pixels near the border.    [The decimation offset is adjustable in JPEG2000, but the default even‐even offset was used for all files in this

experiment.]
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converted to floating point array at 500 ppi that is compatible with the WSQ algorithm. Transcoded B’s goal is to combine the JPEG2000

reduced resolution decoding with the WSQ encoding in a fashion that eliminates unnecessary loss of precision.    Most of the JPEG2000

processing is performed in floating point5, with a final conversion of the image pixels to only 8‐bit accuracy for the purposes of output format

expectations.    Likewise, WSQ reads 8‐bit image data, but immediately converts it to floating point before continuing processing.    This

conversion down to 8‐bits causes numeric loss, which can be avoided by bypassing the down and up conversion steps, and moving floating

point data directly from JPEG2000 machinery into WSQ floating point processing.

Figure 4 shows a typical JPEG2000 reduced resolution decode on the top, moving from left to right, following the blue arrows. On the bottom

of the figure is the typical WSQ encode process, again following the blue arrows.  The full path shown by the blue arrows is Transcoded A.   

Transcoded B eliminates the shaded area at the right, and instead follows the green arrow, directly between the two codecs.   

Figure 4 ‐ Comparison of the Transcoded A and Transcoded B Methods

In addition to the significant speed‐up provided by eliminating decode processing for the extra 1000 ppi sub bands, which is shared by both

Transcoded A and Transcoded B methods, Transcoded B avoids a costly intermediate file save when efficiently implemented6

.

3.1.4. Gaussian Filtering with Decimation  

Gaussian filtering or blurring is applied to an image prior to decimation in order to reduce the expression of frequencies sampled at a higher

rate that would not have been present were the image formed via sampling at a lower rate.  Also, termed “low‐pass” filtering, the Gaussian is

applied to reduce the effects of “aliasing” where in the decimated image the under‐sampled high frequency components appear “aliased” as

low frequency components.  A common example of such is the moiré effect.  Hence, prior to resampling the images at one‐half the sample

rate, we apply a Gaussian filter to the image in order to blur the image, which is equivalent to attenuating the high frequency content.

The Gaussian filter in two dimensions consists of a square array of weights, referred to as a Gaussian kernel, computed according to the

expression 2 2

2 2

2

1 (, ) 2

x y

Gxy e 



 

 (1)

where x and y are respectively distances in pixels from the center or origin, often referred to as the radius of the filter, and  the standard

deviation of the Gaussian. Implemented as a convolution operation on the intensity image, i.e., in the spatial domain, the filter array is

centered on each pixel of the image and the weights multiplied by corresponding image pixels of the neighborhood of the image pixel being

processed.  

                                                                     5 Actual JPEG2000 implementations often use fixed point representations, with up to 32‐bits of accuracy available.    6 For this test, an intermediate output file of 32 bit signed integer data was generated by JPEG2000 and consumed by a customized version of

WSQ.

JPEG2000 file

(1000 ppi)

Retain only 500

ppi Subbands

Decode to

Wavelet

Coefficients

Synthesize

Image from

Wavelets

Convert Image

to 8bit

Raster Image File

(500 ppi)

Convert Image

to Floating

Apply Image

Offset and

Scale

Decompose

Image to

Wavelets

Remainder of

WSQ Encoding

WSQ file

(500 ppi)

Steps Avoided

In Transcoded‐B
NISTIR 7839 ‐ Examination of Downsampling Strategies for Converting 1000 ppi Fingerprint Imagery to 500 ppi

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The weighted sum resulting from this application of the filter is output to a new image. The Gaussian kernel is centered on the next pixel; the

weighted summation again performed, and this continues over all rows of the image.  At the edges of the image where the kernel extends

outside the image region, the missing kernel values are filled in by “mirroring”, or duplicating, the edge pixels.  

Normally, it might be considered possible to design a Gaussian filter specifically to the alteration of sample rate desired. In practice, however,

the specific effects of JPEG2000 and WSQ compression, their interactions with each other and with the original and output sample rates were

considered difficult to predict or to control. Hence, we chose to conduct empirical tests employing a variety of filters in order to select the one

or several best for the Use Case under consideration as described previously. Thus, the Gaussian filtering was repeated using each of the filters

having parameters listed in Table 6.

Table 6 ‐ Gaussian Filter Parameters Selected for This Study

Gaussian Strategy Sigma Radius (r) Width

1 0.3369 2 5

2 0.4220 2 5

3 0.5071 3 7

4 0.5642 3 7

5 0.5922 3 7

6 0.6773 3 7

7 0.7624 3 7

8 0.8475 4 9

9 0.9326 4 9

10 1.0177 4 9

11 1.1028 4 9

12 1.1879 5 11

13 1.2730 5 11

14 1.3581 5 11

15 1.4432 5 11

16 1.5283 6 13

17 1.6134 6 13

18 1.6985 6 13

19 1.7836 6 13

20 1.8687 7 15

21 1.9538 7 15

22 2.0389 7 15

23 2.1240 7 15

Note relative to Table 6, the total width of the Gaussian kernels are computed as 2*radius + 1. The values of x and y inserted into equation (1)

extend from ‐r to +r.

Following each application of the Gaussian filters, the filtered images are reduced to one‐half the sample rate by each of the four decimation

schemes as described in section 3.1.1. The C# computer code used to apply both the Gaussian filter is included in Appendix C.

3.1.5. Spectral Truncation  

The discrete Fourier transform (DFT) converts a grayscale image of the spatial domain to a representation in the frequency domain. Barring

any modification of the frequency space representation of an image, the inverse transform of the frequency representation reproduces the

original grayscale image without loss. The grayscale image, f(x,y), and its discrete Fourier transform, F(u,v), are related by the following

expressions:

   

   

1 1 2//

1 1

1 1 2//

0 0

1 (,) ,

(, ) ,

N M j xu N yv M

x y

N M j xu N yv M

x y

Fuv f xy e NM

and

f xy F uv e





   

 

  

 





 

 

(2)
NISTIR 7839 ‐ Examination of Downsampling Strategies for Converting 1000 ppi Fingerprint Imagery to 500 ppi

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where (x,y) and (u,v) are respectively image pixel coordinates and DFT wave numbers, N and M are width and length of the image and its DFT

and j = 1 ... Notably, an image and its DFT are simply alternate representations of the same information; having the one enables

computation of the other without loss.

The DFT of an image of size N x M represents all frequencies present in an image sampled at 1000 ppi to the Nyquist frequency limit of 500

transitions per inch, scaled as symmetrical N/2 x M/2 matrices.  It follows that the DFT of the image sampled at 500 ppi of size N/2 x M/2 should

then consist of half the frequency range of the higher sample rate or N/4 x M/4.  From this, we realize that a 500 ppi image may be derived

from a 1000 ppi image by extracting from the DFT of the 1000 ppi image those frequency components which would be present in the image

sampled at the lower rate.  Applying the inverse transform to the rectangular region extracted from the DFT of the 1000 ppi yields a 500 ppi

image, thus downsampled by spectral truncation. The mechanics of the procedure are outlined and demonstrated in the following discussion.

Figure 5 depicts a fingerprint impression scanned at 1000 ppi. We wish to downsample this image so as to derive an image sampled at 500 ppi.

The Fourier transform of the image is shown in Figure 6. As has been discussed elsewhere, we might downsample the image by various other

means. However, we can accomplish the adjustment in the sample rate of the image by excluding frequencies that would not be present at

the lower sample rate. Noting the Fourier transform image (scaled logarithmically for display) the magnitudes of frequencies from the zeroth

at the image center (the so‐called direct current or DC level) to limits of one‐half the 1000 ppi sample rate in positive directions to the right and

up and negative to the left and below the DC value centered at (0,0). The rectangle inscribed on the interior of the DFT marks the portion that

is extracted for inversion to create the 500 ppi downsampled image.

Figure 5 ‐ Example of an inked, rolled fingerprint impression digitized at a sample rate of 1000 ppi.

200 400 600 800 1000

200

400

600

800

1000

1200
NISTIR 7839 ‐ Examination of Downsampling Strategies for Converting 1000 ppi Fingerprint Imagery to 500 ppi

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Figure 6  ‐ The DFT of the grayscale image depicted in Figure 5 displayed as an image. The inscribed rectangle marks the portion of the

spectrum to be extracted for construction of the 500 ppi image. (Note that the four quadrants of the spectrum have been translated

diagonally so as to center the zero‐frequency term, and the values have been scaled by the log function to enable display of the spectrum

otherwise overwhelmed by the high magnitude of the DC value.)

Figure 7 ‐ The extracted portion of the DFT exhibited in Figure 6 to be inverted to form the 500 ppi downsampled image shown in Figure 8.

 u

 v

-500 -400 -300 -200 -100 0 100 200 300 400 500

-600

-400

-200

0

200

400

600

 u

 v

-200 -100 0 100 200

-300

-200

-100

0

100

200

300
NISTIR 7839 ‐ Examination of Downsampling Strategies for Converting 1000 ppi Fingerprint Imagery to 500 ppi

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Figure 8 ‐ The 500 ppi image formed from inverting the truncated spectrum (Figure 7) of the fingerprint originally sampled at 1000 ppi.

Several operational points should be noted relative to the spectral truncation method. First the complex valued DFT must be rearranged such

that the four diagonally opposed quadrants are shifted across the center point such that the zero‐frequency (dc) term is centered. Second,

from this geometrically transformed DFT is extracted a rectangular region centered on the dc term having dimensions one half those of the

1000 ppi image and its DFT. Third, prior to application of the inverse transform, the extracted portion of the DFT must be returned to the

conventional DFT geometry by reversing the diagonal translation of the quadrants.  Fourth, the inverse DFT is applied yielding a 500 ppi image.

Finally, it is noted that the grayscale of the resulting image is expanded relative to that of the 1000 ppi source image. Hence, the grayscale of

the downsampled image must be rescaled to the intensity range of the 1000 ppi source image. This may be done by applying the rescaling

function of equation (3) to the pixel values of the downsampled image.

  min

max min

max min

source source

rescaled

I I I II

I I

          (3)

where I is the downsampled image array to be rescaled, min I and max I are the lower and upper limits of the pixel values in I , max

source I and

min

source I are the upper and lower limits of the grayscale of the 1000 ppi source image.

100 200 300 400 500

100

200

300

400

500

600
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3.2. Metrics

3.2.1. Expert Examiners

Each of the native and downsampled images for all treatments/sub‐treatments was shown to exactly three examiners.   The image pairs were

queued on each examiner’s workstation and their presentation order was shuffled randomly on each of the three workstations.  Each image

pair was presented to 3 different examiners, and each image pair was viewed by each examiner only once.    

The examiners were first asked to make an identification decision on the pair of images being shown to them.   The identification decision had

3 possible choices:  Yes, No and Inconclusive.  The three choices were then post‐processed using ground‐truth data into the coded responses

provided below in Table 7.  Observation codes are in ascending order indicating a progressively greater negative impact on the identification

process, with code 1 representing the right decision answer and code 3 representing the incorrect decision answer given the ground truth.  

Table 7 ‐ Identification Decision Coding

Observation Code Description  

1 The examiner answered the identification question correctly based on ground‐truth information on the image pair

shown to the examiner.  

2 The examiner answered the identification question with an “Unknown” response indicating that based on the images

shown, the examiner cannot with confidence note an identification or non‐identification.

3 The examiner answered the identification question incorrectly based on the ground‐truth information.  For example, if

the image pair shown represented a matched pair, they incorrectly indicated a non‐identification.  Similarly, if the

image pair was a non‐identification.

The post‐processed coded responses from each of the 3 examiners were then concatenated so that a response of 1, 3 and 2 becomes 132, for

example.   This concatenated response was then sorted to list the triplet of values in increasing order, so 132 becomes 123.   This process yields

a concatenated response code that establishes a natural cost function as shown below in Table 8.

Table 8 ‐ Sorted Examiner Response Code Classification

Responses from Observers Classification

111

112

113

(BEST) These cases represent either a unanimous or majority ruling of observation code 1

from Table 9 indicating a correct identification or non‐identification decision.

122

123

222

223

These cases represent either a unanimous or majority ruling of observation code 2 from

Table 9.  This case also includes the special split‐decision case of 1, 2, 3.  These cases are

considered borderline cases and are biased towards the examiners being Inconclusive in

their identification decision.

133

233

333

(WORST) These cases represent either a unanimous or majority ruling of observation code

3 from Table 9 which indicates an incorrect identification or non‐identification decision by

the examiner given ground truth data about the pair of images in question.

   
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Following the identification decision step of the process, each examiner was asked to evaluate the image pair on the matter of fidelity loss.   

To aid in analysis and quantification of fidelity loss, the examiner’s evaluation was collected by utilizing a Likert‐type response scale [LIKERT].  

The choices that the examiners were allowed to make are provided in Table 9 below.   Observation codes are ordered in ascending order

indicating a progressively greater amount of degradation from 1 to 4.  Furthermore, the features summarized in observation code 3 are among

those typically used for forensic‐level decisions while features summarized in observation code 4 are those used primarily by automated‐

matchers in rendering a match decision.

Table 9 ‐ Observation Codes for Image Degradation of Downsampling Treatments

Observation Code Description  

1 No apparent image quality degradation and the quality of Level II (2) and Level III (3) detail in either image should

not cause any difficulty in reaching a conclusive decision of identification or exclusion.  

2 A noticeable degradation in the quality of Level II (2) or Level III (3) detail in either image, but not enough to have a

negative impact on reaching a conclusive decision of identification or exclusion, though the amount of time to reach

a decision may increase.

3 Level III (3) detail quality diminished in either image to the extent that Level III (3) identification is questionable or

not possible, and/or is significantly more difficult.

4 Level II (2) detail quality diminished in either image to the extent that Level II (2) identification becomes

questionable or not possible, and/or is significantly more difficult.  

Examiner responses were recorded by custom test apparatus consisting of a commodity computer and software designed and developed

specifically for this study.  More details on the equipment used are available in Appendix B.  The examiners were not provided any time limits

on their responses.

The responses from each of the 3 examiners were concatenated so that a response of 1, 3 and 2 becomes 132.  This concatenated response

was then sorted to list the values in increasing order, so 132 becomes 123.  This process yields a response code that establishes a natural cost

function as shown below in Table 10.

Table 10 ‐ Sorted Examiner Response Code Classification

Responses from Observers Classification

111

112

113

114

(BEST) These cases represent either a unanimous or majority ruling of observation code 1 from

Table 9 indicating no apparent image degradation.

122

123

124

222

223

224

These cases represent either a unanimous or majority ruling of observation code 2 from Table 9.  

This case also includes the special split‐decision cases of 1, 2, 3 and 1, 2, 4.    These cases are

considered borderline cases but are assigned to this bin as they are biased towards an

acceptable image rating by two examiners noting little or no observable loss.

134

234

133

233

333

334

These cases represent either a unanimous or majority ruling of observation code 3 from Table 9.

This case also includes the special split‐decision cases of 1, 3, 4 and 2, 3, 4.    These cases are

considered biased‐towards, and indicative of level‐3 detail loss.

144

244

344

444

(WORST) These cases represent either a unanimous or majority ruling of observation code 4

from Table 9 indicating loss of both level‐3 and level‐2 feature detail.

The examiners were provided the basic ability to independently reposition, rotate, invert and zoom in and out of each of the two images from

the pair being examined.    This provided them with the basic tools that they typically employ in their standard operating environments in

performing their examination duties.  While they were provided with basic tools, more advanced assistive technologies normally available to

some examiners, such as on‐screen feature marking or image adjustments were not provided to them in the interest of experimental control.    
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The image pairs were presented in split‐screen to the examiners in randomized order and randomized placement (left/right split screen

placement) to mitigate potential order effects or positional bias (see Figure 9).  Scientists overseeing the tests were blind to the placement

order of the images, as well as to the downsampling methods represented in the image pairs.    These factors were tracked by the test

apparatus.

Figure 9 ‐ Split‐Screen Presentation of Image Pairs

Each of the 20,000 image pairs was guaranteed to be observed by three different examiners over the course of the study without repeating.  

Due to the physical limitations of even the best modern monitors, it is impossible to show a 500 ppi image without zooming or interpolation.   

The software apparatus enabled the examiner to view images at approximately 5x to 25x of the original size (see Appendix B for more

information).

Once the examiner made a determination for a given pair of images, that pair was marked clearly as complete.   The examiner was allowed to

return to a completed pair and re‐examine that image pair without penalty.   The examiner was also allowed to jump to any image pair in the

queue regardless of that pair’s position in the examiner’s queue.

Examiners were provided basic verbal instructions and a demonstration on how to use their workstations and were allowed a brief practice

session using image pairings that were not part of the study to gain familiarity with the procedure, scoring, and workstation controls.  

Examiners were allowed to freely ask questions or clarification on their workstations or tasking.   The examiners were located in the same

room and were allowed to interact freely as they do in their normal professional practice.   Finally, the examiners were advised that once they

have selected one of the three workstations on which to process images, they were to continue to use that workstation exclusively.   This was

done in order to eliminate the possibility of an examiner processing an image pair more than once, due to the randomized order of image pairs

in each workstation’s queue.

3.2.2. Automated Matching

The goal of the automated (machine) matching portion of the study was to determine how the downsampling treatments impacted an

automated machine matcher’s ability to match that image to a native‐scanned 500 ppi image.    This was done by generating minutiae

templates for all images (native‐scanned and downsampled images) and then generating match scores for the genuine match pairs.    The

following table is an example of a genuine match‐pair:

Image source template Subject ID Finger position Image type

probefile.xyt 01 03 500 ppi native scanned, WSQ compressed

galleryfile.xyt 01 03 1000 ppi scanned, downsampled to 500 ppi,

WSQ compressed
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For the machine matching process, two research applications from the NIST NBIS (NIST Biometric Image Software) distribution v 4.1.o were

utilized:

 mindtct.exe ‐ this application generates a minutiae template according to the ANSI INCITS 378‐2004 standard from a source image in

either WSQ or PNG image format

 bozorth3.exe ‐ this application generates a match score from an input consisting of two minutiae templates to be matched

The image sets used for all minutiae detection and subsequent, automated matching included:

 500 ppi “native” images put through a single‐cycle of WSQ compression using the NBIS distribution cwsq.exe application (v 4.1.0)

 Sample images that have been segmented from 10‐print cards scanned at 1000 ppi, downsampled to 500 ppi using the treatments

outlined in this document, and put through a single‐cycle of WSQ compression using the NBIS distribution cwsq.exe application (v

4.1.0)

All minutiae templates were generated according to ANSI INCITS 378‐2004 standard.  The command line execution of mindtct is as follows:

 mindtct -m1 fp-image-input template-output-root-filename

where ‐m1 specifies the output template to be ANSI INCITS 378‐2004 standard compliant

fp‐image‐input is the image of which to generate its minutiae template

template‐output‐root‐filename is the root filename of the generated minutiae template (file)

The reason that minutiae templates are generated for images is that the matcher application matches an image template and not the image

itself.

All match scores for fingerprint pairs were processed and generated using the NIST Bozorth3 research matcher.  The command‐line execution

of bozorth3 is as follows:

 bozorth3 ‐A outfmt=pgs ‐m1 probefile.xyt galleryfile.xyt

where ‐A outfmt=pgs specifies that output lines will contain (s)core, (p)robe and (g)allery filename

‐m1 specifies the output template to be ANSI INCITS 378‐2004 standard compliant

probefile.xyt is the probe template filename

galleryfile.xyt is the gallery template filename

For each treatment, 2039 match pairs were processed.  The match scores were generated and captured for statistical analysis.
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3.2.3. Spectral Image Validation/Verification Metric (SIVV)

Developed initially as a method to screen fingerprint databases for non‐fingerprint images, segmentation errors, or mislabeled sample rates,

the Spectral Image Validation Verification (SIVV) metric [LIBERT] provides a comparatively straightforward method by which to assess the

frequency structure of an image. Pairwise display of the SIVV signals of images having undergone different processes enables summary

visualization of the effects of the different processes across the composition frequency spectrum of the image. As a 1 dimensional

representation of a 2 dimensional Fourier spectrum, the SIVV metric applied to a fingerprint image exhibits a peak corresponding to the

frequency of the ridge spacing. Also, as shown in Figure 10, comparison of SIVV signals of a 500 ppi image and a corresponding downsampled

1000 ppi image shows the loss or gain of power over various frequencies.  

