August 2009

Information Access Division

Information Technology Laboratory

A 1D Spectral Image

Validation/Verification Metric

for Fingerprints

John M. Libert 

John Grantham 

Shahram Orandi 

NISTIR 7599

John M. Libert

John Grantham 

Shahram Orandi 

U.S. Department of Commerce 

Technology Administration 

National Institute of Standards and Technology 

Information Technology Lab 

Gaithersburg, MD 20899 

August 2009

U.S. Department of Commerce 

Gary Locke, Secretary 

National Institute of Standards and Technology 

 Patrick D. Gallagher, Deputy Director 

NISTIR 7599

A 1D Spectral Image 

Validation/Verification Metric

for Fingerprints

Acknowledgements 

The authors wish to acknowledge the contributions of those who have facilitated the research 

and development work described in the present document. We would like to acknowledge 

and thank Scott Swann of the Federal Bureau of Investigation's (FBI) Criminal Justice 

Information Services (CJIS) as well as other key partners at the FBI who provided both 

sponsorship and support to NIST in facilitating this research.

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Table of Contents

ACKNOWLEDGEMENTS .................................................................................................................................i

ABSTRACT..........................................................................................................................................................1 

1. INTRODUCTION............................................................................................................................................3

2. BACKGROUND ..............................................................................................................................................5

3. SIVV METHOD...............................................................................................................................................7

3.1 IMAGE WINDOWING .............................................................................................................................7

3.2 DISCRETE FOURIER TRANSFORM (DFT) .................................................................................................9

3.3 NORMALIZED POWER SPECTRUM........................................................................................................10

3.4 POLAR TRANSFORM OF POWER SPECTRUM.........................................................................................10

3.5 1D NORMALIZED POWER SPECTRUM...................................................................................................11

3.6 PEAK STRUCTURE OF SPECTRUM.......................................................................................................13

4. RESPONSE OF THE SIGNAL TO IMAGE PARAMETERS..................................................................17

4.1 ROTATION INVARIANCE.....................................................................................................................17

4.2 RESPONSE OF SPECTRUM TO TRANSLATION ......................................................................................17

4.3 SCAN SAMPLE RATE SENSITIVITY (1000 PPI VS. 500 PPI)....................................................................20

5. RESULTS AND DISCUSSION ....................................................................................................................23

6. CONCLUSIONS ............................................................................................................................................29

7. REFERENCES...............................................................................................................................................31

8. APPENDIX A: DEMONSTRATION OF ROTATION INVARIANCE...................................................33

9. APPENDIX B: TEST DATA ........................................................................................................................35

10. APPENDIX C: DISTRIBUTIONS OF SIVV FEATURES......................................................................37

NISTIR 7599 Page iii 08/19/2009 
List of Figures

Fig. 1 2D Blackman window function....................................................................................8 

Fig. 2 Input image (995 x 1090 pixels) and Blackman windowed version..........................8 

Fig. 3 Sample fingerprint image (922 x 860 pixels) and associated 1D spectra computed 

without and with application of a window function....................................................9 

Fig. 4 Diagram showing operation performed by a function that shifts quadrants of the 

DFT such that dc term, P(0,0), is centered in the image..........................................10 

Fig. 5 Illustration of processing steps from image to 1D Normalized Power Spectrum. 

(Image of size 995 x 1090 pixel) Spatial frequency, u and v, are in units of cycles 

per image width as are the unnormalized units of polar radius, ρ. Polar angles, 

θ, are in degrees. In the log power spectrum, radius values of cycles/image width 

are scaled to become cycles/pixel..............................................................................12 

Fig. 6 Fingerprint sampled at 1000 ppi (1107 x 1145 pixels) and associated 1D 

spectrum. The pair of local minimum and maximum having the largest difference 

in power are indicated with green and red marks....................................................14 

Fig. 7 Fingerprint sampled at 1000 ppi (1990 x 790 pixels) and associated 1D 

spectrum........................................................................................................................14 

Fig. 8 Slap-four image sampled at 1000 ppi (2049 x 3116) and spectrum........................15 

Fig. 9 Off-center fingerprint image (1500 x 1600) and associated spectra computed both 

without and with Blackman windowing....................................................................18 

Fig. 10 Image from fig 9 with fingerprint moved toward more centered position 

applying a circular shift to the image.........................................................................18 

Fig. 11 Fingerprint image digitized at 1000 ppi (995 x 1090 pixels).................................21 

Fig. 12 Fingerprint image from fig. 11 resampled at 500 ppi (498 x 545 pixels) using 

bicubic interpolation. The spectral features are shifted by factor of 2 in 

frequency......................................................................................................................21 

Fig. 13 Box plot showing distributions of peak height for non-fingerprint images (0) and 

fingerprint images (1) in a mixed image 

dataset...........................................................................................................................24 

Fig. 14 Box plot showing distributions of frequency location of the valley-peak structure 

for non-fingerprint images (0) and fingerprint images (1) in a mixed image 

dataset...........................................................................................................................24 

Fig. 15 Plot of false positive vs. false negative error rates with variation of threshold 

value of peak height used as a classifier applied to a mixed image dataset. Feature 

frequency maximum was set at 0.15 

cycles/pixel....................................................................................................................25 

Fig. 16 Box plot showing distributions of peak height (dy) for equal numbers of 

fingerprint, face, and iris images in a mixed biometric dataset...............................26 

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Fig. 17 Box plot showing distributions of frequency location of the valley-peak feature 

for equal numbers of fingerprint, face, and iris images in a mixed biometric 

dataset.........................................................................................................................26 

Fig. 18 Peak height (dy) vs. frequency of SIVV output for images of the Mixed 

Biometric 1 dataset. Note the separation of fingerprints into clusters 

corresponding to the 1000 and 500 ppi samples........................................................27 

Fig. 19 Plot of false positive vs. false negative error rates with variation of threshold 

value of peak height used as a classifier applied to the mixed biometric dataset. 

Feature frequency maximum was set at 0.15 cycles/pixel........................................27 

Fig. A-1 Circular sample of a rolled fingerprint image (1029 x 1023) captured at 1000 

ppi. Original orientation (top) is rotated 45° and 90°...............................................33 

Fig. A-2 Circular sample of a slap-four image (2012 x 2064) captured at 1000 ppi. 

Original orientation (top) is rotated 45° and 90°......................................................34 

Fig. C-1 Box plot showing distributions of peak height (dy) by finger for SD27 dataset 

sampled at 1000 ppi. Fingers 1 – 10 are rolled inked prints on FBI 10-print cards; 

11 and 12 are plain impressions of thumbs; and 13 and 14 are slap-four prints of 

left and right hands......................................................................................................38 

Fig. C-2 Box plot showing distributions of peak height (dy) by finger for SD27 dataset 

down-sampled (with anti-aliasing) to 500 ppi. Fingers 1 – 10 are rolled inked 

prints on FBI 10-print cards; 11 and 12 are plain impressions of thumbs; and 13 

and 14 are slap-four prints of left and right hands...................................................38 

Fig. C-3 Box plot showing distributions of peak height (dy) by finger for SD29 dataset 

sampled at 500 ppi. Fingers 1 – 10 are plain inked prints........................................39 

Fig. C-4 Box plot showing distributions of peak frequency location of the valley-peak 

feature by finger for SD27 dataset sampled at 1000 ppi. Fingers 1 – 10 are rolled 

inked prints on FBI 10-print cards; 11 and 12 are plain impressions of thumbs; 

and 13 and 14 are slap-four prints of left and right hands......................................39 

