Development of NFIQ 2.0 

Quality Feature Definitions 

Version 0.5
Development of NFIQ 2.0 Quality Feature Definitions

2 

Contents 

1 Introduction ....................................................................................................................................4

2 Frequency Domain Analysis............................................................................................................4

3 Gabor Segment

Gabor Shen .

Gabor

Local Clarity Score ...

Mu Mu Block

Mu Mu Sigma Block

Mu Sigma Block

Mu

Orientation Flow 

Orientation Certainty Level 

Radial Power Spectrum ..

Ridge Valley Uniformity

Sigma Mu Block ..

Sigma

...............................................................................................................................7

4 ...................................................................................................................................10

5 ............................................................................................................................................13

6 ......................................................................................................................17

7 .................................................................................................................................21

8 ......................................................................................................................21

9 .............................................................................................................................22

10 .............................................................................................................................................22

11 ......................................................................................................................23

12 .......................................................................................................26

13 ...........................................................................................................28

14 ............................................................................................................30

15 .......................................................................................................................33

16 .........................................................................................................................................34

17 References ................................................................................................................................34

List of Figures 

Figure 1-1. Illustration of block and pixel indexing within an image I. Shown is the pixel I(1,1), the 

block V(1,1), the block dimensions Bw, Bh and the image dimensions X and Y. ................................... 4

List of Tables 

Table 1-1. Common notation used in this document. ............................................................................ 3

Table 2-1. Frequency Domain Analysis summary. .................................................................................. 4

Table 2-2. Frequency Domain Analysis input variables. ......................................................................... 4

Table 2-3. Visualization of processing steps for Frequency Domain Analysis. ....................................... 7

Table 3-1. Gabor Segment summary. ..................................................................................................... 7

Table 3-2. Gabor Segment input variables.............................................................................................. 8

Table 3-3. Visualization of processing steps in Gabor Segment. ..........................................................10

Table 4-1. Gabor Shen summary. ..........................................................................................................10

Table 4-2. Gabor Shen input variables. ................................................................................................. 11

Table 4-3. Visualization of processing steps in Gabor Shen. ................................................................13

Table 5-1. Gabor summary. ..................................................................................................................13

Table 5-2. Gabor input variables. ..........................................................................................................14

Table 5-3. Visualization of processing steps in Gabor. .........................................................................16

Table 6-1. Local Clarity Score summary. ...............................................................................................17

Table 6-2. Local Clarity Score input variables. ......................................................................................17

Table 6-3. Visualization of processing steps in Local Clarity Score. ......................................................21

Table 7-1.Summary of Mu Mu Block. ...................................................................................................21

Table 7-2. Mu Mu Block input variables. ..............................................................................................21

Table 8-1. Mu Mu Sigma Block summary. ............................................................................................21
Development of NFIQ 2.0 Quality Feature Definitions

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Table 8-2. Mu Mu Sigma Block input variables. ....................................................................................22

Table 9-1. Mu Sigma Block summary. ...................................................................................................22

Table 9-2. Mu Sigma Block input variables. ..........................................................................................22

Table 10-1. Mu summary. .....................................................................................................................22

Table 10-2. Mu input variables. ............................................................................................................23

Table 11-1. Orientation Flow summary. ...............................................................................................23

Table 11-2. Orientation Flow input variables. ......................................................................................23

Table 11-3. Visualization of processing steps in Orientation Flow. ......................................................25

Table 12-1. Orientation Certainty Level summary. ...............................................................................26

Table 12-2. Orientation Certainty input variables. ...............................................................................26

Table 12-3. Visualization of processing steps in Orientation Certainty Level. ......................................28

Table 13-1. Radial Power Spectrum summary. .....................................................................................28

Table 13-2. Radial Power Spectrum input variables. ............................................................................28

Table 13-3. Visualization of processing steps in Radial Power Spectrum. ............................................30

Table 14-1. Ridge Valley Uniformity summary. ....................................................................................30

Table 14-2. Ridge Valley Uniformity input variables.............................................................................30

Table 14-3. Visualization of processing steps in Ridge Valley Uniformity. ...........................................33

Table 15-1. Sigma Mu Block summary. ................................................................................................. 33

Table 15-2. Sigma Mu Block summary. ................................................................................................. 33

Table 16-1. Sigma summary. .................................................................................................................34

Table 16-2. Sigma input variables. ........................................................................................................34

Notation 

An overview of the common notation used throughout this document is given in Table 1-1 and an 

illustration of the image indexing is given in Figure 1-1. 

Variable Description 

 Image width in pixels (horizontal). 

 Image height in pixels (vertical).

 Image intensity where denotes the pixel in the upper left corner. 

 Block width. 

 Block height. 

 Image block where denotes the block in the upper left corner. 