Figure 10 ‐ NIST SIVV metric applied to a 500 ppi image having undergone 1‐cycle of WSQ encoding/decoding and a corresponding 1000 ppi

fingerprint encoded/decoded using JPEG2000, downsampled to 500 ppi, and encoded and decoded with WSQ.

  

The SIVV signals denoted as s1 and s2 are respectively vectors of SIVV signal values for images having undergone different processing methods

under study. The frequency samples, f, in units of cycles per pixel correspond to image pixels or Fourier transform frequencies along the

length of one half of the minimum dimension of the 2D Fourier transform of the image under examination. Frequency along this dimension is

scaled to the interval [0, 0.5] cycles/pixel. Note that the power value at f=0 is the “direct current” (DC) term, corresponding to the average

intensity of the image and is used to normalize the power spectrum.

Either differences or ratios of SIVV signals can provide quantitative measures for the comparison of compression methods. For the present

study, we examine the Root Mean Squared difference (RMSD)7 between the two SIVV signals, s1 and s2, over the entire frequency range 0 ‐ 0.5

cycles/pixel.

2

, , 1

( ) ( )

n

i i i RMSD n

    1 2

1 2

s s s ,s (4)

where 1 2 n   s s (i.e., the lengths of the signal vectors).  

                                                                     7 It should be noted that RMSE and related image comparison measures such as Peak Signal to Noise Ratio (PSNR) were omitted from the

analysis due to frequent differences in dimensions of downsampled 1000ppi images and 500ppi exemplars. Spectral, i.e. SIVV, comparison

avoids difficulties of misregistration and size disparities. Hence, all mention of RMSD and correlation in this report pertains to comparison of

SIVV signals.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

0.4

0.5

0.6

0.7

0.8

0.9

1

 Log Power (db)

 Frequency (cycles/pixel)

PSNR1 = 23.445 PSNR2 = 25.641

294-U294_R06_F12_500_10.bmp

294-10.bmp Gaussian_0.6773_3
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The RMSD metric defined above can provide a measure of the overall difference between the SIVV spectra of downsampled 1000 ppi image

and that of a corresponding image of the same fingerprint impression scanned at 500 ppi. In addition to global effects, the RMSD may be

evaluated over smaller frequency intervals enabling the comparison of effects over frequency bands that may have particular relevance to

fingerprint image quality or matching, as well as quantifying and isolating changes confined to bands that specifically impact either the

machine matcher or expert examiners.

The RMSD measures the total deviation of point‐wise comparison of the SIVV signals. The Pearson product moment correlation coefficient

measures the parallelism between the two signals irrespective of the magnitude of the difference between them. Accordingly, we compute

the correlation coefficient between s1 and s2 as

  

   

112 2 1

1 2 2 2

11 2 2 1

(, )

n

i

n n

i i

r 

 

  

 



 

s ss s

s s

ss s s

(5)

where 1

s and 2s are the arithmetic means of the two SIVV signal vectors.
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4. Analysis

4.1. Normality Test

Examination of the distribution of data in the normal probability plot [CHAMBERS] and the Q‐Q Plot on a selected subset of data from this

study (Frequency Spectrum Correlation of the Odd‐Odd Decimation Case) in Figure 11 and Figure 12 shows that it is not possible to determine

the distribution of the data and therefore parametric analysis methods are not suitable.  Because of this we utilized non‐parametric statistical

methods in the analysis of data collected in this study.

Figure 11 ‐ Normal Fit Histogram, Frequency Spectrum

Correlation, Decimation (Odd‐Odd) Case

Figure 12 ‐ Q‐Q Normality Plot, Frequency Spectrum Correlation,

Decimation (Odd‐Odd) Case

4.2. Analysis Algorithm

As described in section 2, this study examines 28 treatments and 1 Control Case.  Out of the 28 cases, 23 cases require decimation to perform

geometric correction after processing, and one of the 28 cases is simply decimation without any further processing (see Section 5.7).  

Anecdotal evidence suggests that the decimation method should not result in any measurable change in the treatment pathway given the

random distribution of the underlying data.  Empirical evidence during an exploratory phase of this study demonstrated this to not be true,

and that examination of decimation strategy alone showed measurable bias towards a particular decimation method.  This was the primary

reason why every possible combination of the four decimation strategy was examined for each of the treatments.    At the time of the

experiment the cause of this bias is not known.  This bias is further explored in the Discussion and Future Work (section 7) of this study.   

The pitfall in examining every combination of decimation strategy is that this combinatorial analysis amplifies out 24 of the 28 cases by a factor

of 4, yielding 96 cases.  The 96 cases involving decimation, combined with the 5 cases that did not require a decimation strategy yield a total of

101 cases that can overly complicate the analysis of the underlying problem.

Rather than comparing the full combination of treatments and sub‐treatments together at the same time, a more simplified approach was

devised to conduct the analysis in multiple stages.   

In stage 1 of the analysis (See Figure 13) the 24 cases that each required 4 decimation sub‐treatments (yielding 96 cases) had their sub‐

treatments ranked using Friedman’s analysis.  This allowed for the identification of the best and worst sub‐treatments from the four possible

sub‐treatments.    

In stage 2 of the analysis, the best decimation cases (sub‐treatments) were down‐selected and ranked using Friedman’s analysis and in stage 3

of the analysis the worst decimation cases (sub‐treatments) were down‐selected and ranked using Friedman’s analysis.   

0

10

20

30

40

50

60

70

80

90

0.989 0.994 0.999

Frequency

Histogram

Normal Fit

(Mean=0.9981728077,

SD=0.0017149339)

-6

-5

-4

-3

-2

-1

0

1

2

3

0.989 0.994 0.999

Normal Quantile (Z)

Normality Plot (Q-Q)

Normal Fit

(Skewness=-2.64,

Kurtosis=7.68)

(W = 0.68, p = 0.0000)
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Determination of the best and worst cases allowed for the identification of treatment performance under the best decimation scenarios, as

well as the worst decimation scenarios effectively creating a decision manifold that encompasses what is estimated to be the operational

reality of the system.

While analysis of data primarily relies on mean ranks and Friedman’s test, post‐hoc analysis was performed at each stage of the analysis.

Post‐hoc analysis [WILCOXON] was conducted in stage 1 of the analysis, but primarily for demonstration purposes and the results did not

change selections based on mean rank.  The results of this post‐hoc analysis can however be used to identify other candidates that are “as

good as” the rank 1 candidate (where there are no statistically significant differences in the post‐hoc), in the event that an alternative rank 1

candidate is needed in practice for any reason.  Post‐hoc was also performed in stage 2 and stage 3 of the analysis to identify clustering of

similar treatments.  Additional information on this clustering algorithm has been provided in the results section (section 5) of this study.

For cases that required no decimation (and therefore had no sub‐treatments), the singular case was propagated to phase two without any

change.

Figure 13 – Multi‐Stage Analysis Overview
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4.3. Hypothesis Testing

4.3.1. Friedman’s Procedure

The Friedman test [CONOVER] is a non‐parametric test for analyzing randomized complete block designs and is an extension of the sign test

when there may be more than two treatments of interest.  The Friedman test assumes that there are two or more experimental treatments

(k).  The observations are arranged in b blocks as in the example shown in Table 11.

Table 11 ‐ Block Design Example

Block Treatment

1 2 ... k

1 X11 X12 ... X1k

2 X21 X22 ... X2k

3 X31 X32 ... X3k

... ... ... ... ...

b Xb1 Xb2 ... Xbk

Let R(Xij) be the rank assigned to Xij within block i, and in the case of ties the average rank is used.

The ranks are summed to obtain

 ,

1

b

j i

i

R RX      (6)

for j = 1, 2, ..., k.

Then the Friedman test is

H0:   Null hypothesis, the treatment effects have identical effects (μ1	=	μ1)

Ha:   Alternative hypothesis, at least one treatment is different from at least one other treatment (μ0	≠	μ1)

where μj is the mean rank of treatment j,  j = 1 ... k.

Test Statistic:

      2

1

1

12 1 /2

( 1)

k

i

i

T R bk

bk k 

 

     (7)

If there are ties, then

    2

1

1

1 1

1

1

2

k

i

i

b k

k R

T

A C



         

     (8)

where

    2

1

1 1

b k

ij

i j

A RX                (9)

 2

1

1

4

bk k

C

                      (10)

Note that Conover recommends the statistic

 

 

1

2

1

1

1

b T

T

bk T

                   (11)

since it has a more accurate approximate distribution. The T2 statistic is the two‐way analysis of variance statistic computed on the ranks

R(Xij).
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The significance level, or the accepted probability of incorrectly rejecting the null hypothesis (i.e., making a Type I error) for the Friedman’s

test is set at 0.05.

   

For the T2 test statistic, the critical region for rejection of the null hypothesis is  

2   , 1, 1 1 kbk    T F       (12)

where F is the percent point function of the F distribution.

For the T1 test statistic, the critical region is given as

 

2

1 , 1 k T        (13)

where 2  is the percent point function of the chi‐square distribution.

The T1 approximation is sometimes poor, so the T2 approximation is typically preferred.

4.3.2. Wilcoxon Signed Rank Test

Hypothesis testing was accomplished in two phases. For each assemblage of downsampling methods, the Friedman test was performed to a)

determine if any of the methods differed from at least one of the other methods; and b) to determine the set of mean rank scores of the

downsampling methods under consideration and to sort the methods from “best performing” to “worst performing” on the basis of the

mean rank scores.  Commonly, Friedman’s test is followed by post hoc analysis involving multiple pairwise comparisons to determine which of

the treatments differ from one another at levels of statistical significance. For purposes of the present study, however, the multiple pairwise

comparison procedure was used only to identify which of the cluster of alternative methods near the top of the mean rank score list differed

significantly from that method occupying the top position.  

The Wilcoxon Signed Rank Test [WILCOXON], [CONOVER], [HOLLANDER] was used for the limited number of pairwise comparisons. The

Wilcoxon Signed Rank Test is the non‐parametric analog to the pairwise t‐test. It examines the pairwise (intra‐block) differences between

measurements, |Yi

‐Xi|, to test the null hypothesis that the expected value of the pairwise difference in measurements, E(D), is zero for the two‐

tailed test.

0

1

: ( ) 0 ( . ., ( ) ( ))

: () 0

H E D ie E Y E X i i

H ED

 

   

Given the ordering of the downsampling methods as indicated by the mean rank scores, the Wilcoxon test was applied to the columns of the

original data matrix so as to successively compare pairwise measurements of the treatment deemed the best with those deemed next best,

and so on down the list until a significant difference was found. Thus, we were able to assess if a method deemed best by the mean rank

criterion was statistically significantly different from potential contenders. Moreover, the ordering of the methods with successive pairwise

testing obviated the need to test every method against every other method. That limiting the number of comparisons is important will

become apparent from the discussion which follows.

Use of post hoc analysis requires the use of some measure to control the experiment‐wise Type I error rate, i.e., the probability of incorrectly

rejecting the null hypothesis. The philosophical underpinnings are explained in [CURRAN‐EVERETT], but essentially the idea is that where an

experiment consists of multiple decisions, each carrying a probability of error, the likelihood of making an incorrect decision increases with the

number of decisions. Accordingly, for an experiment involving multiple planned, dependent (non‐orthogonal) decisions to accept or reject the

null hypothesis, the accepted error probability for incorrectly rejecting the null hypothesis must be apportioned among the various decisions

such that the overall error probability does not exceed the acceptable error rate. Various methods for controlling this "family‐wise" Type I

error are described in [CONOVER] and [SOKAL].  

We employ the Bonferonni method to control the experiment‐wise error rate,  . For each of a series of k pairwise comparisons, the adjusted

significance level,  , to be used for each comparison in the experiment, may be computed as

k k

      (14)

where  k = the number of pairwise comparisons. Hence, given a set of downsampling treatments ordered by mean rank score, comparison of

each of several contending methods may be compared to the method in the top position via the Wilcoxon test which tests the probability that

the two methods yield equivalent results. For each comparison, we adjust the threshold for acceptance of the null hypothesis according to

equation (14). We are not interested in all pairwise comparisons, but at most only in comparisons involving the top ranking method of each of

other methods of a group. Thus, we proceed down the list of methods ordered by mean rank to test the difference between the top ranking
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method with others until we find a statistically significant difference. We group these methods as statistically undifferentiable. The method

that was found to be statistically different from the top ranked of the grouping just formed becomes the top ranked of the next group to

which we compare with methods below it in the list of mean ranks. Again, we form a group of methods when we encounter a significant

difference. We proceed similarly to the end of the list.  At the end of the procedure we have a set of groups members of which are statistically

similar to their top ranked member. We employ this rather elaborate procedure in order to facilitate integration of analyses of the various

metrics used in the study as will be discussed later in section 5.

Some of the pairwise tests involved at most three comparisons with a top ranking method. For these pairwise tests we set the number of

comparisons at k = 3 and use    0.05 / 3 0.0167 as the threshold for rejection of the null hypothesis in each pairwise test. For other

pairwise tests, we know that there will be at most comparison of 28 methods with a top ranking method, but we do not know a priori the

number of methods that might form a grouping of methods. Accordingly, we allow that we could have a maximum of 28 pairwise

comparisons, i.e. k = 28 and conservatively use the adjusted alpha value   0.05 / 28 0.0018  as the threshold for rejection of the null

hypothesis in each pairwise test.
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5. Results

5.1. Investigative Goal 1: Expert Examiner Quality Assessment  

5.1.1. Investigative Analysis 1

Data collection from the examiners yielded a series of 200 sorted response codes for each treatment and sub‐treatment as described in Table

3.  The data was coded and ranged from 111 (best) to 444 (worst) to represent the three examiner decisions as described in Table 10 and the

data was arranged in a table.  In the first phase of analysis, the Friedman’s statistical test was performed on each treatment that required a

decimation sub‐treatment.    This resulted in rankings of the sub‐treatments (see Table 12).    This allowed for the identification of the sub‐

treatment from best (lowest mean rank) to worst (highest mean rank), and provided us an indication that at least one statistically significant

difference in distributions exists between the four sub‐treatments via Friedman’s p.  The ranking of the sub‐treatments allows us to select the

best sub‐treatment for each treatment and to propagate that to the next phase of analysis.   In addition to selecting the top ranked sub‐

treatment per the rank analysis, a Wilcoxon post‐hoc analysis was performed between treatments having Rank 1 and Rank 2, Rank 1 and Rank

3 and Rank 1 and Rank 4 to determine if the top ranked sub‐treatment is indeed different from Rank 2/3/4.     

Table 12 ‐ Expert Examiner Quality Data Analysis, Stage One (Sub‐treatment Pare‐Down, Adjusted α = 0.0167)  

Treatment Sub‐treatment, Friedman’s Mean Rank, Lower is Better

Even‐Even Even‐Odd Odd‐Even Odd‐Odd Friedman's p X2

 statistic p, Wilcoxon

Rank 1 ≠ 2

p, Wilcoxon

Rank 1  ≠  3

p, Wilcoxon

Rank 1  ≠  4

Native 500 ppi ‐  ‐  ‐ ‐ ‐ ‐ ‐  ‐

Averaging ‐  ‐  ‐ ‐ ‐ ‐ ‐  ‐

NIST Spectral Truncation ‐  ‐  ‐ ‐ ‐ ‐ ‐  ‐

Decimation 3.39 1.96 2.75 1.91 <0.0001 203.93 0.7153 <0.0001

Transcoded A ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐

Transcoded B ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐

Gaussian σ = 0.3369, r = 2 3.09 1.81 3.14 1.97 <0.0001 200.78 0.1925 <0.0001

Gaussian σ = 0.4220, r = 2 2.99 1.96 3.05 2.01 <0.0001 145.58 0.1066 <0.0001

Gaussian σ = 0.5071, r = 3 2.80 2.07 3.15 1.98 <0.0001 133.05 0.4056 <0.0001

Gaussian σ = 0.5642, r = 3 2.55 2.29 3.00 2.17 <0.0001 55.48 0.2105 0.0003

Gaussian σ = 0.5922, r = 3 2.64 2.11 3.00 2.25 <0.0001 68.09 0.2635 <0.0001

Gaussian σ = 0.6773, r = 3 2.36 2.30 2.98 2.36 <0.0001 42.06 0.7219 0.6156 <0.0001

Gaussian σ = 0.7624, r = 3 2.37 2.31 2.97 2.35 <0.0001 40.40 0.5424 0.5122 <0.0001

Gaussian σ = 0.8475, r = 4 2.30 2.60 2.85 2.25 <0.0001 32.66 0.8418 0.0092

Gaussian σ = 0.9326, r = 4 2.29 2.66 2.81 2.24 <0.0001 33.35 0.8664 0.0008

Gaussian σ = 1.0177, r = 4 2.23 2.81 2.70 2.26 <0.0001 37.51 0.8588 0.0013

Gaussian σ = 1.1028, r = 4 2.25 2.80 2.65 2.30 <0.0001 29.62 0.5904 0.0091

Gaussian σ = 1.1879, r = 5 2.23 2.76 2.78 2.24 <0.0001 40.31 0.8136 <0.0001

Gaussian σ = 1.2730, r = 5 2.22 2.94 2.44 2.41 <0.0001 40.09 0.0920 0.4730 <0.0001

Gaussian σ = 1.3581, r = 5 2.24 2.93 2.31 2.52 <0.0001 42.72 0.1528 0.0127

Gaussian σ = 1.4432, r = 5 2.33 2.91 2.24 2.52 <0.0001 39.61 0.0097

Gaussian σ = 1.5283, r = 6 2.40 2.89 2.12 2.59 <0.0001 45.90 <0.0001

Gaussian σ = 1.6134, r = 6 2.49 2.80 2.07 2.64 <0.0001 43.21 <0.0001

Gaussian σ = 1.6985, r = 6 2.61 2.88 1.85 2.66 <0.0001 90.54 <0.0001

Gaussian σ = 1.7836, r = 6 2.59 2.84 1.99 2.58 <0.0001 58.95 <0.0001

Gaussian σ = 1.8687, r = 7 2.64 2.85 1.87 2.64 <0.0001 84.63 <0.0001

Gaussian σ = 1.9538, r = 7 2.62 2.77 1.98 2.63 <0.0001 57.46 <0.0001

Gaussian σ = 2.0389, r = 7 2.60 2.78 1.92 2.71 <0.0001 71.89 <0.0001

Gaussian σ = 2.1240, r = 7 2.66 2.73 2.00 2.62 <0.0001 52.85 <0.0001

In stage two of analysis, the Rank 1 candidates from each sub‐treatment were compared against each other as well as against the cases that

received no sub‐treatment8.  The data from this phase of analysis was sorted according to mean rank, from smallest (best) to largest (worst)

and an ordinal case number ranging from 1 to 29 was assigned to this sorted list.  Post‐hoc analysis was then performed down this list,

comparing Case 1 to Case 2 and so on.  In each comparison the higher‐ranked of two of the ordinal cases was made the exemplar case, P0

(case no.) compared with a lower‐ranked case, P1 (case no.). These comparisons of P0 to P1 were continued until a statistically significant

difference was  observed at which point the significantly different case was made the new P0 and comparisons continued with lower‐ranked

cases until the condition P0 ≠ P1 (in the sense of statistical significance) became true. The cases that did not demonstrate a statistically

significant difference were clustered into one singular rank, the Clustered Rank Table of Table 13.  This process continued until a list of

                                                                     8 i.e., the treatment did not include decimation as part of its processing.
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clustered of rank values was established, with each clustered rank representing data cases that are not significantly different from the others

(and hence clustered as such).  Each clustered group was then provided an ordinal clustered rank value.