Fig. C-5 Box plot showing distributions of frequency location of the valley-peak feature 

by finger for SD27 dataset down-sampled (with anti-aliasing) to 500 ppi. Fingers 1 

– 10 are rolled inked prints on FBI 10-print cards; 11 and 12 are plain 

impressions of thumbs; and 13 and 14 are slap-four prints of left and right 

hands.............................................................................................................................40 

Fig. C-6 Box plot showing distributions of frequency location of the valley-peak feature 

by finger for SD29 dataset sampled at 500 ppi. Fingers 1 – 10 are plain inked 

prints.............................................................................................................................40 
ABSTRACT

Image validation and verification are important functions in the acquisition of fingerprint 

images from live-scan devices and for assessing and maintaining the fidelity of fingerprint 

image databases. Such databases are used by law enforcement agencies, for which data 

integrity is paramount, and many hours must be devoted to visual inspection of images. In 

addition, such databases are used by the National Institute of Standards and Technology 

(NIST) and others to test automated fingerprint identification system (AFIS) algorithms and 

to aide the advance of this technology. We propose a comparatively simple computational 

mechanism by which to screen fingerprint image databases for specimens improperly 

scanned from fingerprint cards, guide the auto-capture process and flag auto-capture failures, 

identify non-fingerprint images that may have been included in a database, and recognize 

aberrant sampling of fingerprint images. The scheme reduces an input image to a 1-

dimensional power spectrum that makes explicit the characteristic ridge structure of the 

fingerprint that on a global basis differentiates it from most other images. The magnitude of 

the distinctive spectral feature, related directly to the distinctness of the level 1 ridge flow, 

provides a primary diagnostic indicator of the presence of a fingerprint image. The frequency 

of the spectral feature provides a secondary classification metric and, on a coarse level, 

indicates the scan sample rate of the fingerprint image. Test results are reported in which the 

Spectral Image Validation and Verification (SIVV) utility is applied to a variety of databases 

composed of fingerprint and non-fingerprint images. Using only the peak height and 

frequency limit as simple classification criteria, the SIVV utility achieves an equal error rate 

(EER) for false positive and false negative classifications of 10 % for fingerprints mixed with 

a variety of non-fingerprint images, including many chosen to exhibit periodic structure 

similar to that of a fingerprint. An EER of around 7 % is found with a dataset containing 

fingerprints mixed with other biometric samples, i.e. face and iris images. 

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1. INTRODUCTION 

The present investigation explores the use of a 1D summary of the 2D image spectrum to test 

validity of fingerprint images and to diagnose acquisition problems such as aberrant 

sampling, such as misplaced fingers in a single finger capture, or faulty segmentation. The 

preparation of datasets of biometric samples for various development and testing applications 

as well as for law enforcement and homeland security applications requires that the images 

be screened with respect to their validity as examples of the expected biometric. Starting 

with fingerprint acquisition using a live-scan device, detection of the presence of a finger or 

the position of the finger on the platen should aid in automating such a system. A rapid 

fingerprint recognition capability could serve as a preprocess for a more sophisticated image 

quality algorithm, such as the NIST Fingerprint Image Quality (NFIQ) metric [1, 2]. Such a 

system could assist in identifying mislabeled images in a mixed biometric dataset, for 

example where a face image is erroneously labeled as a fingerprint. A validation/verification 

signal might support identification of sampling errors, for example, in which an image fails 

to conform to a specified scan sample rate. Accordingly, the present research activity was 

undertaken to develop and test a computational scheme for fingerprint image validation and 

verification. Our method, computationally simple, differentiates fingerprint images on the 

basis of a power spectral feature related to the periodic texture of friction ridge skin. The 

relative height and frequency of the dominant spectral peak differentiates a fingerprint image 

from a variety of other image types, including other biometrics such as face and iris images. 

In view of its implementation and application we have named the method the Spectral Image 

Validation and Verification (SIVV) utility. 

This report provides in Section 2 a brief survey of previous work on fingerprint image 

validation and verification, related application of spectral analysis, and decomposition of 

fingerprint images. Section 3 details the mathematical and algorithmic underpinnings of the 

SIVV method. Section 4 examines robustness of the diagnostic spectral pattern under 

rotation and translation of the fingerprint, and provides qualitative comparisons of the SIVV 

response to non-fingerprint images. Section 5 provides a quantitative examination of the 

SIVV performance as an aid in classifying fingerprints among assorted non-fingerprint 

images and among face and iris images. Finally, Section 6 summarizes the utility of the 

SIVV in differentiating fingerprint from non-fingerprint images, detecting scan sample rate 

anomalies, and detecting some types of live-scan acquisition errors. 

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2. BACKGROUND 

Local orientation and frequency of ridges are recognized as unique intrinsic properties of 

fingerprint images. Some attention is directed toward examining such ridge structure in order 

to assess quality, enhance quality, and to evaluate suitability of fingerprint images for 

verification/recognition. Most of the work has involved various wavelet representations of 

the fingerprint image directed toward evaluation of the image quality, e.g. [3-6]. Other work 

such as that of Maio [7] and Yin [8] looks specifically at ridge spacing and distinctness of the 

pattern, mainly with respect to characterization of the fingerprint ridge structure as a distinct 

texture to be used in a recognition scheme as well as for evaluation of image quality. 

Lim et al [9] describe a means by which to evaluate the quality as well as to test the validity 

of fingerprint images with respect to the ridge structure of fingerprint images. Local analysis 

of “orientation certainty” is used as an indicator of quality, while the ridge-to-valley structure 

provides indication of fingerprint image validity, i.e., that the image actually exhibits a 

fingerprint. They evaluate quality on a local level as indicated by the strength of energy 

concentration along ridge-valley orientations. Validity is indicated by measures of global 

uniformity and continuity of orientation across adjacent image blocks. 

Tabassi, Wilson, and Watson [1, 2] describe a fingerprint image quality method that 

incorporates a measure of ridge flow based on local (blockwise) analysis of the discrete 

cosine transform signal. While the NIST Image Quality (NFIQ) metric itself primarily 

examines minutia and aims to predict the performance of fingerprint matchers, the reliability 

of minutia detection in each image neighborhood is assessed via local measures of ridge flow 

direction, contrast, and curvature. 

The closest methods to those presently under examination are efforts directed toward using 

the spectral characteristics of images for texture-based image retrieval. Using a mechanism 

somewhat similar to that proposed in the present paper is the RAH (Radius Angle 

Histogram) described by Wang et al [10]. These researchers describe use of power spectral 

histograms for texture-based image retrieval. They construct the polar representation of the 

2D power spectrum and characterize image textures via histograms of the quantized power 

over polar radius and over angle. Power over radius corresponds to spatial frequency content 

of the image texture and that over angle reflects the orientations of the textural components. 

They use a distance metric to evaluate similarity of a query target to library images. Another 

spectral histogram method for texture classification is proposed by Xiuwen [11] that 

decomposes the spectral content of image textures using Gabor wavelets. These methods 

treat orientation of textural components as important to classification; hence make no attempt 

to impose rotational invariance on the representation. 

NISTIR 7599 Page 5 08/19/2009 
Nill and Bouzas [12] propose a measure of image quality derived from the 2D spectrum of 

the image under evaluation. While their quality metric is based on the 2D image spectrum, 

these researchers present a 1D representation of the spectrum that has interesting properties 

in its own right. Nill and Bouzas employ 1D summaries of 2D power spectra to aid in 

visualizing the most significant spectral differences among images. The present investigation 

explores the use of this 1D spectral summary to test validity of fingerprint images directly 

and to diagnose acquisition problems such as aberrant sampling or faulty segmentation. 