Table 1-1. Common notation used in this document. 
Development of NFIQ 2.0 Quality Feature Definitions

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V(1,1) I(1,1)

Bh

Bw X

Y

Figure 1-1. Illustration of block and pixel indexing within an image I. Shown is the pixel I(1,1), the block V(1,1), the block 

dimensions Bw, Bh and the image dimensions X and Y.

1 Introduction 

This document provides definitions of potential quality features implemented for the NIST 

Fingerprint Image Quality 2.0 (NFIQ 2.0) algorithm. The structure of the document is such that each 

quality feature definition contains a summarizing table, a high level feature description, and a stepby-step algorithm listing, which optionally has in depth descriptions of particular steps. Additionally, 

algorithm processing steps are illustrated using two images (one of high quality, one of low quality). 

2 Frequency Domain Analysis 

Quality Feature Summary

Origin ISO/IEC TR 29794-4:2010 (ISO/IEC, 2010) – Clause 6.2.2.3 

NFIQ 2.0 Identifier FDA_#

Acronyms FDA

Table 2-1. Frequency Domain Analysis summary. 

2.1 Description 

The Frequency Domain Analysis algorithm operates in a block-wise manner. A signature of the ridgevalley structure is extracted and the DFT is computed to determine the frequency of the sinusoid 

following the ridge-valley structure. 

2.2 Variables

Name Default Description

- Input image

32 Block height in pixels

32 Block width in pixels 

- Segmentation mask

Table 2-2. Frequency Domain Analysis input variables. 

II

Bh

Bw

Imask
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2.3 Algorithm 

2.a For each block determine the dominant ridge flow orientation. 

2.b Rotate the block such that the dominant ridge flow is perpendicular to the x-axis. 

2.c Crop regions of block such that no invalid regions are included in the block. 

2.d Calculate, in the rotated block, the mean value along the y-axis (ridge flow) to derive the 

ridge-valley signature . 

2.e Calculate the DFT Fourier spectrum of as 

2.f Discard the DC component of resulting in containing the remaining coefficients. 

2.g Determine the term index in as the term with the largest magnitude . 

2.h The final Frequency Domain Analysis score is the mean of scores assigned to foreground 

blocks as defined by . 

2.4 Extracting the ridge-valley signature 

 

 

 

 

 

2.5 Computing the Frequency Domain Analysis score 

 

 

 

 
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2.6 Notes 

The value of is undefined if or as is not a valid index. 

Workaround in that case is to set . Despite ISO recommendation of a high quality value 

indicating a high quality, this is not the case for Frequency Domain Analysis as specified in ISO/IEC TR 

29794-4:2010. 

2.7 Processing steps 

Processing steps for Frequency Domain Analysis

Input (FVC2000Db1 1_1.bmp) Input (FVC200Db1 100_1.bmp)

Input with block grid and current block marked in blue

Zoomed view of current block

Block rotated

Block cropped
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Processing steps for Frequency Domain Analysis

Block mean intensity values

Block DFT

Map of FDA quality values where with grey value correspond to high value (low local quality). 

Table 2-3. Visualization of processing steps for Frequency Domain Analysis. 

3 Gabor Segment 

Quality Feature Summary

Origin

NFIQ 2.0 Identifier GS_#

Acronyms GSG, GaborSeg

Table 3-1. Gabor Segment summary. 

3.1 Feature Description 

Same as Gabor with the exception that the image is initially convolved with a 2D Gaussian kernel 

with instead of . Additionally a quantization to 2 levels is applied before computing the 

final quality score. 
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3.2 Variables 

Name Default Description

 - Input image. 

 6 2D Gaussian standard deviation in x-direction. 

 6 2D Gaussian standard deviation in y-direction. 

 4 Size of filter bank (orientations of the Gabor wave). 

 0.1 Gabor filter frequency .

Table 3-2. Gabor Segment input variables. 

3.3 Algorithm 

3.a Convolve input image with a 2D Gaussian kernel with and subtract from input image 

3.b Compute the Gabor response of the image for each orientation 

3.c Convolve the magnitude (complex modulus) of each Gabor response with a 2D Gaussian 

kernel with 

3.d Compute the standard deviation of the Gabor magnitude response values at each location 

yielding a map of standard deviations. 

3.e Quantize the standard deviation map into two levels. 

3.f Sum the map standard deviations and normalize according to number of sample points 

(typically image size) to produce the final Gabor quality score. 

3.4 Quantize to two levels 

Quantizing the map of standard deviations into two levels is done by first determining the 

cumulative distribution function for pixel intensity values. Next a threshold is determined such that 

the probability of a pixel belonging to background is the same as that for belonging to the 

foreground. Thus the quantized image can serve as a foreground segmentation. 

3.5 Notes 

The Gabor Segment quality feature is resolution dependent. The given defaults assume 500ppi. 