Table 13 ‐ Expert Examiner Quality Data Analysis, Stage Two (Optimistic Decimation Pare‐Down, Adjusted α = 0.0018)

Treatment Rank Sum Mean Rank Case No. P0 (Case No.) P1 (Case No.) Wilcoxon p P0 ≠ P1 Clustered Rank

Gaussian σ = 0.5922, r = 3, Even‐Odd 1725.5 8.63 1 NA NA NA 1

Gaussian σ = 0.5071, r = 3, Odd‐Odd 1820.0 9.10 2 1 2 0.9043 1

Gaussian σ = 0.8475, r = 4, Odd‐Odd 1832.0 9.16 3 1 3 0.4182 1

Gaussian σ = 0.6773, r = 3, Even‐Odd 1853.5 9.27 4 1 4 0.5092 1

Gaussian σ = 0.7624, r = 3, Even‐Odd 1962.5 9.81 5 1 5 0.1837 1

Gaussian σ = 0.9326, r = 4, Odd‐Odd 1969.5 9.85 6 1 6 0.0170 1

Gaussian σ = 1.0177, r = 4, Even‐Even 1976.0 9.88 7 6 7 0.0262 1

Gaussian σ = 0.5642, r = 3, Odd‐Odd 1986.0 9.93 8 6 8 0.2635 1

Gaussian σ = 0.3369, r = 2, Even‐Odd 2010.0 10.05 9 6 9 0.1305 1

Gaussian σ = 0.4220, r = 2, Even‐Odd 2063.0 10.32 10 6 10 0.0346 1

Native 500 ppi 2213.0 11.07 11 6 11 0.0011 Yes 2

Gaussian σ = 1.1028, r = 4, Even‐Even 2294.5 11.47 12 6 12 0.3897 2

Spectral Truncation 2305.0 11.53 13 6 13 0.4197 2

Gaussian σ = 1.1879, r = 5, Even‐Even 2731.5 13.66 14 6 14 0.0015 Yes 3

Decimation, Odd‐Odd 2922.5 14.61 15 14 15 0.6203 3

Gaussian σ = 1.2730, r = 5, Even‐Even 3032.5 15.16 16 14 16 0.0147 3

Transcoded B 3038.5 15.19 17 14 17 0.0340 3

Gaussian σ = 1.3581, r = 5, Even‐Even 3389.0 16.95 18 14 18 <0.0001 Yes 4

Gaussian σ = 1.4432, r = 5, Odd‐Even 3580.5 17.90 19 18 19 0.8652 4

Averaging 3628.0 18.14 20 18 20 0.8508 4

Gaussian σ = 1.5283, r = 6, Odd‐Even 3655.0 18.28 21 18 21 0.5779 4

Gaussian σ = 1.6134, r = 6, Odd‐Even 3957.0 19.79 22 18 22 0.1077 4

Transcoded A 4045.5 20.23 23 18 23 0.0047 4

Gaussian σ = 1.6985, r = 6, Odd‐Even 4121.5 20.61 24 18 24 0.0094 4

Gaussian σ = 1.7836, r = 6, Odd‐Even 4404.5 22.02 25 18 25 <0.0001 Yes 5

Gaussian σ = 1.8687, r = 7, Odd‐Even 4426.0 22.13 26 25 26 0.9484 5

Gaussian σ = 1.9538, r = 7, Odd‐Even 4558.5 22.79 27 25 27 0.0305 5

Gaussian σ = 2.0389, r = 7, Odd‐Even 4711.5 23.56 28 25 28 0.0024 5

Gaussian σ = 2.1240, r = 7, Odd‐Even 4787.5 23.94 29 25 29 <0.0001 Yes 6

n 200

Friedman's statistic 2187.36

DF 28

Friedman’s p <0.0001 (X2 approximation, corrected for ties)

   
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In stage three of analysis, the Rank 4 (worst) decimation candidates from each sub‐treatment were compared against each other as well as

the cases that received no sub‐treatment.   The data from this stage of analysis was sorted according to mean rank, from smallest (best) to

largest (worst) and an ordinal case number ranging from 1 to 29 was assigned to this sorted list (see Table 14).  Post‐hoc analysis was again

performed on this list, comparing Case 1 to Case 2 and so on.   As described above, this comparison continued until a statistically significant

difference was observed.  The values that did not demonstrate a statistically significant difference were clustered into one singular rank.   This

process continued until a list of clustered rank values was established, with each clustered rank representing data cases that are not

significantly different from the others and clustered as such.   Each clustered group was again provided an ordinal clustered rank value.

Table 14 ‐ Expert Examiner Quality Data Analysis, Stage Three (Conservative Decimation Pare‐Down, Adjusted α = 0.0018)

Treatment Rank sum Mean Rank Case No. P0 (Case No.) P1 (Case No.) Wilcoxon p P0 ≠ P1 Clustered Rank

Spectral Truncation 1513.5 7.57 1 NA NA NA 1

Native 500 ppi 1531.0 7.66 2 1 2 0.4197 1

Gaussian σ = 0.9326, r = 4,  Odd‐Even 1847.0 9.24 3 1 3 0.0621 1

Gaussian σ = 1.0177, r = 4,  Even‐Odd 1857.0 9.29 4 1 4 0.0355 1

Gaussian σ = 0.8475, r = 4,  Odd‐Even 1931.0 9.66 5 1 5 0.0896 1

Gaussian σ = 0.6773, r = 3,  Odd‐Even 1993.5 9.97 6 1 6 0.0147 1

Gaussian σ = 0.7624, r = 3,  Odd‐Even 2051.0 10.26 7 1 7 0.0011 Yes 2

Transcoded B 2060.0 10.30 8 7 8 0.0146 2

Gaussian σ = 1.1028, r = 4,  Even‐Odd 2085.5 10.43 9 7 9 0.1849 2

Gaussian σ = 0.5922, r = 3,  Odd‐Even 2182.0 10.91 10 7 10 0.2023 2

Gaussian σ = 0.5642, r = 3,  Odd‐Even 2304.5 11.52 11 7 11 0.1107 2

Gaussian σ = 1.1879, r = 5, Odd‐Even 2346.0 11.73 12 7 12 0.0209 2

Gaussian σ = 0.5071, r = 3, Odd‐Even 2613.0 13.07 13 7 13 0.0006 Yes 3

Gaussian σ = 0.4220, r = 2, Odd‐Even 2785.5 13.93 14 13 14 0.4410 3

Averaging 2832.5 14.16 15 13 15 0.2342 3

Gaussian σ = 1.2730, r = 5, Even‐Odd 3016.0 15.08 16 13 16 <0.0001 Yes 4

Gaussian σ = 0.3369, r = 2, Odd‐Even 3139.5 15.70 17 16 17 0.0598 4

Gaussian σ = 1.3581, r = 5, Even‐Odd 3243.5 16.22 18 16 18 0.0342 4

Transcoded A 3374.5 16.87 19 16 19 0.8303 4

Gaussian σ = 1.4432, r = 5, Even‐Odd 3523.0 17.62 20 16 20 <0.0001 Yes 5

Gaussian σ = 1.5283, r = 6, Even‐Odd 3755.0 18.78 21 20 21 0.0097 5

Gaussian σ = 1.6134, r = 6, Even‐Odd 3933.0 19.67 22 20 22 <0.0001 Yes 6

Decimation Even‐Even 3962.5 19.81 23 22 23 0.0052 6

Gaussian σ = 1.6985, r = 6, Even‐Odd 4216.0 21.08 24 22 24 0.0046 6

Gaussian σ = 1.7836, r = 6, Even‐Odd 4329.5 21.65 25 22 25 0.0003 Yes 7

Gaussian σ = 1.8687, r = 7, Even‐Odd 4559.5 22.80 26 25 26 0.0072 7

Gaussian σ = 1.9538, r = 7, Even‐Odd 4593.0 22.97 27 25 27 0.0009 Yes 8

Gaussian σ = 2.0389, r = 7, Even‐Odd 4661.5 23.31 28 27 28 0.2481 8

Gaussian σ = 2.1240, r = 7, Even‐Odd 4760.5 23.80 29 27 29 0.0309 8

n 200

Friedman's statistic 2210.35

DF 28

Friedman’s p <0.0001 (X2 approximation, corrected for ties)

5.1.2. Investigative Result 1

Based on Friedman’s analysis of the pared down cases, the Gaussian filter with the parameters of σ = 0.5922, radius = 3 utilizing the Even‐Odd

decimation strategy has the best mean rank among the methods utilizing optimistic decimation strategy (stage 2 analysis).   Post‐hoc analysis

using Wilcoxon indicates that this method is equally as effective and has a score distribution that is not significantly different from methods

(Gaussian σ = 0.5071, r = 3, Odd‐Odd), (Gaussian σ = 0.8475, r = 4, Odd‐Odd), (Gaussian σ = 0.6773, r = 3, Even‐Odd) and (Gaussian σ = 0.7624, r =

3, Even‐Odd) therefore these five methods share the top rank and are clustered as the top ranking methods as shown in Table 13.    

Analysis using a conservative decimation strategy (stage 3 analysis) showed that Spectral Truncation has the best mean rank.    Post‐hoc

analysis using Wilcoxon indicates that this method is equally as effective and has a score distribution that is not significantly different from

methods (Gaussian σ = 0.9326, r = 4, Odd‐Even), (Gaussian σ = 1.0177, r = 4, Even‐Odd), (Gaussian σ = 0.8475, r = 4, Odd‐Even) and (Gaussian σ =

0.6773, r = 3, Odd‐Even).   Post‐hoc analysis also showed that all of these methods have a score distribution that is not significantly different

from the Control Case of native 500 ppi images.
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5.2. Investigative Goal 2: Expert Examiner Identification Assessment  

5.2.1. Investigative Analysis 2

Data collection from the examiners yielded a series of 200 sorted response codes for each treatment and sub‐treatment as described in Table

3.   The data was coded and ranged from 111 (best) to 333 (worst) to represent the three examiner identification decisions.  Statistical analysis

showed that there was no significant distinction between the decimation sub‐treatments of the 24 cases that required decimation as shown in

Table 15.    

Table 15 ‐ Expert Examiner Match Data Analysis, Stage One (Sub‐treatment Pare‐Down, Adjusted α = 0.0167)

Treatment Sub‐treatment, Friedman’s Mean Rank, Lower is Better

Even‐Even Even‐Odd Odd‐Even Odd‐Odd Friedman's p X2 statistic p, Wilcoxon

Rank 1 ≠ 2

p, Wilcoxon

Rank 1  ≠  3

p, Wilcoxon

Rank 1  ≠  4

Native 500 ppi ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐

Averaging ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐

NIST Spectral Truncation ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐

Decimation 2.51 2.50 2.50 2.50 0.3916 3.00 ‐ ‐ ‐

Transcoded A ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐

Transcoded B ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐

Gaussian σ = 0.3369, r = 2 2.50 2.50 2.50 2.50 1.0000 0.00 ‐ ‐ ‐

Gaussian σ = 0.4220, r = 2 2.50 2.50 2.50 2.50 1.0000 0.00 ‐ ‐ ‐

Gaussian σ = 0.5071, r = 3 2.50 2.51 2.51 2.50 0.5724 2.00 ‐ ‐ ‐

Gaussian σ = 0.5642, r = 3 2.50 2.50 2.50 2.51 0.3916 3.00 ‐ ‐ ‐

Gaussian σ = 0.5922, r = 3 2.51 2.50 2.50 2.51 0.5724 2.00 ‐ ‐ ‐

Gaussian σ = 0.6773, r = 3 2.50 2.50 2.51 2.50 0.3916 3.00 ‐ ‐ ‐

Gaussian σ = 0.7624, r = 3 2.50 2.51 2.50 2.50 0.3916 3.00 ‐ ‐ ‐

Gaussian σ = 0.8475, r = 4 2.50 2.50 2.50 2.51 0.3916 3.00 ‐ ‐ ‐

Gaussian σ = 0.9326, r = 4 2.50 2.50 2.50 2.50 1.0000 3.00 ‐ ‐ ‐

Gaussian σ = 1.0177, r = 4 2.50 2.50 2.50 2.50 1.0000 0.00 ‐ ‐ ‐

Gaussian σ = 1.1028, r = 4 2.50 2.50 2.50 2.50 1.0000 0.00 ‐ ‐ ‐

Gaussian σ = 1.1879, r = 5 2.50 2.51 2.51 2.50 0.5724 2.00 ‐ ‐ ‐

Gaussian σ = 1.2730, r = 5 2.50 2.50 2.50 2.50 1.0000 0.00 ‐ ‐ ‐

Gaussian σ = 1.3581, r = 5 2.50 2.51 2.50 2.50 0.3916 3.00 ‐ ‐ ‐

Gaussian σ = 1.4432, r = 5 2.50 2.51 2.50 2.51 0.5724 2.00 ‐ ‐ ‐

Gaussian σ = 1.5283, r = 6 2.49 2.49 2.50 2.51 0.2998 3.67 ‐ ‐ ‐

Gaussian σ = 1.6134, r = 6 2.49 2.51 2.49 2.50 0.2998 3.67 ‐ ‐ ‐

Gaussian σ = 1.6985, r = 6 2.50 2.50 2.50 2.50 1.0000 0.00 ‐ ‐ ‐

Gaussian σ = 1.7836, r = 6 2.50 2.52 2.50 2.50 0.1116 6.00 ‐ ‐ ‐

Gaussian σ = 1.8687, r = 7 2.51 2.52 2.49 2.49 0.1447 5.40 ‐ ‐ ‐

Gaussian σ = 1.9538, r = 7 2.50 2.50 2.51 2.51 0.5724 2.00 ‐ ‐ ‐

Gaussian σ = 2.0389, r = 7 2.50 2.50 2.51 2.50 0.3916 3.00 ‐ ‐ ‐

Gaussian σ = 2.1240, r = 7 2.51 2.49 2.50 2.50 0.5724 2.00 ‐ ‐ ‐

   
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In the next stage of analysis, the Rank 1 candidates from each sub‐treatment were compared against each other and against the cases that

received no sub‐treatment.  Since the data from phase one of this analysis indicated no statistically significant difference between the sub‐

treatments, the sub‐treatment with the lowest mean ranks were selected for phase two of the analysis.  Where a tie existed in the mean rank,

an arbitrary selection was made.  The rationale for this is that in cases where a statistically significant difference cannot be observed, nor an

anecdotal difference can be observed, then the cases can be treated as operationally equivalent for the purposes of phase one of this analysis.

The data from this phase of analysis was sorted according to mean rank, from smallest (best) to largest (worst) and an ordinal rank ranging

from 1 to 29 was assigned to this sorted list (see Table 16).  As with the previous stage of analysis, Friedman’s test of the values here indicates

no significant differences (p=0.2060).   Since no significant differences were shown in stage one of analysis between the different decimation

cases, only stage 2 of the analysis was performed and stage 3 was skipped as there were no demonstrated differences between the optimistic

and conservative decimation strategies.

Table 16 ‐ Expert Examiner Match Data Analysis, Stage Two (Optimistic Decimation Pare‐Down, Adjusted α = 0.0018)

Treatment Rank sum Mean Rank Case No. μ0 (Case No.) μ1 (Case No.) Wilcoxon p μ0 ≠ μ1 Clustered Rank

Averaging 2993.5 14.97 1 ‐ ‐ ‐ ‐ ‐

Decimation, Even‐Odd 2993.5 14.97 2 ‐ ‐ ‐ ‐ ‐

Gaussian σ = 0.3369, r = 2, Even‐Even 2993.5 14.97 3 ‐ ‐ ‐ ‐ ‐

Gaussian σ = 0.4220, r = 2, Even‐Odd 2993.5 14.97 4 ‐ ‐ ‐ ‐ ‐

Gaussian σ = 0.5071, r = 3, Odd‐Odd 2993.5 14.97 5 ‐ ‐ ‐ ‐ ‐

Gaussian σ = 0.5922, r = 3, Even‐Odd 2993.5 14.97 6 ‐ ‐ ‐ ‐ ‐

Gaussian σ = 0.6773, r = 3, Odd‐Odd 2993.5 14.97 7 ‐ ‐ ‐ ‐ ‐

Gaussian σ = 0.9326, r = 4, Odd‐Odd 2993.5 14.97 8 ‐ ‐ ‐ ‐ ‐

Gaussian σ = 1.0177, r = 4, Even‐Even 2993.5 14.97 9 ‐ ‐ ‐ ‐ ‐

Gaussian σ = 1.1028, r = 4, Even‐Odd 2993.5 14.97 10 ‐ ‐ ‐ ‐ ‐

Gaussian σ = 1.1879, r = 5, Odd‐Odd 2993.5 14.97 11 ‐ ‐ ‐ ‐ ‐

Gaussian σ = 1.2730, r = 5, Odd‐Even 2993.5 14.97 12 ‐ ‐ ‐ ‐ ‐

Gaussian σ = 1.3581, r = 5, Odd‐Odd 2993.5 14.97 13 ‐ ‐ ‐ ‐ ‐

Gaussian σ = 1.4432, r = 5, Odd‐Even 2993.5 14.97 14 ‐ ‐ ‐ ‐ ‐

Gaussian σ = 1.6134, r = 6, Odd‐Even 2993.5 14.97 15 ‐ ‐ ‐ ‐ ‐

Gaussian σ = 1.6985, r = 6, Odd‐Odd 2993.5 14.97 16 ‐ ‐ ‐ ‐ ‐

Gaussian σ = 1.7836, r = 6, Even‐Even 2993.5 14.97 17 ‐ ‐ ‐ ‐ ‐

Gaussian σ = 1.8687, r = 7, Odd‐Even 2993.5 14.97 18 ‐ ‐ ‐ ‐ ‐

Transcoded A 2993.5 14.97 19 ‐ ‐ ‐ ‐ ‐

Gaussian σ = 0.5642, r = 3, Even‐Odd 3008.0 15.04 20 ‐ ‐ ‐ ‐ ‐

Gaussian σ = 0.7624, r = 3, Even‐Even 3008.0 15.04 21 ‐ ‐ ‐ ‐ ‐

Gaussian σ = 0.8475, r = 4, Even‐Odd 3008.0 15.04 22 ‐ ‐ ‐ ‐ ‐

Gaussian σ = 1.5283, r = 6, Even‐Even 3008.0 15.04 23 ‐ ‐ ‐ ‐ ‐

Gaussian σ = 1.9538, r = 7, Even‐Odd 3008.0 15.04 24 ‐ ‐ ‐ ‐ ‐

Gaussian σ = 2.0389, r = 7, Odd‐Odd 3008.0 15.04 25 ‐ ‐ ‐ ‐ ‐

Gaussian σ = 2.1240, r = 7, Even‐Odd 3008.0 15.04 26 ‐ ‐ ‐ ‐ ‐

Transcoded B 3008.0 15.04 27 ‐ ‐ ‐ ‐ ‐

Spectral Truncation 3022.5 15.11 28 ‐ ‐ ‐ ‐ ‐

Native 500 ppi 3037.0 15.19 29 ‐ ‐ ‐ ‐ ‐

Friedman's statistic 33.85

DF 28

p 0.2060 (X2 approximation, corrected for ties)

5.2.2. Investigative Result 2

Based on the analysis of the data, it is evident that the downsampling methods examined did not appear to cause a significant measurable

impact on examiner objective analysis, and therefore their ability to make an identification decision was not impacted even though they could

detect degradation as a result of the various downsampling methods as shown in the subjective analysis section of this study.  
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5.3. Investigative Goal 3: Automated Matching Assessment

5.3.1. Investigative Analysis 3

Data collection by matching the processed image to the unprocessed native image using the NIST research matcher (Bozorth3) can yield

match scores ranging from 0 to 65535, with higher scores indicative of a higher probability of a true match as determined by the machine.  In

the first phase of analysis, Friedman’s statistical test was performed on each treatment that required the decimation sub‐treatment.   This

resulted in Friedman’s ranking of the sub‐treatments (see Table 17).  This allowed for the stratification of the sub‐treatment from best (highest

mean rank) to worst (lowest mean rank), and provided us an indication that at least one statistically significant difference in distributions

exists between the four sub‐treatments via Friedman’s p.  The ranking of the sub‐treatments allows us to select the best sub‐treatment for

each treatment and propagate that to the next phase of analysis.  In addition to selecting the top ranked sub‐treatment per the rank analysis,

a Wilcoxon post‐hoc analysis was performed between match data of methods having Rank 1 and Rank 2, Rank 1 and Rank 3 and Rank 1 and

Rank 4 to determine if the top ranked sub‐treatment is indeed different from that of Ranks 2, 3, and 4.     