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3. SIVV METHOD

3.1 IMAGE WINDOWING 

The effect of observing the image signal over finite extent with discontinuity at the edges is 

to introduce spurious power into the spectrum (spectral leakage). Windowing reduces this 

effect, narrowing the peak side lobes and concentrating energy at the appropriate spatial 

frequency, thus better defining the location of peaks and resolving separate peaks that 

otherwise might remain merged. In order to enhance resolution and localization of spectral 

features, recommended procedure (see [13]) calls for applying a weighting function to the 

input signal prior to application of the Discrete Fourier Transform (DFT) such that values of 

the input signal taper toward zero at the edges. In the case of single fingerprint images, 

windowing has the additional advantage in reducing the effects of sensor contact artifacts at 

the sensor edge. 

A variety of window functions were applied to several fingerprint image examples and the 

resultant spectra examined by inspection with respect to spatial frequency specificity of 

peaks as indicated by peak height, width, and number of distinct peaks. Such limited testing 

could not support exclusion of alternate window shapes, but the Blackman window seemed 

to produce reasonably well-defined peaks. Hence it was selected for the SIVV tool 

implementation. The 1D Blackman window is defined [14] as 

2 4 ( ) 0.42 0.5cos 0.08cos , 0 . n n

w n n N

N N

⎛⎞ ⎛⎞ π π

=− + ⎜⎟ ⎜⎟ ≤ ≤ ⎝⎠ ⎝⎠ (1) 

The desired length of the window L N1 = + (or L M= +1

1...M

) for windowing rows or columns 

of the imagei. Conveniently, the application of this 1D window function to the input image 

requires only element-wise multiplication of the image rows and columns by 1D window 

functions of the appropriate length. Thus, first each row of the input image, I(i,j), is 

multiplied by the window function wm m ( ), = where M = number of image columns. 

The columns of the output of this operation are then multiplied element wise by 

 where =number of rows of the image. Alternately the entire 2D window 

function, , may be constructed by forming the cross product of the column vector, 

, and the row vector . This cross product yields the 2D window function of the 

appropriate dimensions for element-wise multiplication by the input image, I. 

wn n N ( ), 1... =

W( , n m

w( ) n

N

)

w( ) m

 

i

 Square pixels are assumed here. 
NISTIR 7599 Page 8 08/19/2009 

Fig. 1 illustrates the 2-dimensional Blackman window sized appropriately for application to 

the input image shown in fig. 2. The windowed image is shown on right of fig. 2 illustrating 

the tapering of intensity values toward the image edges. Various window functions share the 

property that they taper the image values toward zero on the borders. 

Fig. 1 2D Blackman window function. 

0

200

400

600

800

1000

1200

0

200

400

600

800

1000

0

0.2

0.4

0.6

0.8

1

2D Blackman Window

Input Image Windowed Image

Fig. 2 Input image (995 x 1090 pixels) and Blackman windowed version. 
NISTIR 7599 Page 9 08/19/2009 

Fig 3 shows an example of spectrum computation without windowing and with application 

of the Blackman window to the image. Windowing increases the sharpness of the main peak 

at around 0.05 cycles/pixel and increases the power of the spectrum overall. A slight shift in 

frequency of the peak reflects the differential weighting applied to the central ridge structure 

relative to that on the periphery of the fingerprint. In this regard, it may be noted that the 

effect of the windowing will be at maximum for textures centered in the image frame. Effects 

of fingerprint offset will be examined later in this paper. 

3.2 DISCRETE FOURIER TRANSFORM (DFT) 

Given a 2D image, having dimensions N rows x M columns, a pixel grey level may be 

specified as h(x,y) with x coordinates ranging 0...M-1 and y coordinates 0...N-1. The 

discrete Fourier transform (DFT), is computed as 

1 1

0 0

( , ) exp 2 exp 2 ( , )

... , ... . 2 2 22

M N

x y

v u Huv iy ix h x y N M

MM NN

u v

π π

− −

= =

⎡ ⎤⎡ ⎤ = ⎢ ⎥⎢ ⎥ ⎣ ⎦⎣ ⎦

= − = −

∑ ∑

 (2) 

where u and v denote frequency components in x and y directions. 

Fig. 3 Sample fingerprint image (922 x 860 pixels) and associated 1D 

spectra computed without and with application of a window 

function. 

Input Img.

0 0.1 0.2 0.3 0.4 0.5

10-6

10-4

10-2

100

102

 Log Power (db)

 Frequency (cycles/pixel)

 Log Power Spectrum

no windowing

windowing
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3.3 NORMALIZED POWER SPECTRUM 

The 2D power spectrum is computed as 

2

2

(,) (,)

(0,0)

Huv

Puv

H = (3) 

The normalization term in the denominator is the square of the average grey level which 

corresponds to the dc term of the spectrum, H (0,0) . 

In the output array of the Fast Fourier Transform (FFT) routine, the 0th frequency term is 

repeated in each corner of the image frame and the spectra are mirrored about the middle 

rows and columns. Therefore, the 2D power spectral array must be rearranged to center the 

dc response, P(0,0), in the image frame. For the 2D DFT this means that the quadrants are 

swapped diagonally such that quadrant 1 is swapped with quadrant 3 and quadrant 2 is 

swapped with quadrant 4 as shown in fig. 4. 

Fig. 4 Diagram showing operation performed by a function that shifts quadrants of the 

DFT such that dc term, P(0,0), is centered in the image. 

3.4 POLAR TRANSFORM OF POWER SPECTRUM 

The polar transform is applied to the 2D power spectrum, converting rectangular coordinates 

of the 2D power spectrum to radius, ρ, and angle, θ, with respect to the origin (center) of the 

2D spectrum, where 

2 2

2

u v

2 M N

ρ

+ = +

 (4) 

1 tan

v

u

θ − ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ (5) 

1 2 

4 3 
NISTIR 7599 Page 11 08/19/2009 

Equation 3 then becomes 

( ) ( ) 2

2

, , (0,0)

H

P

H

ρ θ ρ θ = . (6) 

Values of θ range from 0 - 180°ii and radius values, ρ, correspond to frequencies 0 – N/2 

cycles per image width (or height), where N is the minimum dimension of the input image. 

Noting that the maximum frequency that can be represented in an image requires 2 pixels, 

the spatial frequency scale is expressed as cycles per pixel from 0 to 0.5 cycles/pixel in 

increments of 0.5/(n-1), where n=number of radii specified for the polar transform. 

3.5 1D NORMALIZED POWER SPECTRUM 

To form a 1D representation of the polar transformed power spectrum one need simply sum 

over angle for each of the frequency (radius) values, i.e. 

() ( ) (7) 

180

0

P P , , 0...0.5 / cycles pixel

θ

ρ ρθ ρ == = ∑

Rather than performing the normalization step as described in section 3.3, the present 

software implementation performs the DC level normalization here as 

( ) ( ) , 0...0.5 / (0)P P c

P ycles pixel ρ ρ ρ = = (8) 

Note that the radius, ρ, is expressed in units of cycles per pixel. For application of the polar 

transform, the number of radii is selected nominally as half the minimum of the length and 

width of the input image. Thus the polar transform of the 2D spectrum includes frequencies 

enclosed by the largest circle that can fit within the dimensions of the 2D spectral array. 

In fig. 5, the 2D power spectrum is shown (top right) in image format. The units of 

frequency, u and v, correspond to cycles per image dimension. The log function is applied to 

the magnitude values of this representation in order that small values at high frequencies 

might be displayed as well as the much larger power at low frequencies. The polar transform 

of the 2D spectrum is shown in fig. 5 (lower left). Radius values, ρ, represent cycles per 

image width corresponding to units of the 2D spectrum. Angles, θ, in degrees, range from 0 

to 180. The 1D spectral signal represented in the lower right of fig 5 is formed by summing 

over all angles the power at each radius of the polar transform. In the 1D spectrum, the radius 

units in cycles per image dimension are rescaled to the frequency range (0.0 to 0.5) cycles 

per pixel as described above. 

 

ii As the spectrum repeats over the 360°, it is completely described over the interval 0-180°. 
NISTIR 7599 Page 12 08/19/2009 

It is noted here that units of cycles per pixel may be converted to a more conventional spatial 

frequency specification given that information is available by which to assign a conventional 

length unit to pixel dimensions. For many images this length factor may remain unknown, or 

recoverable only through estimation based on assumptions relative to the image content. For 

fingerprint images, knowledge of the sample rate often is available in metadata supplied with 

the imagery, and required to be conformant to the ANSI/NIST standard (see [15]) for the 

Type 1 fingerprint data record. This information enables assignment of a conventional linear 

dimension, e.g. millimeters, to the pixel. The generic unit, cycles per pixel, is converted to 

cycles per millimeter by multiplying by the appropriate scaling factor. However, for image 

Input Img. 2D Log Power Spectrum

 u

 v

-500 0 500

-400

-200

0

200

400

Polar Log Power Spectrum

θ

ρ

0 50 100 150

0

50

100

150

200

250

300

350

0 0.1 0.2 0.3 0.4 0.5

10-8

10-6

10-4

10-2

100

 Log Power (db)

 Frequency (cycles/pixel)

 Log Power Spectrum

Fig. 5 Illustration of processing steps from image to 1D Normalized Power 

Spectrum. (Image of size 995 x 1090 pixel) Spatial frequency, u and v, are in 

units of cycles per image width as are the unnormalized units of polar radius, 

ρ. Polar angles, θ, are in degrees. In log power spectrum, radius values of 

cycles/image width are scaled to become cycles/pixel. 
applications, where in most cases scale is unknown, it could be argued that cycles per pixel is 

a perfectly acceptable unit of frequency. 

As may be observed via inspection of a variety of examples, the 1D spectral representation of 

fingerprints appears consistently to exhibit a distinctive valley-peak combination (as 

observed in the lower right plot of fig. 5) in the low frequency range, doubtless the 

expression of the characteristic friction-ridge flow structure of the fingerprint, the so-called 

level 1 detail. 

3.6 PEAK STRUCTURE OF SPECTRUM 

The feature of potential diagnostic significance is observed in the appearance of paired local 

minima and maxima of power values in a frequency band related to the ridge spacing. 

Toward further development of this notion as a diagnostic, an algorithm is devised to locate 

peaks and valleys in the spectrum and to select pairs of such features that might be examined 

further with respect to position along the frequency axis, height of the peak relative to 

preceding valley (dy), frequency distance between valley and peak (dx), slope (dy/dx), and 

statistics of these values with respect to image classes. Other features of potential value may 

be the number of peaks detected in the spectrum and the ordinal position of the valley-peak 

pair having the maximum value of dy. Further, total or average power in each of a small set 

of frequency bands might also be taken as diagnostic features. 

Figs 6 - 8 exhibit fingerprint images and their spectra. Red and green dots along the spectrum 

denote local minimum and maximum feature pairs having the largest power difference, i.e., 

dy value. The feature definition requires that the peak be preceded (over increasing 

frequency) by a local minimum. 

In the present implementation, the spectrum may be smoothed (optionally) prior to peak 

localization using a n-point moving average filter, where n is an odd number greater than 1. 

In the examples n=7. The filtering algorithm performs zero-phase digital filtering by 

processing the input data in both forward and reverse directions as described in [16]. 

The peak finder returns coordinates of pairs of local minimum and maximum values. These 

are processed further to yield the pair exhibiting the maximum difference in power, i.e. dy. 

The frequency position of the feature pair for fingerprints on average should be related to the 

ridge spacing, and in most cases the spectra for fingerprints are expected to lack other 

significant peak structure. This aspect is thus proposed as a means to validate fingerprint 

images. 

The feature pattern occurs over a variety of fingerprint formats. Even the more complicated 

slap-four print exhibits the structure rather clearly as shown in fig. 8. 

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Fig. 6 Fingerprint sampled at 1000 ppi (1107 x 1145 pixels) and a

1D spectrum. The pair of local minimum and maximum having the 

largest difference in power are indicated with green and red marks.

ssociated 

Input Img.

0 0.2 0.4

0.4

0.5

0.6

0.7

0.8

0.9

1

 Log Power (db)

 Frequency (cycles/pixel)

 Log Power Spectrum

Fig. 7 Fingerprint sampled at 1000 ppi (1990 x 790 pixels) and 

associated 1D spectrum. 

Input Img.

0 0.2 0.4

0.4

0.5

0.6

0.7

0.8

0.9

1

 Log Power (db)

 Frequency (cycles/pixel)

 Log Power Spectrum
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Fig. 8 Slap-four image sampled at 1000 ppi (2049 x 3116) and spectrum. 

Input Img.

0 0.2 0.4

0.4

0.5

0.6

0.7

0.8

0.9

1

 Log Power (db)

 Log Power Spectrum

 Frequency (cycles/pixel)
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4. RESPONSE OF THE SIGNAL TO IMAGE PARAMETERS 

4.1 ROTATION INVARIANCE 

A demonstration of the rotation invariance of the SIVV signal is provided in Appendix A. 

But rotation invariance is intrinsic to the signal representation itself. The 2D spectrum is not 

rotation invariant in that the 2D components preserve directionality of frequency information 

in the image. Orientation of frequency components is conveyed to the polar transform of the 

2D spectrum in which rotation becomes translation. Thus, polar transformed spectra of 

images rotated with respect to each other may be brought into registration by circular shiftiii

along the angular dimension. The 1D spectral summary used in the SIVV utility, however, is 

rotation invariant without additional manipulation. That is, integration of the polar spectrum 

over angle generates a similar 1D representation regardless of where one places the origin of 

the summation operation. 

4.2 RESPONSE OF SPECTRUM TO TRANSLATION 

Whereas the SIVV signal representation is invariant to rotation of the fingerprint sample, the 

same is not true for translation of the main ridge-flow region of the fingerprint from the 

image center. We find that fingerprint position does not affect the frequency structure of the 

power spectrum. However, with windowing, the power is substantially greater with the 

centered fingerprint. We find further that “white” space surrounding the fingerprint also 

tends to reduce the spectral power. Fortunately, both potential problems are solved easily as 

will be explained. 

To examine the effect of fingerprint offset from the frame center, a test image displaying the 

fingerprint in a non-centered position was selected from an available database of images 

scanned at 1000 pixels per inch (ppi). A second image was created from this image by 

shifting the fingerprint from its placement along one edge toward the center of the frame by 

applying a circular shift to the image. Figs 9 and 10 exhibit the effects of this manipulation 

on the spectrum both with and without pre-DFT application of a weighting window. 