Table 17 ‐ Automated Matching Data Analysis, Stage One (Sub‐treatment Pare‐Down, Adjusted α = 0.0167)

Treatment Sub‐treatment, Friedman’s Mean Rank, Lower is Better

Even‐Even Even‐Odd Odd‐Even Odd‐Odd Friedman's p X2

 statistic p, Wilcoxon

Rank 1 ≠ 2

p, Wilcoxon

Rank 1  ≠  3

p, Wilcoxon

Rank 1  ≠  4

Native 500 ppi ‐  ‐  ‐ ‐ ‐ ‐ ‐  ‐

Averaging ‐  ‐  ‐ ‐ ‐ ‐ ‐  ‐

Spectral Truncation ‐  ‐  ‐ ‐ ‐ ‐ ‐  ‐ ‐

Decimation 2.14 2.70 2.51 2.65 <0.0001 238.45 0.0869 <0.0001 ‐

Transcoded A ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐

Transcoded B ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐

Gaussian σ = 0.3369, r = 2 2.14 2.72 2.45 2.69 <0.0001 264.68 0.0812 <0.0001 ‐

Gaussian σ = 0.4220, r = 2 2.21 2.70 2.50 2.58 <0.0001 159.74 0.0026 ‐ ‐

Gaussian σ = 0.5071, r = 3 2.39 2.59 2.38 2.64 <0.0001 66.24 <0.0001 ‐ ‐

Gaussian σ = 0.5642, r = 3 2.42 2.38 2.66 2.55 <0.0001 60.96 0.0061 ‐ ‐

Gaussian σ = 0.5922, r = 3 2.47 2.37 2.62 2.53 <0.0001 40.94 0.0201 <0.0001 ‐

Gaussian σ = 0.6773, r = 3 2.40 2.58 2.61 2.41 <0.0001 46.77 0.5062 <0.0001 ‐

Gaussian σ = 0.7624, r = 3 2.48 2.53 2.62 2.37 <0.0001 38.33 0.0178 <0.0001 ‐

Gaussian σ = 0.8475, r = 4 2.49 2.50 2.66 2.35 <0.0001 62.57 <0.0001 ‐ ‐

Gaussian σ = 0.9326, r = 4 2.54 2.47 2.61 2.38 <0.0001 35.86 0.0645 <0.0001 ‐

Gaussian σ = 1.0177, r = 4 2.58 2.46 2.61 2.35 <0.0001 54.57 0.6809 0.0001 ‐

Gaussian σ = 1.1028, r = 4 2.59 2.43 2.63 2.35 <0.0001 65.23 0.3539 <0.0001 ‐

Gaussian σ = 1.1879, r = 5 2.60 2.34 2.65 2.42 <0.0001 80.16 0.2758 <0.0001 ‐

Gaussian σ = 1.2730, r = 5 2.59 2.31 2.73 2.37 <0.0001 137.55 0.0015 ‐ ‐

Gaussian σ = 1.3581, r = 5 2.59 2.33 2.71 2.37 <0.0001 120.25 0.0059 ‐ ‐

Gaussian σ = 1.4432, r = 5 2.59 2.28 2.73 2.40 <0.0001 152.61 0.0015 ‐ ‐

Gaussian σ = 1.5283, r = 6 2.61 2.26 2.74 2.39 <0.0001 172.40 0.0009 ‐ ‐

Gaussian σ = 1.6134, r = 6 2.61 2.25 2.70 2.44 <0.0001 144.72 <0.0001 ‐ ‐

Gaussian σ = 1.6985, r = 6 2.63 2.26 2.69 2.42 <0.0001 143.08 0.0457 <0.0001 ‐

Gaussian σ = 1.7836, r = 6 2.67 2.20 2.43 2.70 <0.0001 202.28 <0.0001 ‐ ‐

Gaussian σ = 1.8687, r = 7 2.61 2.22 2.74 2.43 <0.0001 189.73 0.0018 <0.0001 ‐

Gaussian σ = 1.9538, r = 7 2.64 2.19 2.72 2.46 <0.0001 202.75 0.0030 ‐ ‐

Gaussian σ = 2.0389, r = 7 2.63 2.20 2.71 2.46 <0.0001 194.07 0.0078 ‐ ‐

Gaussian σ = 2.1240, r = 7 2.67 2.16 2.72 2.45 <0.0001 245.84 0.0572 <0.0001 ‐

   
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In the next stage of analysis, the Rank 1 candidates from each sub‐treatment were compared against each other and the cases that received

no sub‐treatment.  The data from this phase of analysis was sorted according to mean rank, from largest (best) to smallest and an ordinal case

number ranging from 1 to 29 was assigned to this sorted list (see Table 18).  Post‐hoc analysis was then performed down this list, comparing

Case 1 to Case 2 and so on.  As described in 5.1, this comparison continued until a statistically significant difference was observed.  The values

that did not demonstrate a statistically significant difference were clustered into one singular rank.    This process continued until a list of

clustered rank of values was established, with each clustered rank representing data cases that are not significantly different from the others

(and hence are clustered as such).    

Table 18 ‐ Automated Matching Data Analysis, Stage Two (Optimistic Decimation Pare‐Down, Adjusted α = 0.0018)

Treatment Rank sum Mean Rank Case No. μ0 (Case No.) μ1 (Case No.) Wilcoxon p μ0 ≠ μ1 Clustered Rank

Native 500 ppi 59131.0 29.00 1 NA NA NA 1

Gaussian σ = 1.2730, r = 5, Odd‐Even 37417.0 18.35 2 1 2 <0.0001 Yes 2

Gaussian σ = 1.3581, r = 5, Odd‐Even 37338.0 18.31 3 2 3 0.9017 2

Gaussian σ = 1.1879, r = 5, Odd‐Even 36515.0 17.91 4 2 4 0.0378 2

Gaussian σ = 1.4432, r = 5, Odd‐Even 36423.0 17.86 5 2 5 0.0024 2

Gaussian σ = 1.1028, r = 4, Odd‐Even 36227.5 17.77 6 2 6 0.0403 2

Gaussian σ = 1.5283, r = 6, Odd‐Even 35440.0 17.38 7 2 7 <0.0001 Yes 3

Gaussian σ = 1.0177, r = 4, Odd‐Even 35326.0 17.33 8 7 8 0.7248 3

Gaussian σ = 0.9326, r = 4, Odd‐Even 34803.5 17.07 9 7 9 0.2302 3

Gaussian σ = 0.8475, r = 4, Odd‐Even 34246.0 16.80 10 7 10 0.0645 3

Gaussian σ = 1.6134, r = 6, Odd‐Even 32756.5 16.06 11 7 11 <0.0001 Yes 4

Gaussian σ = 0.7624, r = 3, Odd‐Even 32663.5 16.02 12 11 12 0.7621 4

Gaussian σ = 0.6773, r = 3, Odd‐Even 31352.0 15.38 13 11 13 0.0300 4

Gaussian σ = 1.6985, r = 6, Odd‐Even 30921.5 15.17 14 11 14 <0.0001 Yes 5

Gaussian σ = 0.5922, r = 3, Odd‐Even 29283.5 14.36 15 14 15 0.0058 5

Gaussian σ = 0.5642, r = 3, Odd‐Even 28793.5 14.12 16 14 16 0.0010 Yes 6

Gaussian σ = 0.4220, r = 2, Even‐Odd 27485.5 13.48 17 16 17 0.0006 Yes 7

Gaussian σ = 0.5071, r = 3, Odd‐Odd 27038.0 13.26 18 17 18 0.6643 7

Gaussian σ = 0.3369, r = 2, Even‐Odd 26947.0 13.22 19 17 19 0.0612 7

Averaging 26621.5 13.06 20 17 20 0.0687 7

Gaussian σ = 1.8687, r = 7, Odd‐Even 26348.5 12.92 21 17 21 0.0411 7

Decimation, Even‐Odd 25940.0 12.72 22 17 22 0.0002 Yes 8

Gaussian σ = 1.7836, r = 6, Odd‐Odd 25220.0 12.37 23 22 23 0.4083 8

Transcoded B 24596.5 12.06 24 22 24 0.0031 8

Transcoded A 24571.0 12.05 25 22 25 0.0100 8

Spectral Truncation 23375.5 11.46 26 22 26 <0.0001 Yes 9

Gaussian σ = 1.9538, r = 7, Odd‐Even 23269.0 11.41 27 26 27 0.8483 9

Gaussian σ = 2.0389, r = 7, Odd‐Even 19999.0 9.81 28 26 28 <0.0001 Yes 10

Gaussian σ = 2.1240, r = 7, Odd‐Even 16916.0 8.30 29 28 29 <0.0001 Yes 11

n 2039

Friedman's statistic 11487.77

DF 28

p <0.0001 (X2 approximation, corrected for ties)

   
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In stage three of analysis, the Rank 4 (worst) decimation candidates from each sub‐treatment were compared against each other as well as

the cases that received no sub‐treatment.   The data from this stage of analysis was sorted according to mean rank, from smallest (best) to

largest (worst) and an ordinal case number ranging from 1 to 29 was assigned to this sorted list (see Table 19).  Post‐hoc analysis was then

performed down this list, comparing Case 1 to Case 2 and so on.   As described in section 5.1.1, this comparison continued until a statistically

significant difference was observed.  The values that did not demonstrate a statistically significant difference were clustered into one singular

rank.   This process continued until a list of clustered rank values was established, with each clustered rank representing data cases that are

not significantly different from the others in the cluster.   Each clustered group was then provided an ordinal clustered rank value.

Table 19 ‐ Automated Matching Data Analysis, Stage Three (Conservative Decimation Pare‐Down, Adjusted α = 0.0018)

Treatment Rank sum Mean Rank Case No. μ0 (Case No.) μ1 (Case No.) Wilcoxon p μ0 ≠ μ1 Clustered Rank

Native 500 ppi 59131.0 29.00 1 NA NA NA 1

Gaussian σ = 1.1879, r = 5, Even‐Odd 37065.0 18.18 2 1 2 <0.0001 Yes 2

Gaussian σ = 1.1028, r = 4, Odd‐Odd 36742.0 18.02 3 2 3 0.4044 2

Gaussian σ = 1.2730, r = 5, Even‐Odd 36529.5 17.92 4 2 4 0.0958 2

Gaussian σ = 1.3581, r = 5, Even‐Odd 36373.5 17.84 5 2 5 0.0146 2

Gaussian σ = 1.0177, r = 4, Odd‐Odd 36061.0 17.69 6 2 6 0.1022 2

Gaussian σ = 0.9326, r = 4, Odd‐Odd 35416.0 17.37 7 2 7 0.0016 Yes 3

Gaussian σ = 1.4432, r = 5, Even‐Odd 35139.5 17.23 8 7 8 0.1463 3

Gaussian σ = 0.8475, r = 4, Odd‐Odd 34016.0 16.68 9 7 9 0.0002 Yes 4

Gaussian σ = 1.5283, r = 6, Even‐Odd 33613.0 16.49 10 9 10 0.1735 4

Gaussian σ = 0.7624, r = 3, Odd‐Odd 33439.5 16.40 11 9 11 0.4342 4

Gaussian σ = 0.6773, r = 3, Even‐Even 32740.5 16.06 12 9 12 0.0023 4

Gaussian σ = 1.6134, r = 6, Even‐Odd 31678.0 15.54 13 9 13 <0.0001 Yes 5

Gaussian σ = 0.5071, r = 3, Odd‐Even 30596.5 15.01 14 13 14 0.2406 5

Averaging 30417.5 14.92 15 13 15 0.1141 5

Gaussian σ = 0.5922, r = 3, Even‐Odd 29691.0 14.56 16 13 16 0.0014 Yes 6

Gaussian σ = 1.6985, r = 6, Even‐Odd 29469.0 14.45 17 16 17 0.3494 6

Gaussian σ = 0.5642, r = 3, Even‐Odd 28953.0 14.20 18 16 18 0.0073 6

Transcoded A 28501.0 13.98 19 16 19 0.0073 6

Transcoded B 28208.5 13.83 20 16 20 0.0033 6

Spectral Truncation 26960.0 13.22 21 16 21 <0.0001 6

Gaussian σ = 1.7836, r = 6, Even‐Odd 26817.5 13.15 22 21 22 0.6007 6

Gaussian σ = 0.4220, r = 2, Even‐Even 25362.0 12.44 23 21 23 0.0012 Yes 7

Gaussian σ = 1.8687, r = 7, Even‐Odd 24283.5 11.91 24 23 24 0.0298 7

Gaussian σ = 0.3369, r = 2, Even‐Even 23056.5 11.31 25 23 25 <0.0001 Yes 8

NIST Decimation Even‐Even 22149.0 10.86 26 25 26 0.0163 8

Gaussian σ = 1.9538, r = 7, Even‐Odd 21112.0 10.35 27 25 27 0.0001 Yes 9

Gaussian σ = 2.0389, r = 7, Even‐Odd 18217.5 8.93 28 27 28 <0.0001 Yes 10

Gaussian σ = 2.1240, r = 7, Even‐Odd 15226.0 7.47 29 280 29 <0.0001 Yes 11

n 2039

Friedman's statistic 12111.46

DF 28

p <0.0001 (X2 approximation, corrected for ties)

5.3.2. Investigative Result 3

Based on rank analysis of the pared down cases, the Native 500 ppi Control Case yielded the best performance for the machine matcher

among the methods utilizing the optimistic decimation strategy (stage 2 analysis).  This was followed by several Gaussian methods.  Post‐hoc

analysis using Wilcoxon indicates that the Native Control Case exhibits operational behavior that is statistically better than the Gaussian cases

that follow it and can clearly be identified as the best.  Post‐hoc analysis also showed that the five Gaussian cases that followed the control

case (Gaussian σ = 1.2730, r = 5, Odd‐Even), (Gaussian σ = 1.3581, r = 5, Odd‐Even), (Gaussian σ = 1.1879, r = 5, Odd‐Even), (Gaussian σ = 1.4432, r

= 5, Odd‐Even) and (Gaussian σ = 1.1028, r = 4, Odd‐Even) are equally as effective and have a score distribution that is not significantly different

from each other and therefore these five methods share clustered rank after the Control Case as the next best performing case.

Analysis using the conservative decimation strategy (stage 3 analysis) showed that the Native 500 ppi Control Case again yields the best mean

rank.  Post‐hoc analysis using Wilcoxon indicates that the Native Control Case exhibits operational behavior that is statistically better than the

Gaussian cases that follow it and can clearly be identified as the best.  Post‐hoc analysis also showed that the five Gaussian cases that followed

the Control Case (Gaussian σ = 1.1879, r = 5, Even‐Odd), (Gaussian σ = 1.1028, r = 4, Odd‐Odd), (Gaussian σ = 1.2730, r = 5, Even‐Odd), (Gaussian σ 
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PAGE 53 OF 84

= 1.3581, r = 5, Even‐Odd) and (Gaussian σ = 1.0177, r = 4, Odd‐Odd) are equally as effective and have a score distribution that is not significantly

different from each other and therefore these five methods share clustered rank after the Control Case as the next best performing case.

5.4. Investigative Goal 4: Signal Analysis and Assessment

5.4.1. Investigative Analysis 4

Frequency Spectrum Correlation Analysis

Data analysis by conducting a frequency spectrum correlation analysis using SIVV (see 3.2.3) yielded correlation scores potentially ranging

from 0 to 1, with 1 representing 100% spectrum fidelity to the original sample.  In the first phase of analysis, Friedman’s statistical test was

performed on each treatment that required the decimation sub‐treatment.   This resulted in Friedman’s ranking of the sub‐treatments (see

Table 20).   This allowed for stratification of the sub‐treatments from best (highest mean rank) to worst (lowest mean rank), and provided an

indication that at least one statistically significant difference in distributions exists between the four sub‐treatments via Friedman’s p.   Mean

ranks of the sub‐treatments allows us to select the best sub‐treatment for each treatment and propagate that to the next phase of analysis.   

In addition to selecting the top ranked sub‐treatment, a Wilcoxon post‐hoc analysis was performed between treatments at Rank 1 and at Rank

2 to determine if the top ranked sub‐treatment is indeed different from that at Rank 2. Given a finding of no significant difference for this test,

Wilcoxon comparison would have been made between treatment at Rank 1 with that at Rank 3 and Rank 4.    For this metric, the Rank 1

candidate in all cases was shown to be significantly different than Rank 2, hence no further analysis for Rank 3 or Rank 4 was conducted.

  

Table 20 ‐ Frequency Spectrum Correlation Analysis, Stage One (Sub‐treatment Pare‐Down, Adjusted α = 0.0167)

Treatment Sub‐treatment, Friedman’s Mean Rank, Lower is Better

Even‐Even Even‐Odd Odd‐Even Odd‐Odd Friedman's p X2 statistic p, Wilcoxon

Rank 1 ≠ 2

p, Wilcoxon

Rank 1  ≠  3

p, Wilcoxon

Rank 1  ≠  4

Native 500 ppi ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐

Averaging ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐

NIST Spectral Truncation ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐

Decimation 1.03 3.18 2.18 3.61 <0.0001 474.94 <0.0001 ‐ ‐

Transcoded A ‐ ‐

Transcoded B ‐ ‐

Gaussian σ = 0.3369, r = 2 1.03 3.17 2.20 3.61 <0.0001 469.70 <0.0001 ‐ ‐

Gaussian σ = 0.4220, r = 2 1.04 3.15 2.26 3.57 <0.0001 450.78 <0.0001 ‐ ‐

Gaussian σ = 0.5071, r = 3 1.17 2.97 2.36 3.51 <0.0001 362.50 <0.0001 ‐ ‐

Gaussian σ = 0.5642, r = 3 1.40 2.82 2.32 3.47 <0.0001 275.83 <0.0001 ‐ ‐

Gaussian σ = 0.5922, r = 3 1.50 2.74 2.32 3.44 <0.0001 236.83 <0.0001 ‐ ‐

Gaussian σ = 0.6773, r = 3 1.71 2.69 2.30 3.31 <0.0001 162.03 <0.0001 ‐ ‐

Gaussian σ = 0.7624, r = 3 1.93 2.54 2.32 3.22 <0.0001 106.18 <0.0001 ‐ ‐

Gaussian σ = 0.8475, r = 4 2.00 2.32 2.39 3.30 <0.0001 111.32 <0.0001 ‐ ‐

Gaussian σ = 0.9326, r = 4 1.96 2.28 2.41 3.36 <0.0001 129.76 <0.0001 ‐ ‐

Gaussian σ = 1.0177, r = 4 2.03 2.16 2.41 3.41 <0.0001 140.05 <0.0001 ‐ ‐

Gaussian σ = 1.1028, r = 4 2.02 2.02 2.51 3.46 <0.0001 167.06 <0.0001 ‐ ‐

Gaussian σ = 1.1879, r = 5 2.18 1.92 2.46 3.45 <0.0001 161.59 <0.0001 ‐ ‐

Gaussian σ = 1.2730, r = 5 2.23 1.85 2.55 3.38 <0.0001 151.57 <0.0001 ‐ ‐

Gaussian σ = 1.3581, r = 5 2.28 1.80 2.58 3.35 <0.0001 150.97 <0.0001 ‐ ‐

Gaussian σ = 1.4432, r = 5 2.34 1.77 2.55 3.35 <0.0001 152.95 <0.0001 ‐ ‐

Gaussian σ = 1.5283, r = 6 2.38 1.71 2.58 3.34 <0.0001 160.96 <0.0001 ‐ ‐

Gaussian σ = 1.6134, r = 6 2.38 1.70 2.53 3.40 <0.0001 176.95 <0.0001 ‐ ‐

Gaussian σ = 1.6985, r = 6 2.41 1.62 2.61 3.37 <0.0001 187.35 <0.0001 ‐ ‐

Gaussian σ = 1.7836, r = 6 2.46 1.58 2.62 3.35 <0.0001 191.15 <0.0001 ‐ ‐

Gaussian σ = 1.8687, r = 7 2.50 1.54 2.58 3.39 <0.0001 205.25 <0.0001 ‐ ‐

Gaussian σ = 1.9538, r = 7 2.53 1.48 2.64 3.36 <0.0001 215.00 <0.0001 ‐ ‐

Gaussian σ = 2.0389, r = 7 2.53 1.39 2.65 3.44 <0.0001 257.99 <0.0001 ‐ ‐

Gaussian σ = 2.1240, r = 7 2.56 1.35 2.67 3.43 <0.0001 265.07 <0.0001 ‐ ‐

   
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In stage two of analysis, the treatments combined with the best (Rank 1) decimation sub‐treatment were compared against each other as well

as to the downsampling methods that included no decimation sub‐treatment.   The data from this phase of analysis was sorted according to

mean rank, from largest (best) to smallest (worst) and an ordinal case number ranging from 1 to 29 was assigned to this sorted list (Table 21).  