 

iii Columns of pixels are removed from one edge of the array and inserted along the opposite 

edge. Some number of such operations should bring polar transform arrays of rotated 

images into correspondence. 
NISTIR 7599 Page 18 08/19/2009 

The spectra of figs 9 and 10 confirm that the position of the fingerprint in the image has only 

negligible effect on the position of the peaks in the spectrum. Moreover, power is almost 

identical for centered and offset fingerprints in the “no windowing” case. Significant increase 

in the power is seen with application of the Blackman window to the centered fingerprint as 

shown in fig 10.Windowing has little effect on the spectrum of the offset fingerprint shown 

in fig 9. Thus, while fingerprint position has little effect on the pattern of spectral peaks with 

respect to frequency localization, the power and definition of the peaks can be increased by 

centering the fingerprint in the frame prior to application of the weighting window. 

Fig. 9 Off-center fingerprint image (1500 x 1600) and associated spectra 

computed both without and with Blackman windowing. 

Input Img.

0 0.1 0.2 0.3 0.4 0.5

10-5

100

 Log Power (db)

 Frequency (cycles/pixel)

 Log Power Spectrum

no windowing

windowing

Fig. 10 Image from fig 9 with fingerprint moved toward more centered 

position applying a circular shift to the image. 

Input Img.

0 0.1 0.2 0.3 0.4 0.5

10-5

100

 Log Power (db)

 Frequency (cycles/pixel)

 Log Power Spectrum

no windowing

windowing
NISTIR 7599 Page 19 08/19/2009 

The latter result suggests advantages and perhaps even the necessity of centering the 

fingerprint in the image before estimating the spectrum, particularly if windowing is to be 

employed. The spectral power response is maximized by centering the fingerprint in the 

image frame. Also, we find that the spectral power is enhanced further and the signature 

made more consistent by excluding empty space surrounding the fingerprint. Sophisticated 

image segmentation schemes might be used to center and crop the fingerprint from 

surrounding white space, but simple, less computationally expensive methods are quite 

effective. 

For example, in the current MATLABivv implementation of the SIVV, the average row and 

column coordinates of the binary output of a Sobel [17] edge filter are taken as the center of 

the fingerprint. A circular shift in row and column is then performed to shift the centroid to 

the geometric center of the image prior to windowing and spectrum computation. Except in 

cases having significant stray marks in the surrounding of the fingerprint, this method does a 

good job of centering the ridge-flow of the image. Where edge “noise” is significant in the 

background, cropping is necessary. The same edge map can be used fro cropping as well as 

for centering. 

In the C++ implementation of the SIVV method to be detailed in a subsequent document, 

both centering and cropping functions are implemented using the output of a Canny[18] edge 

detector. The fingerprint center is determined as described above. Then row and column 

cropping boundaries are set by examining edge point density statistics along rows and 

columns with respect to a threshold density value. Only the image region bounded by edge 

densities above threshold is processed further. 

Thus, the sensitivity of the SIVV signal to translation and background is corrected easily. Yet 

this sensitivity of the SIVV method to translation points to the additional diagnostic capacity 

of the method to detect fingerprints offset from the ideal centered position. Difference 

between power spectra before and after centering operations would indicate that the original 

fingerprint was not centered in the original image frame and provide an estimate of the 

degree of offset. 

 

iv Registered trademark of The Mathworks, Inc. 3 Apple Hill Drive Natick, MA 01760-2098. 

v Any mention of commercial products within this report is for information only; it does not 

imply recommendation or endorsement by NIST 
4.3 SCAN SAMPLE RATE SENSITIVITY (1000 PPI VS. 500 PPI) 

Fingerprints, typically, have been scanned at a sample rate of 500 ppi. With improvements in 

scanner technology, data storage capacity, processing capability, and growing interest in 

extending analysis to smaller features of the fingerprint, movement has been rapid toward 

scaning at higher rates of 1000 ppi and even up to 2000 ppi. Accordingly, the potential for 

matching failures due to an unrecognized disparity between image sample rates has become 

significant. Verification of image sample rate, accordingly, has become an important 

component of database screening. 

Given that the 1D spectral frequency is scaled as cycles per pixel, one might expect that 

reducing the sample rate by a factor of two should expand the frequency representation by a 

proportional degree and shift the peak toward higher frequency. Indeed this occurs and may 

be useful for detecting large differences in scan sample rate. Given some variation in the 

precise frequency position of the valley-peak feature among fingerprints at a constant scan 

sample rate, the spectrum may not be sufficiently sensitive to detect small differences in 

sample rate. However, the method can signal disparities on the order of several hundreds of 

ppi. 

Identical fingerprints sampled at both 1000 ppi and 500 ppi were not available, so the 

comparison images are prepared by resampling a 1000 ppi fingerprint at half the original 

rate. The software function employed for this operation applies an “anti-aliasing” (low-pass) 

filter to the image prior to resampling the image. This ensures that under-sampling the high 

frequency components of the original image will not create spurious low frequencies, i.e., the 

Nyquist sampling criterion [19, 20] will be satisfied. Resampling was done using a bicubic 

interpolation method. 

Example 1000 ppi and 500 ppi images and their spectra are shown in figs. 11 and 12. As 

expected, the structure of the spectrum is essentially the same in the two cases but the 

features are stretched out, i.e. redistributed, over the frequency dimension for the lower 

sample rate. At the half the sampling rate, the spectrum at 500 ppi covers only 1⁄2 of the 

actual frequency range of that of the 1000 ppi sampling. Hence a 500 ppi image should be 

easy to recognize among 1000 ppi images. 

NISTIR 7599 Page 20 08/19/2009 
NISTIR 7599 Page 21 08/19/2009 

Fig. 11 Fingerprint image digitized at 1000 ppi (995 x 1090 pixels). 

Input Img.

0 0.1 0.2 0.3 0.4 0.5

0.4

0.5

0.6

0.7

0.8

0.9

1

 Log Power (db)

 Frequency (cycles/pixel)

 Log Power Spectrum

Fig. 12 Fingerprint image from fig. 11 resampled at 500 ppi (498 x 545 

pixels) using bicubic interpolation. The spectral features are shifted 

by factor of 2 in frequency. 

Input Img.

0 0.1 0.2 0.3 0.4 0.5

0.4

0.5

0.6

0.7

0.8

0.9

1

 Log Power (db)

 Frequency (cycles/pixel)

 Log Power Spectrum
NISTIR 7599 Page 22 08/19/2009 
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5. RESULTS AND DISCUSSION 

The SIVV code was run on each of the mixed datasets (described in Appendix B) and the 

output piped to a text file for analysis. As indicated elsewhere in this document, the current 

output of the SIVV consists of the following: 

 • image file name 

 • ordinal location of the maximum peak among the array of peaks returned by the peak 

finder 

 • number of peaks returned by the peak detector 

 • power difference (dy) between the maximum peak and the signal minimum (valley) 

immediately preceding it 

 • frequency difference (dx) between the valley and peak 

 • slope between the valley and peak (dy/dx) 

 • frequency of the midpointvi between the valley and the peak 

The output of the SIVV routine is examined for each of the datasets with respect to the 

distributions of the feature values among fingers in the case of the fingerprint databases (see 

Appendix C), and with respect to fingerprint compared to non-fingerprint images. Then 

assessment is made of the error rates in classifying images as fingerprint or non-fingerprint 

considering the peak height relative to the valley (dy) feature with a rough constraint on the 

acceptable frequency location of the valley-peak feature. 

Figs 13 and 14 contrast distributions of peak height and feature frequency location for 

fingerprints and non-fingerprint images of the mixed dataset. Fig. 13 shows fingerprint 

images to exhibit significantly higher peak height values in comparison to non-fingerprint 

images. Thus, this feature appears effective at discriminating fingerprints from other images. 

 

vi Initial analysis considered the diagnostic feature to consist of both a minimum and a 

succeeding maximum. Given this feature definition, the midpoint seemed a reasonable 

means to locate the feature. Currently, however, we are considering the frequency 

position of the peak alone as a feature, particularly in differentiating various sample scan 

rates, and have plans to test such. 
NISTIR 7599 Page 24 08/19/2009 

Frequency location is less discriminating, though the range of frequency location is much 

smaller for fingerprints than for non-fingerprint images as is shown in fig. 14. This suggests 

0

0.02

0.04

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0.08

0.1

0.12

0.14

0.16

0.18

0.2

0 1

Fingerprint (0/1)

Peak Height - Mixed Images

Peak Height (dB)

Fig. 13 Box plot showing distributions of peak height for nonfingerprint images (0) and fingerprint images (1) in a 

mixed image dataset. 

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 1

Fingerprint (0/1)

Frequency - Mixed Images

Frequency (cycles/pixel)

Fig. 14 Box plot showing distributions of frequency location of the 

valley-peak structure for non-fingerprint images (0) and 

fingerprint images (1) in a mixed image dataset. 
NISTIR 7599 Page 25 08/19/2009 

that frequency location may not be particularly diagnostic in its own right but rather may 

provide a constraint or filter in selection of peak height values for classification. Fig 15 

shows the relative error rates for fingerprint vs. non-fingerprint classification fixing a 

maximum frequency location at 0.15 cycles/pixel and varying the threshold of peak height. 

An equal proportion of false positives and false negatives, equal error rate (EER), of 

approximately 10 % is achieved at a peak height (dy) threshold of around 0.024 dB. 

Figs. 16 and 17 exhibit distributions of peak height and feature frequency location for 

fingerprint, face, and iris images of the mixed biometric dataset, Mixed Biometric 1. As with 

the general mixed image dataset, the distribution of peak heights of fingerprints are quite 

distinct from the much lower values for face and iris images. Again, frequency location is not 

unique for fingerprints, but may serve as a limiting filter for selection of peak height as a 

classification criterion. 

The composite consideration of both peak height and frequency is illustrated in the scatter 

plot of fig. 18. The fingerprint responses are largely separated from those of both face and 

iris images. Moreover, separate clusters are evident for fingerprints at the two scan sample 

rates, 1000 ppi and 500 ppi. Face images represented within the fingerprint clusters are 

actually very small area faces against a brick wall background. Iris images among the 

fingerprints exhibit prominent eye lashes and eyebrows generating the periodic structure. 

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Proportion

Peak Height Threshold

False Positive

False Negative

Fig. 15 Plot of false positive vs. false negative error rates with 

variation of threshold value of peak height used as a 

classifier applied to a mixed image dataset. Feature 

frequency maximum was set at 0.15 cycles/pixel. 
NISTIR 7599 Page 26 08/19/2009 

Fig. 19 shows the error rate as a function of threshold in peak height for classification of 

fingerprint vs. non-fingerprint (face or iris). Again the upper frequency limit is set at 0.15 

cycles/pixel. An EER of 6.6 % is achieved at a peak height of 0.02 dB. 

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Fingerprint Face Iris

Image Type

Peak Height - Mixed Biometric

Peak Height (dB)

Fig. 16 Box plot showing distributions of peak height (dy) for 

equal numbers of fingerprint, face, and iris images in a 

mixed biometric dataset. 

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Fingerprint Face Iris

Image Type

Frequency - Mixed Biometric

Valley-Peak Central Frequency (cycles/pixel)

Fig. 17 Box plot showing distributions of frequency location of the valleypeak feature for equal numbers of fingerprint, face, and iris images 

in a mixed biometric dataset. 
NISTIR 7599 Page 27 08/19/2009 

Fig.19 Plot of false positive vs. false negative error rates with 

variation of threshold value of peak height used as a 

classifier applied to the mixed biometric dataset. Feature 

frequency maximum was set at 0.15 cycles/pixel. 

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

X: 0.02

Y: 0.066

Proportion

Peak Height Threshold

False Positive

False Negative

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Frequency (cycles/pixel)

Peak Height (dB)

Peak Height vs. Frequency - Mixed Biometric

Fingerprint

Face

Iris

Fig. 18 Peak height (dy) vs. frequency of SIVV output for images of the Mixed 

Biometric 1 dataset. Note the separation of fingerprints into clusters 

corresponding to the 1000 ppi and 500 ppi samples. 
In the preceding EER analysis only the peak height feature is used for classification, though 

constrained via a maximum limit on frequency position. From examination of the 

distributions of all the features, however, it is not clear that consideration of the other 

features in a simple fashion will be adequate to enhance the classification performance 

beyond that reported here. Training a support vector machine (SVM) or other learning model 

would yield a more sophisticated integration of the multiple features. However, it is also 

possible that a more precise representation of the spectral shape, i.e. beyond merely the 

major peak, would provide greater classification accuracy. That is, examination of some of 

the non-fingerprint images that exhibited a peak feature similar to that of the fingerprint also 

exhibited peaks at higher frequencies that would differentiate them from fingerprints. Hence 

a follow-on effort will examine the spectrum itself in greater detail via additional features 

representing average or total power in each of some small number of frequency bands of the 

spectrum in addition to the features currently output. For example, the frequency extending 

from 0.0 to 0.5 cycles/pixel might be examined over each of 10 intervals of 0.05 cycles/pixel 

in width. A classification model based on these additional 10 features together with those 

already discussed might improve the classification accuracy. 

NISTIR 7599 Page 28 08/19/2009 
6. CONCLUSIONS 

The spectral image validation and verification (SIVV) method proposed here demonstrates 

its utility as a means for screening fingerprint databases for poorly segmented specimens and 

for non-fingerprint images that may have been included in the database. The magnitude of 

the distinctive spectral feature related directly to the level 1 ridge flow feature of the 

fingerprint provides a primary diagnostic indicator of the presence of a fingerprint image. 

The frequency location of the feature provides a secondary classification metric and on a 

coarse level verifies the reported scan sample rate of the fingerprint image. Using only a 

simple threshold criterion based on these two features, the SIVV utility was able to limit 

classification EER to 10% or less for a mixed image dataset, including many images 

intentionally selected to confuse the algorithm, and a dataset including fingerprints amidst 

face and iris images. Efforts toward improving performance may include use of a more 

sophisticated classification model using additional features available in the 1D power 

spectrum. 

NISTIR 7599 Page 29 08/19/2009 
NISTIR 7599 Page 30 08/19/2009 
7. REFERENCES 

[1] E. Tabassi, C. L. Wilson, C. I. Watson, "Fingerprint Image Quality: NISTIR 7151:," 

National Institute of Standards and Technology, Gaithersburg, NISTIR 08/19/2004 

2004. 

[2] E. Tabassi and C. L. Wilson, "A novel approach to fingerprint image quality," in Image 

Processing, 2005. ICIP 2005. IEEE International Conference on, 2005, pp. II-40. 

[3] F. Alonso-Fernandez, J. Fierrez, J. Ortega-Garcia, J. Gonzalez-Rodriguez, H. Fronthaler, 

K. Kollreider, and J. Bigun, "A Comparative Study of Fingerprint Image-Quality 

Estimation Methods," Information Forensics and Security, IEEE Transactions on, 

vol. 2, pp. 734-743, 2007. 