Post‐hoc analysis was then performed down this list, comparing Case 1 to Case 2 and so on.   As described previously, this comparison

continued until a statistically significant difference was observed.  The cases that did not demonstrate a statistically significant difference were

clustered into one singular rank.   This process continued until a list of clustered rank values was established, with each clustered rank

representing data cases that are not significantly different from the others (and hence are clustered as such).   Each clustered group was then

provided an ordinal clustered rank value.

Table 21 ‐ Frequency Spectrum Correlation Analysis, Stage Two (Optimistic Decimation Pare‐Down, Adjusted α = 0.0018)

Treatment Rank sum Mean Rank Case No. P0 (Case No.) P1 (Case No.) Wilcoxon p P0 ≠ P1 Clustered Rank

Native 500 ppi 5800.0 29.00 1 NA NA NA 1

Gaussian σ = 0.8475, r = 4, Odd‐Odd 4351.0 21.76 2 1 2 <0.0001 Yes 2

Gaussian σ = 0.7624, r = 3, Odd‐Odd 4336.0 21.68 3 2 3 0.1938 2

Gaussian σ = 0.5642, r = 3, Odd‐Odd 4335.0 21.68 4 2 4 0.0326 2

Gaussian σ = 0.5922, r = 3, Odd‐Odd 4330.0 21.65 5 2 5 0.0231 2

Gaussian σ = 0.6773, r = 3, Odd‐Odd 4330.0 21.65 6 2 6 0.0524 2

Gaussian σ = 0.5071, r = 3, Odd‐Odd 4242.0 21.21 7 2 7 0.0847 2

Gaussian σ = 0.9326, r = 4, Odd‐Odd 4232.0 21.16 8 2 8 <0.0001 Yes 3

Gaussian σ = 0.4220, r = 2, Odd‐Odd 4173.0 20.87 9 8 9 0.0779 3

Gaussian σ = 0.3369, r = 2, Odd‐Odd 4070.0 20.35 10 8 10 0.2308 3

Gaussian σ = 1.0177, r = 4, Odd‐Odd 4052.0 20.26 11 8 11 <0.0001 Yes 4

Decimation, Odd‐Odd 3866.0 19.33 12 11 12 0.1347 4

Gaussian σ = 1.1028, r = 4, Odd‐Odd 3852.0 19.26 13 11 13 <0.0001 Yes 5

Gaussian σ = 1.1879, r = 5, Odd‐Odd 3581.0 17.91 14 13 14 <0.0001 Yes 6

Gaussian σ = 1.2730, r = 5, Odd‐Odd 3270.0 16.35 15 14 15 <0.0001 Yes 7

Gaussian σ = 1.3581, r = 5, Odd‐Odd 2980.0 14.90 16 15 16 <0.0001 Yes 8

Averaging 2761.0 13.81 17 16 17 0.5565 8

Gaussian σ = 1.4432, r = 5, Odd‐Odd 2678.0 13.39 18 16 18 <0.0001 Yes 9

Spectral Truncation 2457.0 12.29 19 18 19 0.0382 9

Gaussian σ = 1.5283, r = 6, Odd‐Odd 2353.0 11.77 20 18 20 <0.0001 Yes 10

Gaussian σ = 1.6134, r = 6, Odd‐Odd 2015.0 10.08 21 20 21 <0.0001 Yes 11

Gaussian σ = 1.6985, r = 6, Odd‐Odd 1684.0 8.42 22 21 22 <0.0001 Yes 12

Transcoded B 1501.0 7.51 23 22 23 0.0001 Yes 13

Transcoded A 1436.0 7.18 24 23 24 <0.0001 Yes 14

Gaussian σ = 1.7836, r = 6, Odd‐Odd 1382.0 6.91 25 24 25 0.0255 14

Gaussian σ = 1.8687, r = 7, Odd‐Odd 1112.0 5.56 26 24 26 0.7372 14

Gaussian σ = 1.9538, r = 7, Odd‐Odd 857.0 4.29 27 24 27 0.0766 14

Gaussian σ = 2.0389, r = 7, Odd‐Odd 603.0 3.02 28 24 28 <0.0001 Yes 15

Gaussian σ = 2.1240, r = 7, Odd‐Odd 361.0 1.81 29 28 29 <0.0001 Yes 16

n 200

Friedman's statistic 3956.95

DF 28

p <0.0001 (X2 approximation, corrected for ties)

   
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In stage three of analysis, the Rank 4 (worst) decimation candidates from each sub‐treatment were compared against each other as well as

the cases that received no sub‐treatment.   The data from this stage of analysis was sorted according to mean rank, from largest (best) to

smallest (worst) and an ordinal case number ranging from 1 to 29 was assigned to this sorted list (see Table 22) .  Post‐hoc analysis was then

performed down this list, comparing Case 1 to Case 2 and so on.   As described in section 5.1.1, this comparison continued until a statistically

significant difference was observed.  The cases that did not demonstrate a statistically significant difference were clustered into one singular

rank.   This process continued until a clustered list of rank values was established, with each clustered rank representing data cases that are

not significantly different from the others in the cluster.  Each clustered group was then provided an ordinal clustered rank value.

Table 22 ‐ Frequency Spectrum Correlation Analysis, Stage Three (Conservative Decimation Pare‐Down, Adjusted α = 0.0018)

Treatment Rank sum Mean Rank Case No. P0 (Case No.) P1 (Case No.) Wilcoxon p P0 ≠ P1 Clustered Rank

Native 500 ppi 5800.0 29.00 1 NA NA NA 1

Gaussian σ = 0.7624 r = 3, Even‐Even 4496.0 22.48 2 1 2 <0.0001 Yes 2

Gaussian σ = 0.8475 r = 4, Even‐Even 4420.0 22.10 3 2 3 0.3998 2

Gaussian σ = 0.9326 r = 4, Even‐Even 4320.0 21.60 4 3 4 0.0277 2

Gaussian σ = 0.6773 r = 3, Even‐Even 4247.0 21.24 5 3 5 0.0001 Yes 3

Gaussian σ = 1.1879 r = 5, Even‐Odd 4215.0 21.08 6 5 6 0.5426 3

Averaging 4207.0 21.04 7 5 7 0.4270 3

Gaussian σ = 1.0177 r = 4, Even‐Even 4188.0 20.94 8 5 8 0.6605 3

Gaussian σ = 1.1028 r = 4, Even‐Even 3993.0 19.97 9 5 9 0.4723 3

Gaussian σ = 1.2730 r = 5, Even‐Odd 3917.0 19.59 10 5 10 0.0836 3

Gaussian σ = 0.5922 r = 3, Even‐Even 3693.0 18.47 11 5 11 <0.0001 Yes 4

Gaussian σ = 1.3581 r = 5, Even‐Odd 3608.0 18.04 12 11 12 0.8682 4

Spectral Truncation 3477.0 17.39 13 11 13 0.9942 4

Gaussian σ = 0.56419 r = 3, Even‐Even 3371.0 16.86 14 11 14 <0.0001 Yes 5

Gaussian σ = 1.4432 r = 5, Even‐Odd 3278.0 16.39 15 14 15 0.8615 5

Gaussian σ = 1.5283 r = 6, Even‐Odd 2940.0 14.70 16 14 16 0.3284 5

Gaussian σ = 0.5071 r = 3, Even‐Even 2817.0 14.09 17 14 17 <0.0001 Yes 6

Gaussian σ = 1.6134 r = 6, Even‐Odd 2588.0 12.94 18 17 18 0.5738 6

Transcoded B 2383.0 11.92 19 17 19 <0.0001 Yes 7

Transcoded A 2323.0 11.62 20 19 20 <0.0001 Yes 8

Gaussian σ = 1.6985 r = 6, Even‐Odd 2240.0 11.20 21 20 21 0.4242 8

Gaussian σ = 1.7836 r = 6, Even‐Odd 1905.0 9.53 22 20 22 0.4046 8

Gaussian σ = 0.4220 r = 2, Even‐Even 1780.0 8.90 23 20 23 <0.0001 Yes 9

Gaussian σ = 1.8687 r = 7, Even‐Odd 1595.0 7.98 24 23 24 0.6015 9

Gaussian σ = 0.3369 r = 2, Even‐Even 1301.0 6.51 25 23 25 <0.0001 Yes 10

Gaussian σ = 1.9538 r = 7, Even‐Odd 1266.0 6.33 26 25 26 0.0345 10

Decimation‐Only, Even‐Even 1010.0 5.05 27 25 27 <0.0001 Yes 11

Gaussian σ = 2.0389 r = 7, Even‐Odd 962.0 4.81 28 27 28 0.1725 11

Gaussian σ = 2.1240 r = 7, Even‐Odd 660.0 3.30 29 27 29 0.4442 11

n 200

Friedman's statistic 3353.31

DF 28

p <0.0001 (X2 approximation, corrected for ties)
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Root Mean Square Difference (RMSD) Analysis of Spectra

Analysis of the RMS difference between SIVV frequency spectra (see 3.2.3) yields values that may range from 0 to , with 0 representing 100%

fidelity to the frequency spectrum of the 500 ppi exemplar image.  In the first phase of analysis, Friedman’s statistical test was performed on

each treatment that required the decimation sub‐treatment.   This resulted in Friedman’s ranking of the sub‐treatments (see Table 23).   This

allowed for stratification of the sub‐treatments from best (lowest mean rank for RMSD) to worst (highest mean rank for RMSD), and provided

an indication that at least one statistically significant difference in distributions exists between the four sub‐treatments via Friedman’s p.   

Friedman’s ranking of the sub‐treatments allows us to select the best sub‐treatment for each treatment and propagate that to the next phase

of analysis.    In addition to selecting the top ranked sub‐treatment per Friedman’s analysis, a Wilcoxon post‐hoc analysis was performed

between Rank 1 and Rank 2 to determine if the top ranked sub‐treatment is indeed different from Rank 2‐4.     

Table 23 ‐ Root Mean Square Difference Analysis, Stage One (Sub‐treatment Pare‐Down, Adjusted α = 0.0167)

Treatment Sub‐treatment, Friedman’s Mean Rank, Lower is Better

Even‐Even Even‐Odd Odd‐Even Odd‐Odd Friedman's p X2 statistic p, Wilcoxon

Rank 1 ≠ 2

p, Wilcoxon

Rank 1  ≠  3

p, Wilcoxon

Rank 1  ≠  4

Native 500 ppi ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐

Averaging ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐

NIST Spectral Truncation ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐

Decimation 3.94 1.86 2.75 1.47 <0.0001 432.78 <0.0001

Transcoded A

Transcoded B

Gaussian σ = 0.3369, r = 2 3.94 1.90 2.72 1.45 <0.0001 429.68 <0.0001

Gaussian σ = 0.4220, r = 2 3.91 1.91 2.68 1.52 <0.0001 399.47 <0.0001

Gaussian σ = 0.5071, r = 3 3.74 2.00 2.71 1.56 <0.0001 326.72 <0.0001

Gaussian σ = 0.5642, r = 3 3.56 2.15 2.75 1.55 <0.0001 263.77 <0.0001

Gaussian σ = 0.5922, r = 3 3.46 2.27 2.75 1.52 <0.0001 239.69 <0.0001

Gaussian σ = 0.6773, r = 3 3.20 2.61 2.65 1.56 <0.0001 168.97 <0.0001

Gaussian σ = 0.7624, r = 3 2.80 2.89 2.56 1.76 <0.0001 94.37 <0.0001

Gaussian σ = 0.8475, r = 4 2.54 3.04 2.48 1.95 <0.0001 70.84 <0.0001

Gaussian σ = 0.9326, r = 4 2.36 3.07 2.50 2.08 <0.0001 62.33 <0.0001

Gaussian σ = 1.0177, r = 4 2.24 3.13 2.54 2.10 <0.0001 74.69 <0.0001

Gaussian σ = 1.1028, r = 4 2.16 3.30 2.39 2.16 <0.0001 105.45 0.0142

Gaussian σ = 1.1879, r = 5 2.07 3.21 2.42 2.31 <0.0001 88.40 0.1591 0.0166

Gaussian σ = 1.2730, r = 5 2.03 3.09 2.41 2.48 <0.0001 69.44 0.0072

Gaussian σ = 1.3581, r = 5 2.09 3.06 2.37 2.49 <0.0001 60.35 0.0899 0.4349 <0.0001

Gaussian σ = 1.4432, r = 5 2.13 3.07 2.34 2.47 <0.0001 57.95 0.1344 0.3978 <0.0001

Gaussian σ = 1.5283, r = 6 2.15 3.06 2.42 2.37 <0.0001 55.13 0.3320 0.1049 <0.0001

Gaussian σ = 1.6134, r = 6 2.18 3.06 2.39 2.38 <0.0001 53.62 0.3236 0.3094 <0.0001

Gaussian σ = 1.6985, r = 6 2.21 3.06 2.35 2.39 <0.0001 52.41 0.4589 0.3903 <0.0001

Gaussian σ = 1.7836, r = 6 2.21 3.06 2.37 2.36 <0.0001 52.10 0.4671 0.2991 <0.0001

Gaussian σ = 1.8687, r = 7 2.23 3.06 2.45 2.27 <0.0001 53.63 0.3711 0.1395 <0.0001

Gaussian σ = 1.9538, r = 7 2.16 3.06 2.48 2.31 <0.0001 52.10 0.4284 0.0431 <0.0001

Gaussian σ = 2.0389, r = 7 2.20 3.06 2.44 2.31 <0.0001 53.79 0.5029 0.1988 <0.0001

Gaussian σ = 2.1240, r = 7 2.21 3.06 2.43 2.30 <0.0001 53.11 0.5655 0.0750 <0.0001

   
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In stage two of analysis, the Rank 1 candidates from each sub‐treatment were compared against each other as well as the cases that received

no sub‐treatment.   The data from this phase of analysis was sorted according to mean rank, from smallest (best) to largest (worst) and an

ordinal case number ranging from 1 to 29 was assigned to this sorted list (see Table 24).  Post‐hoc pairwise comparison was then performed

down this list, comparing Case 1 to Case 2 and so on.   As described above, this comparison continued until a statistically significant difference

was observed.  The cases that did not demonstrate a statistically significant difference were clustered into one singular rank.   This process

continued until a list of clustered ranks was established, with each clustered rank representing cases that are not significantly different from

the others (and hence are clustered as such).   Each clustered group was then provided an ordinal clustered rank value.

Table 24 ‐ Root Mean Square Difference Analysis, Stage Two (Optimistic Decimation Pare‐Down, Adjusted α = 0.0018)

Treatment Rank sum Mean Rank Case No. P0 (Case No.) P1 (Case No.) Wilcoxon p P0 ≠ P1 Clustered Rank

Native 500 ppi 200.0 1.00 1 NA NA NA 1

Gaussian σ = 0.5922, r = 3, Odd‐Odd 1318.0 6.59 2 1 2 <0.0001 Yes 2

Gaussian σ = 0.6773, r = 3, Odd‐Odd 1321.0 6.61 3 2 3 0.2347 2

Gaussian σ = 0.5642, r = 3, Odd‐Odd 1369.0 6.85 4 2 4 0.0012 Yes 3

Gaussian σ = 0.7624, r = 3, Odd‐Odd 1412.0 7.06 5 4 5 0.6756 3

Gaussian σ = 0.5071, r = 3, Odd‐Odd 1473.0 7.37 6 4 6 <0.0001 Yes 4

Gaussian σ = 0.8475, r = 4, Odd‐Odd 1576.0 7.88 7 6 7 0.2474 4

Gaussian σ = 0.4220, r = 2, Odd‐Odd 1623.0 8.12 8 6 8 <0.0001 Yes 5

Gaussian σ = 0.3369, r = 2, Odd‐Odd 1740.0 8.70 9 8 9 <0.0001 Yes 6

Gaussian σ = 0.9326, r = 4, Odd‐Odd 1857.0 9.29 10 9 10 0.1642 6

Decimation, Odd‐Odd 1923.0 9.62 11 9 11 <0.0001 Yes 7

Gaussian σ = 1.0177, r = 4, Odd‐Odd 2194.0 10.97 12 11 12 0.0126 7

Spectral Truncation 2429.0 12.15 13 11 13 <0.0001 Yes 8

Gaussian σ = 1.1028, r = 4, Odd‐Odd 2568.0 12.84 14 13 14 0.5830 8

Averaging 2673.0 13.37 15 13 15 0.0781 8

Gaussian σ = 1.1879, r = 5, Even‐Even 2990.0 14.95 16 13 16 <0.0001 Yes 9

Gaussian σ = 1.2730, r = 5, Even‐Even 3355.0 16.78 17 16 17 <0.0001 Yes 10

Transcoded B 3489.0 17.45 18 17 18 0.0556 10

Transcoded A 3589.0 17.95 19 17 19 0.0636 10

Gaussian σ = 1.3581, r = 5, Even‐Even 3681.0 18.41 20 17 20 <0.0001 Yes 11

Gaussian σ = 1.4432, r = 5, Even‐Even 3961.0 19.81 21 20 21 <0.0001 Yes 12

Gaussian σ = 1.5283, r = 6, Even‐Even 4215.0 21.08 22 21 22 <0.0001 Yes 13

Gaussian σ = 1.6134, r = 6, Even‐Even 4460.0 22.30 23 22 23 <0.0001 Yes 14

Gaussian σ = 1.6985, r = 6, Even‐Even 4703.0 23.52 24 23 24 <0.0001 Yes 15

Gaussian σ = 1.7836, r = 6, Even‐Even 4938.0 24.69 25 24 25 <0.0001 Yes 16

Gaussian σ = 1.8687, r = 7, Even‐Even 5160.0 25.80 26 25 26 <0.0001 Yes 17

Gaussian σ = 1.9538, r = 7, Even‐Even 5384.0 26.92 27 26 27 <0.0001 Yes 18

Gaussian σ = 2.0389, r = 7, Even‐Even 5599.0 28.00 28 27 28 <0.0001 Yes 19

Gaussian σ = 2.1240, r = 7, Even‐Even 5800.0 29.00 29 28 29 <0.0001 Yes 20

n 200

Friedman's statistic 4659.04

DF 28

p <0.0001 (X2 approximation, corrected for ties)

   
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In stage three of analysis, the Rank 4 (worst) decimation candidates from each sub‐treatment were compared against each other as well as

the cases that received no sub‐treatment.   The data from this stage of analysis was sorted according to mean rank, from smallest (best) to

largest (worst) and an ordinal case number ranging from 1 to 29 was assigned to this sorted list (see Table 25).  Post‐hoc analysis was then

performed down this list, comparing Case 1 to Case 2 and so on.   As above, this comparison continued until a statistically significant difference

was observed.  The cases that did not demonstrate a statistically significant difference were clustered into one singular rank.   This process

continued until a list of clustered ranks was established, with each clustered rank representing data that is not significantly different from the

others (and hence are clustered as such).   Each clustered group was then provided an ordinal clustered rank value.