[4] M. S. Altarawneh, W. L. Woo, and S. S. Dlay, "Objective Fingerprint Image Quality 

Assessment using Gabor Spectrum Approach," in Digital Signal Processing, 2007 

15th International Conference on, 2007, pp. 248-251. 

[5] T. P. Chen, x. Jiang, and W. Y. Yau, "Fingerprint image quality analysis," in Image 

Processing, 2004. ICIP '04. 2004 International Conference on, pp. 24-27. 

[6] H. Lin, W. Yifei, and A. Jain, "Fingerprint image enhancement: algorithm and 

performance evaluation," Pattern Analysis and Machine Intelligence, IEEE 

Transactions on, vol. 20, pp. 777-789, 1998. 

[7] D. Maio and D. Maltoni, "Ridge-line density estimation in digital images," in Pattern 

Recognition, 1998. Proceedings. Fourteenth International Conference on, pp. 534-

538. 

[8] Y. Yin, J. Tian, and X. Yang, "Ridge distance estimation in fingerprint images: 

Algorithm and performance evaluation," Eurasip Journal on Applied Signal 

Processing, vol. 2004, pp. 495-502, 2004. 

[9] E. Lim, J. Xudong, and Y. Weiyun, "Fingerprint quality and validity analysis," in Image 

Processing. 2002. Proceedings. 2002 International Conference on, 2002, pp. I-469. 

[10] C.-j. Wang, Y.-b. Yang, W.-j. Li, and S.-f. Chen, "Image texture representation and 

retrieval based on power spectral histogram," in Tools with Artificial Intelligence, 

2004. ICTAI 2004. 16th IEEE International Conference on, 2004, pp. 491-495. 

[11] L. Xiuwen and W. DeLiang, "Texture classification using spectral histograms," 

Image Processing, IEEE Transactions on, vol. 12, pp. 661-670, 2003. 

[12] N. B. a. B. Nill, B. H., "Objective Image Quality Measure Derived from Digital 

Image Power Spectra," Optical Engineering, vol. 31, pp. 813-825, 1992. 

[13] F. J. Harris, "On the use of windows for harmonic analysis with the discrete Fourier 

transform," Proceedings of the IEEE, vol. 66, pp. 51-83, 1978. 

[14] A. V. a. R. W. S. Oppenheim, "Discrete-Time Signal Processing," Upper Saddle 

River, NJ: Prentice-Hall, 1999, pp. pp. 468-471. 

NISTIR 7599 Page 31 08/19/2009 
[15] I. American National Standards Institute, NIST Special Publication 500-275 - 

American National Standard for Information Systems -- Data Format for the 

Interchange of Fingerprint, Facial, & Other Biometric Information - Part 2: XML 

Version. Gaithersburg, MD: U.S. DOC/National Institute of Standards and 

Technology, 2008. 

[16] F. Gustafsson, "Determining the initial states in forward-backward filtering," IEEE 

Transactions on Signal Processing, vol. 44, pp. pp.988–992, April 1996, 1996. 

[17] I. Sobel, and G. Feldman, "A 3x3 Isotropic Gradient Operator for Image Processing, 

presented talk at the Stanford Artificial Project 1968, unpublished," in Pattern 

Classification and Scene Analysis, R. a. P. H. Duda, Ed. Menlo Park, CA: John Wiley 

& Sons, 1973, p. 482. 

[18] J. Canny, "A Computational Approach to Edge Detection," Pattern Analysis and 

Machine Intelligence, IEEE Transactions on, vol. PAMI-8, pp. 679-698, 1986. 

[19] C. E. Shannon, "Communication in the Presence of Noise (Classic Paper Reprint) " 

Proceedings of the IEEE, vol. 86, pp. 447-457, February 1998 1998. 

[20] M. Unser, "Sampling - 50 Years After Shannon," Proceedings of the IEEE, vol. 88, 

pp. 569-587, April 2000 2000. 

[21] M. Frigge, David C. Hoaglin, and Boris Iglewicz, "Some implementations of the 

Boxplot," The American Statistician, vol. 43, pp. 50-54, 1998. 

[22] J. W. Tukey, Exploratory Data Analysis. Reading, MA: Addison-Wesley, 1977. 

NISTIR 7599 Page 32 08/19/2009 
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8. APPENDIX A: DEMONSTRATION OF ROTATION INVARIANCE 

Experiments indicate the 1D spectrum to be largely invariant to in-plane rotation of the 

fingerprint. In order to avoid effects of cropping or scale change that would result from 

rotating a rectangular image, circular regions of interest are extracted from the original 

images. The fingerprint samples are rotated by resampling using bicubic interpolation. In the 

case of 90° rotation, the image transpose is used. Figs A-1 & A-2 demonstrate the stability of 

the 1D spectral representation over rotation for two images. 

Fig. A-1 Circular sample of a rolled fingerprint image (1029 x 

1023) captured at 1000 ppi. Original orientation (top) is 

rotated 45° and 90°. 

Input Img.

0 0.2 0.4

0.4

0.5

0.6

0.7

0.8

0.9

1

 Log Power (db)

 Frequency (cycles/pixel)

 Log Power Spectrum

Input Img.

0 0.2 0.4

0.4

0.5

0.6

0.7

0.8

0.9

1

 Log Power (db)

 Frequency (cycles/pixel)

 Log Power Spectrum

Input Img.

0 0.2 0.4

0.4

0.5

0.6

0.7

0.8

0.9

1

 Log Power (db)

 Frequency (cycles/pixel)

 Log Power Spectrum
NISTIR 7599 Page 34 08/19/2009 

Fig. A-2 Circular sample of a slap-four image (2012 x 

2064) captured at 1000 ppi. Original orientation 

(top) is rotated 45° and 90°. 

Input Img.

0 0.2 0.4

0.4

0.5

0.6

0.7

0.8

0.9

1

 Log Power (db)

 Frequency (cycles/pixel)

 Log Power Spectrum

Input Img.

0 0.2 0.4

0.4

0.5

0.6

0.7

0.8

0.9

1

 Log Power (db)

 Frequency (cycles/pixel)

 Log Power Spectrum

Input Img.

0 0.2 0.4

0.4

0.5

0.6

0.7

0.8

0.9

1

 Log Powe

 Frequency (cycles/pixel)

r (db)

 Log Power Spectrum
9. APPENDIX B: TEST DATA 

Performance of the software relative to the designed use of fingerprint image validation and 

verification (IV&V) is evaluated with respect to several fingerprint and non-fingerprint 

databases. The databases used are characterized as follows: 

A fingerprint database, here referred to as SD27_1000, consists of images digitized at a 

sample rate of 1000 ppi from FBI standard 10-print cards. The individual images include 

rolled ink prints of each of the 10 fingers, plain impressions of each of the two thumbs, and 

plain “slap-four” impressions of the right and left hands. The dataset includes images from 

212 fingerprint cards with 14 images per card for a total of 2968 images. 

A second dataset is derived from this image set by resampling the 1000 ppi images to 500 

ppi, with application of a low-pass filter to reduce the effects of aliasing due to undersampling the original images. This dataset is referred to as SD27_500. 

A third fingerprint dataset, referred to as SD29_Plain consists of 1188 plain impressions of 

fingers 1-10. These fingerprints were digitized at 500 ppi via scanning of the inked 

impressions. 

The mixed data set referred to as ImagesTest02 consists of a variety of images largely 

downloaded from the Internet (e.g. Google Images collection) and various other public 

sources. The 331 downloaded images include a small number of biometric data samples such 

as fingerprints, iris, and face at various scales included in website libraries. Many nonbiometric images in this sample were selected on the basis of their exhibiting periodic 

structure that might generate a spectrum similar to that of a fingerprint. Others images 

include portraits, trees, landscapes, buildings, textured materials, and other subjects at a 

variety of pixel resolutions. 

ImagesTest02 contained a relatively small number of actual fingerprint images. Accordingly, 

the dataset was expanded for testing by adding a random sample of fingerprint images drawn 

from the three fingerprint datasets, SD27_1000, SD27_500, and SD29. Thus, to the original 

331 images of the mixed set were added 300 additional images including 100 images drawn 

from each of the fingerprint datasets for a total of 631 images. We refer to this fourth dataset 

as ImagesTest03. 

Finally, fifth and sixth datasets, Mixed Biometric1 and Mixed Biometric2, were constructed 

to examine relative distributions of the three biometrics and to examine classification rates 

for fingerprints against the background of non-fingerprint biometrics. A suite of face and iris 

NISTIR 7599 Page 35 08/19/2009 
NISTIR 7599 Page 36 08/19/2009 

images was obtained from Phillips and Scallan of NIST. These images are part of the dataset 

assembled for use in the Multi-Biometric Grand Challenge (MBGC)vii conducted by these 

researchers. The face images consist of frontal posed subjects imaged at a range of scales 

from full-frame face to images in which the subject is at a considerable distance from the 

camera with the face occupying only a very small area of a natural scene image. In a number 

of these images the comparatively small area face is imaged against a background often 

consisting of a brick wall. In some cases subjects are wearing striped or plaid clothing. The 

iris images are acquired using short wavelength infra-red (near-IR) lighting and include the 

entire eye, including eyelashes. In most of the images, the iris is nearly all visible or only 

slightly cropped. In many of the iris images, the eyebrow is visible. 

Mixed Biometric 1 used to compare distributions of spectral features was constructed from 

equal sized random samples of face, iris, and fingerprint images (3000 of each). For the 

classification experiment, fingerprint vs. non-fingerprint, a random sample of 3000 

fingerprint images was combined with 1500 each of face and iris images to form Mixed 

Biometric 2. 

 

vii http://face.nist.gov/mbgc/
10. APPENDIX C: DISTRIBUTIONS OF SIVV FEATURES 

Figs C-1 – C-3 exhibit box and whisker plots [21, 22] summarizing the distributions of the 

peak height (dy) values grouped by finger designation for the three fingerprint datasets. In 

each figure, the enclosed region, the box, includes observations within the 25th and 75th

percentiles with the median (50th percentile) indicated by the red line. The vertical lines 

terminated by a short horizontal line extend for 1.5 times the lower and upper interquartile 

ranges. Observations beyond these intervals are considered to be outliers and are indicated by 

the red "plus" symbols. The notches centered on the medians indicate the 95 % confidence 

intervals of the medians and can be used to compare medians across the various boxes. For 

example, a median included within the notched region of another is not significantly different 

in the statistical sense, though one is advised to make such an interpretation with caution. In 

practice, we are more impressed with significant offset between boxes. 

Figs C-1 and C-2 show respectively the peak height distributions for the 1000 ppi and 500 

ppi images of the SD27 dataset. Within each of the figures, the distributions are similar 

among the rolled prints, having the designations 1 – 10, though heights are slightly higher for 

the lower sample rate. In both cases the peak heights are reduced significantly for the plain 

thumb impressions, 11 and 12, and for the slap-four plain impressions of 13 and 14. 

Inspection of images finds that in general the contrast is higher with the rolled prints, and the 

ridge pattern occupies a greater proportion of the image area than in the plain impressions. 

Moreover, handwritten content on many cards is placed over the plain print regions of the 

card, introducing frequency content in potential conflict with that of the ridge pattern. 

The position of the valley-peak structure, taken as the midpoint between the valley minimum 

and the peak maximum, are also consistent among the rolled prints 1 – 10, with the bulk of 

the values falling between 0.03 cycles/pixel and 0.05 cycles/pixel for the 1000 ppi images 

(see fig. C-4) and between 0.07 cycles/pixel and 0.09 cycles/pixel for 500 ppi images as 

shown in figs C-5 and C-6. Inasmuch as the ridge frequency metric for each print represents 

an average over the entire print, and in fact, the entire image, a more precise position is not 

expected. The distribution for the plain single thumb prints, 11 and 12, exhibit much greater 

variability and a noticeable shift toward higher frequency relative to the distributions for the 

rolled prints. By contrast, the frequency position for the plain slap-four prints, 13 and 14, is 

distributed with smaller variance than the other distributions and the frequency position is 

slightly lower than that of the rolled prints. 

NISTIR 7599 Page 37 08/19/2009 
NISTIR 7599 Page 38 08/19/2009 

0

0.02

0.04

0.06

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0.1

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0.14

0.16

0.18

0.2

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Finger

Peak Height - SD27_1000ppi

Peak Height (dB)

Fig. C-1 Box plot showing distributions of peak height (dy) by finger for SD27 

dataset sampled at 1000 ppi. Fingers 1 – 10 are rolled inked prints on 

FBI 10-print cards; 11 and 12 are plain impressions of thumbs; and 13 

and 14 are slap-four prints of left and right hands. 

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Finger

Peak Height - SD27_500ppi

Peak Height (dB)

Fig. C-2 Box plot showing distributions of peak height (dy) by finger for SD27 

dataset down-sampled (with anti-aliasing) to 500 ppi. Fingers 1 – 10 are 

rolled inked prints on FBI 10-print cards; 11 and 12 are plain impressions of 

thumbs; and 13 and 14 are slap-four prints of left and right hands. 
NISTIR 7599 Page 39 08/19/2009 

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

1 2 3 4 5 6 7 8 9 10

Finger

Peak Height - SD29_500ppi

Peak Height (dB)

Fig. C-3 Box plot showing distributions of peak height (dy) by 

finger for SD29 dataset sampled at 500 ppi. Fingers 1 – 10 are 

plain inked prints. 

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Finger

Frequency - SD27_1000ppi

Feature Frequency (cycles/pixel)

Fig. C-4 Box plot showing distributions of peak frequency location of the 

valley-peak feature by finger for SD27 dataset sampled at 1000 ppi. 

Fingers 1 – 10 are rolled inked prints on FBI 10-print cards; 11 and 12 

are plain impressions of thumbs; and 13 and 14 are slap-four prints of 

left and right hands. 
NISTIR 7599 Page 40 08/19/2009 

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Finger

Frequency - SD27_500ppi

Feature Frequency (cycles/pixel)

Fig. C-5 Box plot showing distributions of frequency location of the valley-peak 

feature by finger for SD27 dataset down-sampled (with anti-aliasing) to 500 

ppi. Fingers 1 – 10 are rolled inked prints on FBI 10-print cards; 11 and 12 

are plain impressions of thumbs; and 13 and 14 are slap-four prints of left 

and right hands. 

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

1 2 3 4 5 6 7 8 9 10

Finger

Frequency - SD29_500ppi

Feature Frequency (cycles/pixel)

Fig. C-6 Box plot showing distributions of frequency location of the 

valley-peak feature by finger for SD29 dataset sampled at 500 

ppi. Fingers 1 – 10 are plain inked prints. 
NISTIR 7599 Page 41 08/19/2009