Table 25 ‐ Root Mean Square Difference Analysis, Stage Three (Conservative Decimation Pare‐Down, Adjusted α = 0.0018)

Treatment Rank sum Mean Rank Case No. P0 (Case No) P1 (Case No) Wilcoxon p P0 ≠ P1 Clustered Rank

Native 500 ppi 200.0 1.00 1 NA NA NA 1

Gaussian σ = 0.7624, r = 3, Even‐Odd 1086.0 5.43 2 1 2 <0.0001 Yes 2

Gaussian σ = 0.6773, r = 3, Even‐Even 1242.0 6.21 3 2 3 0.0011 Yes 3

Averaging 1287.0 6.44 4 3 4 <0.0001 Yes 4

Gaussian σ = 0.8475, r = 4, Even‐Odd 1317.0 6.59 5 4 5 0.1192 4

Spectral Truncation 1366.0 6.83 6 4 6 0.0781 4

Gaussian σ = 0.9326, r = 4, Even‐Odd 1622.0 8.11 7 4 7 0.5402 4

Gaussian σ = 0.5922, r = 3, Even‐Even 1679.0 8.40 8 4 8 <0.0001 Yes 5

Gaussian σ = 0.5642, r = 3, Even‐Even 1949.0 9.75 9 8 9 <0.0001 Yes 6

Gaussian σ = 1.0177, r = 4, Even‐Odd 1970.0 9.85 10 9 10 0.6998 6

Gaussian σ = 1.1028, r = 4, Even‐Odd 2359.0 11.80 11 9 11 0.0285 6

Transcoded B 2487.0 12.44 12 9 12 <0.0001 Yes 7

Gaussian σ = 0.5071, r = 3, Even‐Even 2572.0 12.86 13 12 13 0.0468 7

Transcoded A 2595.0 12.98 14 12 14 <0.0001 Yes 8

Gaussian σ = 1.1879, r = 5, Even‐Odd 2738.0 13.69 15 14 15 0.0128 8

Gaussian σ = 1.2730, r = 5, Even‐Odd 3095.0 15.48 16 14 16 <0.0001 Yes 9

Gaussian σ = 0.4220, r = 2, Even‐Even 3230.0 16.15 17 16 17 0.1748 9

Gaussian σ = 1.3581, r = 5, Even‐Odd 3415.0 17.08 18 16 18 <0.0001 Yes 10

Gaussian σ = 0.3369, r = 2, Even‐Even 3601.0 18.01 19 18 19 0.1113 10

Gaussian σ = 1.4432, r = 5, Even‐Odd 3725.0 18.63 20 18 20 <0.0001 Yes 11

Decimation, Even‐Even 3865.0 19.33 21 20 21 0.0011 Yes 12

Gaussian σ = 1.5283, r = 6, Even‐Odd 4007.0 20.04 22 21 22 <0.0001 Yes 13

Gaussian σ = 1.6134, r = 6, Even‐Odd 4291.0 21.46 23 22 23 <0.0001 Yes 14

Gaussian σ = 1.6985, r = 6, Even‐Odd 4588.0 22.94 24 23 24 <0.0001 Yes 15

Gaussian σ = 1.7836, r = 6, Even‐Odd 4857.0 24.29 25 24 25 <0.0001 Yes 16

Gaussian σ = 1.8687, r = 7, Even‐Odd 5121.0 25.61 26 25 26 <0.0001 Yes 17

Gaussian σ = 1.9538, r = 7, Even‐Odd 5357.0 26.79 27 26 27 <0.0001 Yes 18

Gaussian σ = 2.0389, r = 7, Even‐Odd 5584.0 27.92 28 27 28 <0.0001 Yes 19

Gaussian σ = 2.1240, r = 7, Even‐Odd 5795.0 28.98 29 28 29 <0.0001 Yes 20

n 200

Friedman's statistic 4482.30

DF 28

p <0.0001 (X2 approximation, corrected for ties)

   
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5.4.2. Investigative Result 4

Using data obtained by frequency spectrum correlation analysis, Friedman’s test identifies the native 500 ppi control (Case No.1) as the best at

Rank 1 among the cases based on an optimistic decimation strategy (stage 2 analysis).  Following the Control Case were six Gaussian cases of

(Gaussian σ = 0.8475, r = 4, Odd‐Odd), (Gaussian σ = 0.7624, r = 3, Odd‐Odd), (Gaussian σ = 0.5642, r = 3, Odd‐Odd), (Gaussian σ = 0.5922, r = 3,

Odd‐Odd), (Gaussian σ = 0.6773, r = 3, Odd‐Odd) and (Gaussian σ = 0.5071, r = 3, Odd‐Odd).  Post‐hoc analysis indicated the Rank 1 control (Case

No.1) is different from Case No.2, but the difference between Case No.2 through Case No.7 was not statistically significant and are clustered as

Rank 2.  For cases based on a conservative decimation strategy (stage 3 analysis), Friedman’s test identifies the native 500 ppi control (Case

No.1) as the best at Rank 1. Following the control cases were 3 Gaussian cases of (Gaussian σ = 0.7624 r = 3, Even‐Even), (Gaussian σ = 0.8475 r

= 4, Even‐Even) and (Gaussian σ = 0.9326 r = 4, Even‐Even).  Post‐hoc analysis indicated the Rank 1 control (Case No.1) is statistically different

from Case No.2, but the difference between Case No.2 through Case No.4 was not statistically significant and they are therefore clustered as

Rank 2.

Using data obtained by RMSD analysis, Friedman’s test again identifies the Native 500 ppi Control (Case No.1) as the best at Rank 1 among the

cases based on an optimistic decimation strategy (stage 2 analysis).  Following the control cases were the two Gaussian cases of (Gaussian σ =

0.5922, r = 3, Odd‐Odd) and (Gaussian σ = 0.6773, r = 3, Odd‐Odd).  Post‐hoc analysis indicated the Rank 1 control (Case No.1) is different from

Case No.2, but the difference between Case No.2 and Case No.3 was not statistically significant and are clustered as Rank 2.  For cases based

on a conservative decimation strategy (stage 3 analysis), Friedman’s test identifies the native 500 ppi control (Case No.1) as the best at rank‐1.

Following the control is the Gaussian case of (Gaussian σ = 0.7624, r = 3, Even‐Odd).  Post‐hoc analysis indicated the Rank 1 control (Case No.1)

is statistically different from Case No.2, and Case No.2 is statistically different from Case No.3.

   
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5.5. Investigate Goal 5:  Optimal Strategy Determination

Several approaches were explored with the goal of optimizing a process given multiple success measures across multiple treatments.  Many of

these approaches were geared towards a winner‐take‐all strategy or were not suitable in cases where different treatments and success

measures yielded similar behaviors that may not consistently stratify operational behavior and result in ambiguous results.   In this section we

explore two such methods and present those findings.

5.5.1. Clustered Rank Summation Analysis

In the process of analyzing the data, the results of all experimental treatments were first stratified using a clustered rank summation strategy

(See 5.1 ‐ 5.4).  Next, the clustered ranks for each metric across all treatments were summed, and the optimal strategy is represented by the

minima of the sum of all clustered rank for each treatment.

Table 26 shows the clustered rank summation analysis of the optimistic decimation cases yielding an optimistic gauge of performance, while

Table 27 shows the clustered rank summation analysis of the conservative decimation cases yielding a conservative gauge of performance.  In

both approaches, the Native 500 ppi Control Case emerges as the best all‐around using all performance measures and metrics.

The treatment cases that expert examiners gauged as best are marked by a dashed border.

Table 26 ‐ Clustered Rank Summation Using Optimistic Decimation Strategy

Treatment

Expert

Examiner

Automated

Matching

Frequency Spectrum

Correlation

Root Mean Square

Difference

Sum of Clustered

Ranks (lower is better)

Native 500 ppi 2 1 1 1 5 BEST (Control)

Gaussian σ = 0.6773, r = 3 1 4 2 2 9

Gaussian σ = 0.7624, r = 3 1 4 2 3 10

Gaussian σ = 0.5922, r = 3 1 5 2 2 10

Gaussian σ = 0.8475, r = 4 1 3 2 4 10

Gaussian σ = 0.5642, r = 3 1 6 2 3 12

Gaussian σ = 0.9326, r = 4 1 3 3 6 13

Gaussian σ = 0.5071, r = 3 1 7 2 4 14

Gaussian σ = 1.0177, r = 4 1 3 4 7 15

Gaussian σ = 0.4220, r = 2 1 7 3 5 16

Gaussian σ = 1.1028, r = 4 2 2 5 8 17

Gaussian σ = 0.3369, r = 2 1 7 3 6 17

Gaussian σ = 1.1879, r = 5 3 2 6 9 20

Gaussian σ = 1.2730, r = 5 3 2 7 10 22

Decimation 3 8 4 7 22

Gaussian σ = 1.3581, r = 5 4 2 8 11 25

Gaussian σ = 1.4432, r = 5 4 2 9 12 27

Averaging 4 7 8 8 27

Spectral Truncation 2 9 9 8 28

Gaussian σ = 1.5283, r = 6 4 3 10 13 30

Gaussian σ = 1.6134, r = 6 4 4 11 14 33

Transcoded B 3 8 13 10 34

Transcoded A 4 8 14 10 36

Gaussian σ = 1.6985, r = 6 4 5 12 15 36

Gaussian σ = 1.7836, r = 6 5 8 14 16 43

Gaussian σ = 1.8687, r = 7 5 7 14 17 43

Gaussian σ = 1.9538, r = 7 5 9 14 18 46

Gaussian σ = 2.0389, r = 7 5 10 15 19 49

Gaussian σ = 2.1240, r = 7 6 11 16 20 53

   
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Table 27 ‐ Clustered Rank Summation Using Conservative Decimation Strategy

Treatment

Expert

Examiner

Automated

Matching

Frequency Spectrum

Correlation

Root Mean Square

Difference

Sum of Clustered Ranks

(lower is better)

Native 500 ppi 1 1 1 1 4 BEST (Control)

Gaussian σ = 0.9326, r = 4 1 3 2 4 10

Gaussian σ = 0.7624, r = 3 2 4 2 2 10

Gaussian σ = 0.8475, r = 4 1 4 2 4 11

Gaussian σ = 0.6773, r = 3 1 4 3 3 11

Gaussian σ = 1.0177, r = 4 1 2 3 6 12

Gaussian σ = 1.1028, r = 4 2 2 3 6 13

Gaussian σ = 1.1879, r = 5 2 2 3 8 15

Spectral Truncation 1 6 4 4 15

Averaging 3 5 3 4 15

Gaussian σ = 0.5922, r = 3 2 6 4 5 17

Gaussian σ = 1.2730, r = 5 4 2 3 9 18

Gaussian σ = 0.5642, r = 3 2 6 5 6 19

Gaussian σ = 1.3581, r = 5 4 2 4 10 20

Gaussian σ = 0.5071, r = 3 3 5 6 7 21

Transcoded B 2 6 7 7 22

Gaussian σ = 1.4432, r = 5 5 3 5 11 24

Transcoded A 4 6 8 8 26

Gaussian σ = 1.5283, r = 6 5 4 5 13 27

Gaussian σ = 0.4220, r = 2 3 7 9 9 28

Gaussian σ = 1.6134, r = 6 6 5 6 14 31

Gaussian σ = 0.3369, r = 2 4 8 10 10 32

Gaussian σ = 1.6985, r = 6 6 6 8 15 35

Decimation 6 8 11 12 37

Gaussian σ = 1.7836, r = 6 7 6 8 16 37

Gaussian σ = 1.8687, r = 7 7 7 9 17 40

Gaussian σ = 1.9538, r = 7 8 9 10 18 45

Gaussian σ = 2.0389, r = 7 8 10 11 19 48

Gaussian σ = 2.1240, r = 7 8 11 11 20 50

   
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5.5.2. Ordinal Rank Summation Analysis

A more conservative approach in selecting an optimal strategy is to add the ordinal rankings of each treatment together.   Next the ordinal

rankings for all treatments were summed, and the optimal strategy is represented by the minima of the sum of all ranks for each treatment.  

Since this method utilizes integer ranks, summation of results for each treatment may yield a higher probability of ties.

Table 28 shows the mean rank summation analysis of the optimistic decimation cases yielding an optimistic gauge of performance, while Table

29 shows the mean rank summation analysis of the conservative decimation cases yielding a conservative gauge of performance.   

The case ranked best by expert examiners is emphasized by a dashed rectangle in the table.  This case is traditionally considered operational

ground truth.

Table 28 ‐ Ordinal Rank Summation Using Optimistic Decimation Strategy

Treatment Expert Examiner

Automated

Matching

Frequency Spectrum

Correlation

Root Mean Square

Difference

Sum of Mean Ranks

(lower is better)

Native 500 ppi 11 1 1 1 14 BEST (Control)

Gaussian σ = 0.8475, r = 4 3 10 2 7 22

Gaussian σ = 0.5922, r = 3 1 15 5 2 23

Gaussian σ = 0.7624, r = 3 5 12 3 5 25

Gaussian σ = 0.6773, r = 3 4 13 6 3 26

Gaussian σ = 0.5642, r = 3 8 16 4 4 32

Gaussian σ = 0.9326, r = 4 6 9 8 10 33

Gaussian σ = 0.5071, r = 3 2 18 7 6 33

Gaussian σ = 1.0177, r = 4 7 8 11 12 38

Gaussian σ = 0.4220, r = 2 10 17 9 8 44

Gaussian σ = 1.1028, r = 4 12 6 13 14 45

Gaussian σ = 0.3369, r = 2 9 19 10 9 47

Gaussian σ = 1.1879, r = 5 14 4 14 16 48

Gaussian σ = 1.2730, r = 5 16 2 15 17 50

Gaussian σ = 1.3581, r = 5 18 3 16 20 57

Decimation 15 22 12 11 60

Gaussian σ = 1.4432, r = 5 19 5 18 21 63

Gaussian σ = 1.5283, r = 6 21 7 20 22 70

Spectral Truncation 13 26 19 13 71

Averaging 20 20 17 15 72

Gaussian σ = 1.6134, r = 6 22 11 21 23 77

Transcoded B 17 24 23 18 82

Gaussian σ = 1.6985, r = 6 24 14 22 24 84

Transcoded A 23 25 24 19 91

Gaussian σ = 1.7836, r = 6 25 23 25 25 98

Gaussian σ = 1.8687, r = 7 26 21 26 26 99

Gaussian σ = 1.9538, r = 7 27 27 27 27 108

Gaussian σ = 2.0389, r = 7 28 28 28 28 112

Gaussian σ = 2.1240, r = 7 29 29 29 29 116

   
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Table 29 ‐ Ordinal Rank Summation Using Conservative Decimation Strategy

Treatment

Expert

Examiner

Automated

Matching

Frequency Spectrum

Correlation

Root Mean Square

Difference

Sum of Mean Ranks

(lower is better)

Native 500 ppi 2 1 1 1 5 BEST (Control)

Gaussian σ = 0.9326, r = 4 3 7 4 7 21

Gaussian σ = 0.8475, r = 4 5 9 3 5 22

Gaussian σ = 0.7624, r = 3 7 11 2 2 22

Gaussian σ = 0.6773, r = 3 6 12 5 3 26

Gaussian σ = 1.0177, r = 4 4 6 8 10 28

Gaussian σ = 1.1028, r = 4 9 3 9 11 32

Gaussian σ = 1.1879, r = 5 12 2 6 15 35

Spectral Truncation 1 21 13 6 41

Averaging 15 15 7 4 41

Gaussian σ = 0.5922, r = 3 10 16 11 8 45

Gaussian σ = 1.2730, r = 5 16 4 10 16 46

Gaussian σ = 0.5642, r = 3 11 18 14 9 52

Gaussian σ = 1.3581, r = 5 18 5 12 18 53

Gaussian σ = 0.5071, r = 3 13 14 17 13 57

Transcoded B 8 20 19 12 59

Gaussian σ = 1.4432, r = 5 20 8 15 20 63

Gaussian σ = 1.5283, r = 6 21 10 16 22 69

Transcoded A 19 19 20 14 72

Gaussian σ = 1.6134, r = 6 22 13 18 23 76

Gaussian σ = 0.4220, r = 2 14 23 23 17 77

Gaussian σ = 1.6985, r = 6 24 17 21 24 86

Gaussian σ = 0.3369, r = 2 17 25 25 19 86

Gaussian σ = 1.7836, r = 6 25 22 22 25 94

Decimation 23 26 27 21 97

Gaussian σ = 1.8687, r = 7 26 24 24 26 100

Gaussian σ = 1.9538, r = 7 27 27 26 27 107

Gaussian σ = 2.0389, r = 7 28 28 28 28 112

Gaussian σ = 2.1240, r = 7 29 29 29 29 116
NISTIR 7839 ‐ Examination of Downsampling Strategies for Converting 1000 ppi Fingerprint Imagery to 500 ppi

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5.5.3. Mean Rank Summation Analysis

An even more conservative and sensitive approach in selecting an optimal strategy is to simply add the mean rankings of each treatment

together.   Next the mean ranking for all treatment measures were summed, and the optimal strategy is represented by the minima of the sum

of all ranks for each treatment.   Since this method utilizes mean ranks, summation of results for each treatment has a lesser chance of yielding

ties and can more easily stratify treatments.

Table 30 shows the mean rank summation analysis of the optimistic decimation cases yielding an optimistic gauge of performance, while Table

31 shows the mean rank summation analysis of the conservative decimation cases yielding a conservative gauge of performance.   

The case ranked best by expert examiners is emphasized by a dashed rectangle in the table.  This case is traditionally considered operational

ground truth.

Table 30 ‐ Mean Rank Summation Using Optimistic Decimation Strategy

Treatment

Expert

Examiner

Automated

Matching

Frequency Spectrum

Correlation

Root Mean Square

Difference

Sum of Mean Ranks

(lower is better)

Native 500 ppi 11.07 1.00 1.00 1.00 14.07 BEST (Control)

Gaussian σ = 0.8475, r = 4 9.16 13.20 8.25 7.88 38.49

Gaussian σ = 0.6773, r = 3 9.27 14.62 8.35 6.61 38.85

Gaussian σ = 0.7624, r = 3 9.81 13.98 8.32 7.06 39.17

Gaussian σ = 0.5922, r = 3 8.63 15.64 8.35 6.59 39.21

Gaussian σ = 0.9326, r = 4 9.85 12.93 8.84 9.29 40.90

Gaussian σ = 0.5642, r = 3 9.93 15.88 8.33 6.85 40.98

Gaussian σ = 0.5071, r = 3 9.10 16.74 8.79 7.37 41.99

Gaussian σ = 1.0177, r = 4 9.88 12.67 9.74 10.97 43.26

Gaussian σ = 0.4220, r = 2 10.32 16.52 9.14 8.12 44.09

Gaussian σ = 0.3369, r = 2 10.05 16.78 9.65 8.70 45.18

Gaussian σ = 1.1028, r = 4 11.47 12.23 10.74 12.84 47.29

Decimation 14.61 17.28 10.67 9.62 52.18

Gaussian σ = 1.1879, r = 5 13.66 12.09 12.10 14.95 52.79

Gaussian σ = 1.2730, r = 5 15.16 11.65 13.65 16.78 57.24

Spectral Truncation 11.53 18.54 17.72 12.15 59.92

Gaussian σ = 1.3581, r = 5 16.95 11.69 15.10 18.41 62.14

Averaging 18.14 16.94 16.20 13.37 64.64

Gaussian σ = 1.4432, r = 5 17.90 12.14 16.61 19.81 66.45

Gaussian σ = 1.5283, r = 6 18.28 12.62 18.24 21.08 70.20

Transcoded B 15.19 17.94 22.50 17.45 73.07

Gaussian σ = 1.6134, r = 6 19.79 13.94 19.93 22.30 75.95

Transcoded A 20.23 17.95 22.82 17.95 78.94

Gaussian σ = 1.6985, r = 6 20.61 14.83 21.58 23.52 80.54

Gaussian σ = 1.7836, r = 6 22.02 17.63 23.09 24.69 87.43

Gaussian σ = 1.8687, r = 7 22.13 17.08 24.44 25.80 89.45

Gaussian σ = 1.9538, r = 7 22.79 18.59 25.72 26.92 94.02

Gaussian σ = 2.0389, r = 7 23.56 20.19 26.99 28.00 98.73

Gaussian σ = 2.1240, r = 7 23.94 21.70 28.20 29.00 102.84

   
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Table 31 ‐ Mean Rank Summation Using Conservative Decimation Strategy

Treatment Expert Examiner Automated Matching

Frequency Spectrum

Correlation

Root Mean Square

Difference

Sum of Mean Ranks

(lower is better)

Native 500 ppi 7.66 1.00 1.00 1.00 10.66 BEST (Control)

Gaussian σ = 0.7624, r = 3 10.26 13.60 7.52 5.43 36.81

Gaussian σ = 0.8475, r = 4 9.66 13.32 7.90 6.59 37.46

Gaussian σ = 0.9326, r = 4 9.24 12.63 8.40 8.11 38.38

Gaussian σ = 0.6773, r = 3 9.97 13.94 8.77 6.21 38.89

Gaussian σ = 1.0177, r = 4 9.29 12.31 9.06 9.85 40.51

Spectral Truncation 7.57 16.78 12.62 6.83 43.79

Gaussian σ = 1.1028, r = 4 10.43 11.98 10.04 11.80 44.24

Averaging 14.16 15.08 8.97 6.44 44.64

Gaussian σ = 1.1879, r = 5 11.73 11.82 8.93 13.69 46.17

Gaussian σ = 0.5922, r = 3 10.91 15.44 11.54 8.40 46.28

Gaussian σ = 0.5642, r = 3 11.52 15.80 13.15 9.75 50.21

Gaussian σ = 1.2730, r = 5 15.08 12.08 10.42 15.48 53.05

Gaussian σ = 0.5071, r = 3 13.07 14.99 15.92 12.86 56.83

Transcoded B 10.30 16.17 18.09 12.44 56.99

Gaussian σ = 1.3581, r = 5 16.22 12.16 11.96 17.08 57.41

Gaussian σ = 1.4432, r = 5 17.62 12.77 13.61 18.63 62.62

Transcoded A 16.87 16.02 18.39 12.98 64.25

Gaussian σ = 1.5283, r = 6 18.78 13.51 15.30 20.04 67.62

Gaussian σ = 0.4220, r = 2 13.93 17.56 21.10 16.15 68.74

Gaussian σ = 1.6134, r = 6 19.67 14.46 17.06 21.46 72.64

Gaussian σ = 0.3369, r = 2 15.70 18.69 23.50 18.01 75.89

Gaussian σ = 1.6985, r = 6 21.08 15.55 18.80 22.94 78.37

Decimation 19.81 19.14 24.95 19.33 83.22

Gaussian σ = 1.7836, r = 6 21.65 16.85 20.48 24.29 83.26

Gaussian σ = 1.8687, r = 7 22.80 18.09 22.03 25.61 88.52

Gaussian σ = 1.9538, r = 7 22.97 19.65 23.67 26.79 93.07

Gaussian σ = 2.0389, r = 7 23.31 21.07 25.19 27.92 97.48

Gaussian σ = 2.1240, r = 7 23.80 22.53 26.70 28.98 102.01
NISTIR 7839 ‐ Examination of Downsampling Strategies for Converting 1000 ppi Fingerprint Imagery to 500 ppi

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5.5.4. Mean Rank Summation Analysis for Expert Examiner Winner‐Take‐All

Since examiner opinion is widely recognized as the ground truth in fingerprint examination processing pathways, Table 32 below shows expert

examiner mean rank analysis as a product of the mean rank for both the optimistic and conservative decimation strategies.  The Native 500 ppi

Control Case emerged as the best, while Gaussian (Gaussian σ = 0.8475, r = 4) emerged as the next best, followed by (Gaussian σ = 0.9326, r =

4) and Spectral Truncation.

Table 32 ‐ Expert Examiner Winner‐Take‐All Mean Rank Analysis

Treatment Optimistic Decimation Mean Rank Conservative Decimation Mean Rank Mean Rank Summation

Native 500 ppi 11.07 7.66 18.72

Gaussian σ = 0.8475, r = 4 9.16 9.66 18.82

Gaussian σ = 0.9326, r = 4 9.85 9.24 19.08

Spectral Truncation 11.53 7.57 19.09

Gaussian σ = 1.0177, r = 4 9.88 9.29 19.17

Gaussian σ = 0.6773, r = 3 9.27 9.97 19.24

Gaussian σ = 0.5922, r = 3 8.63 10.91 19.54

Gaussian σ = 0.7624, r = 3 9.81 10.26 20.07

Gaussian σ = 0.5642, r = 3 9.93 11.52 21.45

Gaussian σ = 1.1028, r = 4 11.47 10.43 21.90

Gaussian σ = 0.5071, r = 3 9.10 13.07 22.17

Gaussian σ = 0.4220, r = 2 10.32 13.93 24.24

Gaussian σ = 1.1879, r = 5 13.66 11.73 25.39

Transcoded B 15.19 10.30 25.49

Gaussian σ = 0.3369, r = 2 10.05 15.70 25.75

Gaussian σ = 1.2730, r = 5 15.16 15.08 30.24

Averaging 18.14 14.16 32.30

Gaussian σ = 1.3581, r = 5 16.95 16.22 33.16

Decimation 14.61 19.81 34.43

Gaussian σ = 1.4432, r = 5 17.90 17.62 35.52

Gaussian σ = 1.5283, r = 6 18.28 18.78 37.05

Transcoded A 20.23 16.87 37.10

Gaussian σ = 1.6134, r = 6 19.79 19.67 39.45

Gaussian σ = 1.6985, r = 6 20.61 21.08 41.69

Gaussian σ = 1.7836, r = 6 22.02 21.65 43.67

Gaussian σ = 1.8687, r = 7 22.13 22.80 44.93

Gaussian σ = 1.9538, r = 7 22.79 22.97 45.76

Gaussian σ = 2.0389, r = 7 23.56 23.31 46.87

Gaussian σ = 2.1240, r = 7 23.94 23.80 47.74

5.6. Uncertainty Measurement

We compare the various downsampling methods via the ordered mean rank scores output from the Friedman’s tests applied to the

measurements as there is no conventional statistic by which to assess the uncertainty or standard error of the mean rank scores. However, we

are able to provide an estimate of uncertainty using a bootstrap procedure [WU1], [WU2], [WU3]. We first generate a set of mean rank scores

by applying the Friedman test to each set of measurements. For the methods requiring decimation, the best decimation case was selected

(sub‐treatment pare‐down, as described in 4.2) prior to conducting the Friedman test. We sort these mean rank scores in either ascending or

descending order depending upon the nature of the particular metric, i.e., whether lowest or highest score is “best”. We sort columns of the

data matrix in the same order and resample randomly with replacement to generate 500 replicates of the data. We apply the Friedman’s test

to each of the data replicates to generate 2000 sets (vectors) of the measure of interest (such as sample mean or median) and assemble these

into a matrix. Each column of the matrix represents a distribution of that measure for each of the k downsampling methods. The 95 %

confidence intervals for the measures are then taken as the 0.025th and 0.975th quantiles of the distribution of mean ranks.  This bootstrap

procedure was applied to sample mean and sample median and to the Friedman’s mean rank for each of the metrics examined in this study

(see Table 4).

5.6.1. Expert Examiner Subjective Assessment Uncertainty

Figure 14 shows 95 % Confidence Intervals for Expert Examiner Subjective assessments based on 2000 replicates of Friedman’s Mean Rank

analysis.  While this bootstrap analysis can be performed on the Friedman’s mean rank, it cannot easily be performed on the sample mean and

sample median.  The reason for this is that while the scores for the expert examiner analysis portion of this study take on numeric form (111,

222, etc.), these scores are actually classifiers of the observations from the examiners, do not form a continuous scale and therefore

examination of the means or medians of these classifiers has no meaning and cannot be used to formulate a conclusions.  The classifiers on
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the other hand can be ordered and lend themselves well to ranking tests and analysis such as Friedman’s.    To mitigate this shortfall, the

classifier decisions were assigned a relative score.  The relative score provides a fractional scale that ranges from 0 (best) to 1 (worst) and

uniformly distributed to the all possible classification decisions as shown below in Table 33.  Bootstrap analysis was then performed on sample

mean and sample median of these values and the results are shown in Figure 14.

Table 33 ‐ Classifier Score Assignments

Case Number Decision Classifier Assigned Score

1      111 (best) 0.0000

2      112 0.0526

3      113 0.1053

4      122 0.1579

5      114 0.2105

6      123 0.2632

7      222 0.3158

8      124 0.3684

9      133 0.4211

10      223 0.4737

11      134 0.5263

12      224 0.5789

13      233 0.6316

14      144 0.6842

15      234 0.7368

16      333 0.7895

17      244 0.8421

18      334 0.8947

19      344 0.9474

20      444 (worst) 1.0000

Mean Rank (Range 1‐29, Lower is Better) Sample Mean (Range 0 to 1, Lower is Better) Sample Median (Range 0 to 1, Lower is Better)

Figure 14 ‐ Expert Examiner Subjective Assessment 95 % Confidence Intervals for Mean Rank, Mean and Median using Bootstrap Analysis
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5.6.2. Automated Matching Assessment Uncertainty

Figure 15 below shows 95 % Confidence Intervals for Automated Matching assessment based on 2000 replicates of mean rank, sample mean

and sample median.   Due to the operational nature of the research matcher used, native 500 ppi control images yielded very high match

scores outside of the range of the other treatments.   To improve readability of the charts, sample mean and sample median data for the

Native 500 ppi Case have been omitted from the graphs.  The 95 % confidence intervals for the sample mean were (Lower=714.5, Mean=721.1,

Upper=727.9) and for the sample median CIs were (Lower=704, Median=712, Upper=721).

Mean Rank (Range 1‐29, Higher is Better) Sample Mean (Range 0 to 65535, Higher is Better) Sample Median (Range 0 to 65535, Higher is Better)

Figure 15 ‐ Automated Matching Assessment 95 % Confidence Intervals for Mean Rank, Mean and Median using Bootstrap Analysis

   
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5.6.3. Signal Analysis and Assessment

Figure 16 and Figure 17 below shows 95 % Confidence Intervals for Frequency Spectrum Correlation and Root Mean Square Difference

assessments based on 2000 replicates of mean rank, sample mean and sample median for each of these metrics.

Mean Rank (Range 1‐29, Higher is Better) Sample Mean (Range 0 to 1, Higher is Better) Sample Median (Range 0 to 1, Higher is Better)

Figure 16 ‐ Frequency Spectrum Correlation Analysis 95 % Confidence Intervals for Mean Rank, Mean and Median using Bootstrap Analysis
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Mean Rank (Range 1‐29) Sample Mean (Range 0 to ) Sample Median (Range 0 to )

Figure 17 ‐ Root Mean Square Difference Analysis 95 % Confidence Intervals for Mean Rank, Mean and Median using Bootstrap Analysis

   
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5.6.4. Normalized Score Comparative Analysis

In another approach for the analysis of results, a method of score normalization was utilized.    In this method, the scores from all metrics were

normalized to fit into a scale of 0 (worst/lowest) to 1 (best/highest) and the resulting values were plotted against each other as show in.  This

analysis shows that RMSD is perhaps the most sensitive measure and exhibits the most fluctuation relative to the various treatment processes

as it reacts to subtle changes to the image.    Correlation analysis (frequency based) appears to exhibit the least amount of fluctuation.  

Examiner subjective analysis appears to have an optimal peak in the Gaussian range of (0.3369) and (1.1028).

Figure 18 ‐ Normalized Score Comparative Analysis

5.7. Other Considerations

In addition to the metrics explored in this study, there are other considerations that are significant when selecting a method.  For example,

each treatment may pose a significantly different impact from an operational perspective on certain aspects of the processing pathway

through differences in processing needs and memory utilization as compared to other treatments and some treatments may have particular

advantages over others in a given scenario.   A comprehensive investigation of these operational ramifications was not conducted in the scope

of this study but this section describes some of the notable differences.

The process of downsampling in the scope of this study involves three basic steps:

1. Decoding of compressed image data from a JPEG‐2000‐encoded file

2. Processing the image data in order to reduce the geometric dimensions (width and height) of the image by half

3. Encoding the resulting processed image data into a WSQ file

All of the treatments explored in this study follow those basic steps, though there is much variation among the processing of the image data in

step 2 above. Some treatments even include two separate processing steps, such as the Gaussian treatments which involve the application of

a processing filter followed by the decimation of the processed result in order to reduce the dimensions of the image.  

Table 34 summarizes the fundamental differences between the treatments in terms of the above operational steps.  As shown, Transcoded A

and B require the fewest operational steps since only limited decompression of the 1000 ppi image is required, as well as no intermediate file

saving of the decompressed image data, which may give it an advantage in terms of memory utilization as well as computational cycles

(processing time).  Gaussian on the other end of the scale requires the most operational steps, with an additional step required for decimation

after filtering, but generally produces images that earned higher subjective ratings by expert examiners.   It should also be noted that the

Gaussian filter incurs a growing penalty as the kernel size increases.  In the scope of this study the lower end of the Gaussian kernel was bound

between (r=3) and (r=7), depending on the treatment.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

RMSD Correlation Automated Matcher Examiner (Subjective)
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Empirical testing of the various treatments (Figure 19 and Figure 20) confirms these results and shows that the Transcoded methods provide

far superior throughput performance than all other methods examined in this study.

Table 34 ‐ Generalized Comparison of Resource Requirements by Treatment

Treatment Class Decompression

Decompressed

File Save Processing Filter Post‐Filter Decimation Encoding to WSQ

Averaging Full Required Required Required Unnecessary Required

Decimation Full Required Required Unnecessary Unnecessary Required

Spectral Truncation Full Required Required Required Unnecessary Required

Transcoded A Partial Only Required Unnecessary Unnecessary Required

Transcoded B Partial Only Unnecessary Unnecessary Unnecessary Required

Gaussian Full Required Required Required Required Required

Figure 19 ‐ Average Processing Time(s) by Treatment Class

Figure 20 ‐ Median Processing Time(s) by Treatment Class

0.0

0.2

0.4

0.6

0.8

1.0

Transcode A Transcode B Gaussian Spectral

Truncation

Decimation

Only

Averaging

Average Processing Time(s) by Treatment Class

AVERAGE ENCODE TIME

AVERAGE DECODE TIME

0.0

0.2

0.4

0.6

0.8

1.0

Transcode A Transcode B Gaussian Spectral

Truncation

Decimation

Only

Averaging

Median Processing Time(s) by Treatment Class

MEDIAN ENCODE TIME

MEDIAN DECODE TIME
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6. Conclusions

Several different analysis methodologies/algorithms were used to identify an optimal strategy.    These methods included various different

fidelity measures (such as expert examiners or machine matcher score assessment) for each treatment as well as several different methods of

fusing the results of these measures such as clustering ranks.  As shown in Table 35, all the methods used to fuse the experimental measures

indicated that the native 500 ppi control case yielded the best results versus a 1000 ppi image that has been downsampled to 500ppi.    The

next best method identified by each fusion methodology was one of the Gaussian treatments.    The results from Table 35 also reinforce

anecdotal evidence that it is best to capture at the resolution one intends to operate in rather than post‐process the image further where the

native 500 ppi control case bested images generated by downsampling treatments.

Table 35 ‐ Summary of Findings

Measure Fusion Method Best Treatment Case (Optimal) Second Best Treatment Case

Clustered Rank Summation (Optimistic Decimation) Native 500 ppi Control Case Gaussian σ = 0.6773, r = 3

Clustered Rank Summation (Conservative Decimation) Native 500 ppi Control Case Gaussian σ = 0.9326, r = 4

Ordinal Rank Summation (Optimistic Decimation) Native 500 ppi Control Case Gaussian σ = 0.8475, r = 4

Ordinal Rank Summation (Conservative Decimation) Native 500 ppi Control Case Gaussian σ = 0.9326, r = 4

Mean Rank Summation (Optimistic Decimation) Native 500 ppi Control Case Gaussian σ = 0.8475, r = 4

Mean Rank Summation(Conservative Decimation) Native 500 ppi Control Case Gaussian σ = 0.7624, r = 3

Expert Examiner Winner‐Take‐All Native 500 ppi Control Case Gaussian σ = 0.8475, r = 4

Based on the findings in this study, the Gaussian treatment (σ = 0.8475, r = 4) is identified as an optimal all‐around downsampling strategy for

the measure fusion methods of Ordinal Rank Summation‐Optimistic, Mean Rank Summation‐Optimistic and Expert Examiner Winner‐Take‐All

(which further fuses optimistic and conservative decimation strategies).   Where Gaussian treatment (σ = 0.8475, r = 4) is not identified as

optimal following the control case, it is identified as third best (or tied as such) counting the control case as the best method and is not a

radical compromise in terms of the fidelity measures that didn’t identify it as the top candidate.

Looking deeper into the various individual measures did uncover some surprises.   In the case of expert examiner quality assessment, the

downsampled images yielded better subjective quality than the native 500 ppi control case which indicates that some signal noise reduction

may ultimately impact the perception of image quality by expert examiners.

With respect to objective examiner assessments of the images where the examiner was asked to make an identification decision between a

downsampled image and the native 500 ppi version of that image, a statistically significant difference could not be established.  This reinforces

findings from NISTIR‐7778 [NISTIR7778] where the examiners could nearly universally detect degradation in the various aspects of the

fingerprint ridge structure as a result of lossy compression, but this effect did not appear to measurably impact their ability to conduct their

identification tasks.    This is analogous to operating a motor vehicle with a “dirty windshield”, where the driver’s ability and experience

mitigates any effect from occlusions large or small in their field of view.

An examination of automated matching shows that the Control Case outperformed all other treatments, followed by several Gaussian

treatments including (σ = 1.2730, r = 5, Odd‐Even) for the optimistic decimation strategies and (σ = 1.1879, r = 5, Even‐Odd) for the conservative

decimation strategy.   Based on the results of this study however, it appears that a strategy that optimized performance of the research

matcher used for this study (via very large Gaussian filters) yielded degradation from subjective assessment of the image by expert examiners.  

While the images favored by the matcher were not the worst in terms of expert examiner assessments, they did rank far lower by examiners.  

While it is possible to apply further filtering to an image, it is not possible undo signal loss as a result of Gaussian filtering therefore a potential

strategy to favor both the expert examiners as well as the matcher may involve applying one pass of Gaussian filtering in the downsampling

process, and a second pass just prior to identifying feature vectors on the fingerprint images.

Examination of system throughput however points to Transcoded A and Transcoded B as the optimal solution in terms of operational

efficiency and lower resource demands by eliminating several processing steps in the downsampling pathway.  The elimination of processing

steps by operating on the wavelet data directly helped avoid some of the intermediate steps needed for traditional downsampling and avoid

the associated throughput penalty for these intermediate steps.  Cursory studies show that these methods may be up to 10 times faster than

the more computationally intensive Gaussian methods.

Finally, with regard to Gaussian filter sizes, it was shown that the automated matching favors Gaussian cases with larger sigma & radius values

while other fidelity measures favor smaller sigma & radius value indicating that cases that are optimized for automated matching specifically

may not be optimal for other fidelity measures including expert human perception.
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7. Discussions and Future Work

This study showed that a certain amount of noise reduction in the image may have a positive effect both on the subjective analysis of the

image, as well as automated machine matcher efficacy.    Further research is needed to see if the introduction of controlled/targeted high

frequency noise filtering yields a positive net benefit in the processing and operational pathway of friction ridge imagery, especially in terms of

impact on expert examiner identification error rates.

Another finding from the phase‐one decimation portion of analysis used in several segments of this study showed that the scanning process

may be more deterministic than previously thought.  Specifically, certain post‐processing or conditional operations may not exhibit random

behavior as previously thought (given expected outcome probabilities for the number of cases). Does the scanner introduce a bias into the

sampling of fingerprints that favors one decimation method over the others?  Is the effect limited to the scanner used in the present study or

do other scanners exhibit similar effects? In addition, preliminary experiments do indicate limits of scanner repeatability that have not been

quantified and may pose certification issues, particularly among aging devices. Accordingly, further study of factors impacting the scanning

process is planned.

   
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References

Publications and Reports

BERGEN Bergen, J. R., Anandan, P., Hanna, K. J., and Hingorani, R. (1992) “Heirarchical model‐based motion estimation” in

Proceedings of Second European Conference on Computer Vision, Springer‐Verlag, p. 237‐252.

CHAMBERS Chambers, John; William Cleveland, Beat Kleiner, and Paul Tukey (1983). Graphical Methods for Data Analysis.

Wadsworth

CIA “The World Factbook”, https://www.cia.gov/library/publications/the‐world‐factbook/geos/us.html, Retrieved

2010‐12‐06.

CONOVER “Practical Nonparametric Statistics”, Third Edition, Wiley, 1999, pp. 367‐373.

CURRAN‐EVERETT Curran‐Everett, Douglas (2000). “Multiple comparisons: philosophies and illustrations”, American Journal of

Physiology ‐ Regulatory, Integrative and Comparative Physiology, 279, R1 ‐ R8.

DOJ "The Science of Fingerprints" [rev. December 1984], United States Department of Justice, Federal Bureau of

Investigation, USGPO, ISBN 0‐16‐050541‐0, Page 18.

FITZPATRICK Fitzpatrick, M. et al. 1994, “WSQ Compression / Decompression Algorithm Test Report”, IAI Annual Conference.

HOLLANDER Hollander, M.,  Wolfe, D. A. (1999). Non‐Parametric Statistical Methods, 2nd Ed, John Wiley & Sons:NY, 787 pages.

LIBERT “A 1D Spectral Image Validation/Verification Metric for Fingerprints”. Libert, J.M.; Grantham, J.; Orandi, S. August

19, 2009. http://www.nist.gov/customcf/get_pdf.cfm?pub_id=903078. Retrieved 2011‐01‐12.

LIKERT Likert, R. (1932). A Technique for the Measurement of Attitudes, Archives of Psychology 140, 55.

MTR "Profile for 1000 ppi Fingerprint Compression". Lepley, M.A.

http://www.mitre.org/work/tech_papers/tech_papers_04/lepley_fingerprint/lepley_fingerprint.pdf. Retrieved

2011‐01‐11.

SD27 M.D. Garris & R.M. McCabe, "NIST Special Database 27: Fingerprint Minutiae from Latent and Matching Tenprint

Images," NIST Technical Report NISTIR 6534 & CD‐ROM, June 2000.

NISTIR7778 Orandi, S., Libert, J. M., Grantham, J. D., Ko, K., Wood, S.S., Wu, J. Effects of JPEG2000 Image Compression on

1000 ppi Fingerprint Imagery, NIST Interagency Report 7778, National Institutes of Standards and Technology,

Gaithersburg, MD.  http://www.nist.gov/customcf/get_pdf.cfm?pub_id=911122. Retrieved from on 09/01/2012.

SOKAL Sokal, Robert R. and Rolf, F. James (1969) Biometry: The Principals and Practice of Statistics in Biological

Research, Third Edition, W. H. Freeman & Co., NY, 887 pages.

WILCOXON Wilcoxon, Frank (Dec 1945). "Individual comparisons by ranking methods". Biometrics Bulletin 1 (6): 80‐83.

WRIGHT Wright, Paul, S. P‐values for simultaneous inference. Biometrics, Vol. 48, No. 4 (Dec. 1992), pp. 1005‐1013.  

WU1 Wu, Jin Chu, Alvin F. Martin, and Raghu N. Kacker. Measures, uncertainties, and significance test in operational

ROC analysis, Journal of Research of the National Institute of Standards and Technology, 116(1), 517‐537, (2011).

WU2 Wu, Jin Chu. Studies of Operational Measurement of ROC Curve on Large Fingerprint Data Sets Using Two‐

Sample Bootstrap. NISTIR 7449, U.S. Department of Commerce, National Institute of Standards and Technology,

September 2007, 25 pages.

WU3 Wu, Jin Chu. Operational Measures and Accuracies of ROC Curve on Large Fingerprint Data Sets. NISTIR 7495,

U.S. Department of Commerce, National Institute of Standards and Technology, May 2008, 23 pages.

   
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Standards

ANSI/NIST‐ITL 1‐

2011

ANSI/NIST‐ITL 1‐2011, NIST Special Publication 500‐290 Data Format for the Interchange of Fingerprint, Facial & Other

Biometric Information. http://www.nist.gov/itl/iad/ig/ansi_standard.cfm . Retrieved 2012‐09‐11.

ISO/IEC

15948:2004

ISO/IEC 15948:2004 ‐ Information technology ‐ Computer graphics and image processing ‐‐ Portable Network Graphics

(PNG): Functional specification.

http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=29581 Retrieved 2012‐01‐11.

ISO/IEC  

19794‐1:2011

ISO/IEC 19794‐1:2011‐  Information technology  ‐‐  Biometric data interchange formats  ‐‐  Part 1: Framework.

http://www.iso.org/iso/catalogue_detail.htm?csnumber=50862. Retrieved 2012‐09‐10.  

JPEG "T.81 : Information technology ‐ Digital compression and coding of continuous‐tone still images ‐ Requirements and

guidelines". http://www.itu.int/rec/T‐REC‐T.81. Retrieved 2011‐01‐12.

JPEG2K "ISO/IEC 15444‐1:2004 ‐ Information technology ‐‐ JPEG2000 image coding system: Core coding system".

http://www.iso.org/iso/iso_catalogue/catalogue_ics/catalogue_detail_ics.htm?csnumber=27687. Retrieved 2009‐11‐01.

WSQ "WSQ Gray‐Scale Fingerprint Image Compression Specification" Version 3.1.

https://www.fbibiospecs.org/docs/WSQ_Gray‐scale_Specification_Version r = 3, 1.pdf. Retrieved 2010‐01‐11.
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Appendix A. ‐ Dataset Makeup

For the ink card scan portion of the tests, the study utilized fingerprint images based on the Base Demonstration Model (BDM) fingerprints

utilized in early tests of the FBI IAFIS system, and later used as the basis for the NIST SD‐27 special database [SD27]. This ink card scan data was

collected as a result of law enforcement activities and represents actual field data with collection dates ranging from 08/18/1973 through

04/12/1994. The original FD‐249 fingerprint collection cards with these images were retrieved by NIST and rescanned at both 500 ppi and 1000

ppi by NIST personnel under controlled conditions and without repositioning the cards between scans at 500 ppi and 1000 ppi. The images

were scanned at 8‐bits per pixel gray‐scale using FBI certified software (Appendix F compliant) and stored in a non‐compressed format to

ensure no compression anomalies are introduced into the original set.

Where possible, the image sets were equally balanced by gender, finger, pattern class and hand. It should be noted that balancing equally

does not follow the natural demographic behavior of the population such as gender (48 % males/52 % female [CIA]) or pattern class (65 %

Loops, 30 % Whorls, 5 % Arches [DOJ]).  The goal in having equal distributions of each subsample was to present a sufficiently large set of each

subsample so that they avoid the potential statistical bias of very small subsamples.  That is, all subsamples are equally important with respect

to compression irrespective of their relative incidence in the population.

Demographic Make‐up of Ink Card Scan Datasets

Ink card scan images used in this study consisted of 200 rolled images.  Each subject contributed exactly one fingerprint to the dataset.  

Table 36 ‐ Ink Card Scan Data classification by Impression Type

All Data

Impression Type Males Females Right Left

Rolled Single Finger 183 17 100 100

Table 37 ‐ Ink Card Scan Pattern Classification for Single Finger Images by Impression Type

Data From Females (Single Finger) Data From Males (Single Finger)

Pattern Class Rolled Right Left Pattern Class Rolled Right Left

Arch 1 0 1 Arch 16 9 7

Loop 8 4 4 Loop 104 53 51

Whorl 8 5 3 Whorl 63 29 34

Total 17 9 8 Total 183 91 92

Table 38 ‐ Ink Card Scan Pattern Classification for Single Finger Images by Finger (Females)

Data From Females (Single Finger)

Pattern Class

R. ThumbR. IndexR. MiddleR. RingR. LittleL. ThumbL. IndexL. MiddleL. RingL. LittleTotal

Arch 0 0 0 0 0 0 1 0 0 0 1

Loop 1 0 2 1 0 0 3 0 0 1 8

Whorl 2 2 1 0 0 0 1 0 1 1 8

Total 3 2 3 1 0 0 4 0 1 2 17

   
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Table 39 ‐ Ink Card Scan Pattern Classification for Single Finger Images by Finger (Males)

Data From Males (Single Finger)

Pattern Class

R. ThumbR. IndexR. MiddleR. RingR. LittleL. ThumbL. IndexL. MiddleL. RingL. LittleTotal

Arch 1 6 1 1 0 2 1 3 0 1 16

Loop 10 8 10 8 17 9 4 12 10 16 104

Whorl 6 4 6 10 3 9 10 5 9 1 63

Total 17 18 17 19 20 20 15 20 19 18 183

Table 40 ‐ Gender Breakdown for Data

Subjects by Gender and Race

Males Females White Black Hispanic Asian Native American

Ink Capture Dataset 183 17 97 89 7 6 1

Table 41 ‐ Age Breakdown for Data

Subjects by Age

Under 18 18‐24 25‐29 30‐34 35‐39 40‐44 45‐49 50+ UNKNOWN

Ink Card Scan Dataset 7 128 31 15 5 4 5 2 3

Table 42 ‐ Other Metadata: Height and Weight

Subjects by Height and Weight

Height Weight <5’0” 5’0” ‐ 5’5” 5’6” ‐ 5’11” 6’0”+ UNKNOWN <100 lbs 100 ‐ 149 lbs 150 ‐ 199 lbs 200 ‐ 249 lbs

250+ lbsUNKNOWN

Ink Card Scan Dataset 0 20 127 52 1 0 58 115 21 5 1

Table 43 ‐ Other Metadata: Eye Color

Subjects by Eye Color

Brown Black Blue Green Hazel UNKNOWN

Ink Card Scan Dataset 147 3 30 8 11 1
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Appendix B. ‐ Equipment Used for Study

The equipment utilized for the processing of the image data described in this study with the algorithms described was comprised of a single

PC customized specifically for the purposes of imaging software development, research, and testing. The specifications of this PC are as

follows:

Model: Dell Precision T7500

CPU: 2x Intel Xeon W5580 @ 3.20 GHz

Memory: 12.0 GB DDR3 (Registered ECC)

Storage: 2x OCZ Vertex 2 240GB SSD (RAID 1), 4x Western Digital 2TB HDD (RAID 0+1)  

Operating System: Microsoft Windows 7 64‐bit Ultimate Edition

A different set of equipment was used in the data collection portion of this study and consisted of the following:  

1 x Commodity Router: The router provides connectivity among the three workstations and NAS device, as well as providing remote access to

the workstations and NAS for administration.  

3 x Commodity Workstations: The workstations are configured with 8 GB RAM, 300 GB HD, 64‐bit operating system, FIXT software and data.

3 x 24 inch Monitors: The IPS‐panel monitors are connected via DVI‐D and calibrated (see below) for optimal accuracy and consistency.  The

monitors were operated at their native resolution of 1920x1200, yielding a dpi measurement of approximately 94.3ppi.    The zoom

functionality in software allowed the examiners to zoom in and out of the image, and view them in the range of approximately 10x to 50x

given these specific monitors.

1 x Network Attached Storage (NAS): The NAS contains master copies of the FIXT software and data, as well as iterative copies of each

stations logs/results (saved at the end of each session).  

1 x Monitor Calibration Device: The monitors were calibrated using a system which consists of a colorimeter paired with proprietary software

designed specifically for use with the colorimeter and for the purpose of monitor calibration. The colorimeter is a sensor which provides an

accurate measurement of colors as they actually appear on the monitor screen. During the calibration process, the colorimeter is physically

attached to the monitor while the software displays a series of solid colors on the screen. The colorimeter measures the actual color values

displayed on the monitor and then provides these measurements to the software. The software uses these measurements to calculate the

difference between the color values as they are displayed on the monitor against the true color values within the software. The software then

applies configuration changes to the system in order to correct the color values displayed by the monitor, ensuring accurate color

reproduction. Due to the fact that each monitor, even of the same model, performs slightly differently in terms of the accuracy of color

reproduction, this process was completed independently on each of the three FIXT workstations.  

   
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Appendix C. ‐ Gaussian filter code

// The Following code segment has been developed in the C#.NET platform 

// Runs image through a Gaussian filter with the parameters specified 

 public void GaussianFilter(double sigma, int radius) 

 { 

 Console.WriteLine("\tRunning Gaussian filter..."); 

 // Construct Gaussian function 

 int length = radius * 2 + 1; 

 double[,] gaussian = new double[length, length]; 

 Point center = new Point(radius, radius); 

 

 // set distances from center 

 

 for (int x = 0; x < length; x++) 

 for (int y = 0; y < length; y++) 

 gaussian[x, y] = Distance(new Point(x, y), center); 

 // run distances through Gaussian function 

 double sum = 0; 

 for (int x = 0; x < length; x++) 

 for (int y = 0; y < length; y++) 

 { 

 gaussian[x, y] = Gaussian(gaussian[x, y], 0, sigma); 

 sum += gaussian[x, y]; 

 } 

 for (int x = 0; x < length; x++) 

 for (int y = 0; y < length; y++) 

 gaussian[x, y] = gaussian[x, y] / sum; 

 // Apply filter to image 

 int height = bitmap.Height; 

 int width = bitmap.Width; 

 Bitmap tmpbmp = new Bitmap(width, height); 

 for (int y = 0; y < height; y++) 

 for (int x = 0; x < width; x++) 

 { 

 // get surrounding pixels 

 int[,] area = new int[length, length]; 

 for (int y2 = 0; y2 < length; y2++) 

 for (int x2 = 0; x2 < length; x2++) 

 { 

 int xbound = x - radius + x2; 

 int ybound = y - radius + y2; 

 if (xbound >= 0 && xbound < width && ybound >= 0 && ybound < height) 

 area[x2, y2] = array[x - radius + x2, y - radius + y2]; 

 else // if filter goes off the edge, use nearest pixel 

 area[x2, y2] = array[x, y]; 

 } 

 // find weighted sum 

 double wsum = 0; 

 for (int x2 = 0; x2 < length; x2++) 

 for (int y2 = 0; y2 < length; y2++) 

 wsum += area[x2, y2] * gaussian[x2, y2]; 

 tmpbmp.SetPixel(x, y, Value2Color((int)(wsum))); 

 } 

 // save 

 bitmap = tmpbmp; 

 InitArray(); 

 } 

 // Downsamples image by 50% in both dimensions 

 public void Downsample50(int dstype) 

 { 

 Console.WriteLine("\tDownsampling..."); 

 int height = bitmap.Height; 

 int width = bitmap.Width; 

 Bitmap dsbitmap; 

 switch (dstype) 

 { 

 case Constants.EE: // save even columns and rows 
NISTIR 7839 ‐ Examination of Downsampling Strategies for Converting 1000 ppi Fingerprint Imagery to 500 ppi

PAGE 84 OF 84

 dsbitmap = new Bitmap((bitmap.Width + 1) / 2, (bitmap.Height + 1) / 2); 

 for (int y = 0; y < height; y++) 

 if (y % 2 == 0) 

 for (int x = 0; x < width; x++) 

 if (x % 2 == 0) 

 dsbitmap.SetPixel((x + 1) / 2, (y + 1) / 2, Value2Color(array[x, y])); 

 break; 

 case Constants.EO: // save even columns and odd rows 

 dsbitmap = new Bitmap((bitmap.Width + 1) / 2, bitmap.Height / 2); 

 for (int y = 0; y < height; y++) 

 if (y % 2 == 1) 

 for (int x = 0; x < width; x++) 

 if (x % 2 == 0) 

 dsbitmap.SetPixel((x + 1) / 2, y / 2, Value2Color(array[x, y])); 

 break; 

 case Constants.OE: // save odd columns and even rows 

 dsbitmap = new Bitmap(bitmap.Width / 2, (bitmap.Height + 1) / 2); 

 for (int y = 0; y < height; y++) 

 if (y % 2 == 0) 

 for (int x = 0; x < width; x++) 

 if (x % 2 == 1) 

 dsbitmap.SetPixel(x / 2, (y + 1) / 2, Value2Color(array[x, y])); 

 break; 

 case Constants.OO: // save odd rows and columns 

 dsbitmap = new Bitmap(bitmap.Width / 2, bitmap.Height / 2); 

 for (int y = 0; y < height; y++) 

 if (y % 2 == 1) 

 for (int x = 0; x < width; x++) 

 if (x % 2 == 1) 

 dsbitmap.SetPixel(x / 2, y / 2, Value2Color(array[x, y])); 

 break; 

 default: 

 throw new Exception("Illegal value for downsampling type. Needs to be 1-4."); 

 } 

 // save 

 bitmap = dsbitmap; 

 InitArray(); 

 } 

 private void InitArray() 

 { 

 array = new int[bitmap.Width, bitmap.Height]; 

 for (int x = 0; x < bitmap.Width; x++) 

 for (int y = 0; y < bitmap.Height; y++) 

 array[x, y] = bitmap.GetPixel(x, y).R; 

 } 

 // converts int value to a Color 

 private Color Value2Color(int pixval) 

 { 

 int ARGB_val; 

 Color color; 

 ARGB_val = pixval * 256 * 256 + pixval * 256 + pixval; 

 color = Color.FromArgb(ARGB_val); 

 return color; 

 } 

 private double Distance(Point a, Point b) 

 { 

 return Math.Sqrt((a.X - b.X) * (a.X - b.X) + (a.Y - b.Y) * (a.Y - b.Y)); 

 } 

 // returns value of Gaussian function with given x, mu, and sigma 

 private double Gaussian(double x, int mu, double sigma) 

 { 

 return (1 / Math.Sqrt(2 * Math.PI * sigma * sigma)) * Math.Exp(-((x - mu) * (x - mu)) / (2 * sigma * sigma)); 

 }