3.6 Processing steps 

Processing steps for Gabor Segment

Real part of Gabor filter Imaginary part of Gabor filter
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Processing steps for Gabor Segment

Input (FVC2000Db1 1_1.bmp) Input (FVC200Db1 100_1.bmp)

Input image subtracted with input image convolved with Gaussian

Gabor response at orientation 0

Gabor response at orientation 1/4

Gabor response at orientation 2/4
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Processing steps for Gabor Segment

Gabor response at orientation 3/4

Standard deviation of filter responses

Segmentation of standard deviation of filter responses into two levels 

Table 3-3. Visualization of processing steps in Gabor Segment. 

4 Gabor Shen 

Quality Feature Summary 

Origin L. Shen, A. C. Kot, and W. M. Koo. Quality measures of fingerprint images. 

(Shen, et al., 2001) 

NFIQ 2.0 Identifier GSh_#

Acronyms GSH

Table 4-1. Gabor Shen summary. 

4.1 Feature Description 

Gabor based feature separating blocks into two classes: good and bad. Quality is the ratio between 

number of foreground blocks and number of foreground blocks marked as poor. 
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4.2 Variables 

Name Default Description 

 - Input image. 

 1 Threshold for foreground/background segmentation. 

 2 Threshold for poor/good block segmentation. 

Table 4-2. Gabor Shen input variables. 

4.3 Algorithm 

4.a Divide the image into blocks of size . 

4.b Compute the Gabor filters. 

4.c For each block centered at pixel compute the Gabor responses. 

4.d For each block, compute the standard deviation of the Gabor responses in that block. 

4.e Use to segment foreground/background of the image 

4.f Determine the set of blocks, , belonging to the foreground as those where 

4.g Determine the set of blocks, , which are of poor quality and foreground as those where 

 

4.h Compute the quality score as 

 

4.4 Notes 

The Gabor Shen quality feature is resolution dependant. The given defaults assume 500ppi. 

Shen et. al suggest the following : 

 

 

 

 

 and are manually determined according to dataset. 

4.5 Processing steps 

Processing steps for Gabor Shen 

Real part of Gabor filter Imaginary part of Gabor filter
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Processing steps for Gabor Shen 

Input (FVC2000Db1 1_1.bmp) Input (FVC200Db1 100_1.bmp) 

Gabor response at orientation 0 

Gabor response at orientation 1/4 

Gabor response at orientation 2/4 

Gabor response at orientation 3/4 
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Processing steps for Gabor Shen 

Standard deviation of filter responses 

Blockwise mean of filter responses

Foreground blocks

Blocks marked as poor

Table 4-3. Visualization of processing steps in Gabor Shen. 

5 Gabor 

Quality Feature Summary 

Origin Olsen, Xu, Busch, Gabor Filters as Candidate Quality Measure for NFIQ 

2.0.(Olsen, et al., 2012) 

NFIQ 2.0 Identifier GABOR_#

Acronyms GAB

Table 5-1. Gabor summary. 
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5.1 Feature Description 

The Gabor quality feature operates on a per-pixel basis by calculating the standard deviation of the 

Gabor filter bank responses. The size of the filter bank is used to determine a number of filters 

oriented evenly across the half circle. The strength of the response at a given location corresponds 

to the agreement between filter orientation and frequency in the location neighborhood. For areas 

in the fingerprint image with a regular ridge-valley pattern there will be a high response from one or 

a few filter orientations. In areas containing background or unclear ridge-valley structure the Gabor 

response of all orientations will be low and constant. 

5.2 Variables 

Name Default Description

 - Input image

 6 2D Gaussian standard deviation in x-direction 

 6 2D Gaussian standard deviation in y-direction 

 4 Size of filter bank (orientations of the Gabor wave)

 0.1 Gabor filter frequency 

Table 5-2. Gabor input variables. 

5.3 Algorithm 

5.a Convolve input image with a 2D Gaussian kernel with and subtract it from the input 

image to give 

5.b Compute the Gabor response of for each orientation 

5.c Convolve the magnitude (complex modulus) of each Gabor response with a 2D Gaussian 

kernel with 

5.d Compute the standard deviation of the Gabor magnitude response values at each location 

yielding a map of standard deviations. 

5.e Sum the map of standard deviations and normalize according to number of sample points 

(typically image size) to produce the final Gabor quality score. 

5.4 The Gabor filter 

The general form of the complex 2D Gabor(Daugman, 1985) filter in the spatial domain is given 

by: 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

where 

 

and 

 

and f is the frequency (cycles/pixel) of the sinusoidal plane wave along the orientation . The size of 

the Gaussian smoothing window is determined by 
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The filter bank size n is used to compute the differently oriented Gabor filters composing the filter 

bank. Computing given n is done as : 

 

 

 

 

5.5 Notes 

The Gabor quality feature is resolution dependent. The given defaults assume 500ppi. 

5.6 Processing steps 

Processing steps for Gabor

Real part of Gabor filter Imaginary part of Gabor filter

Input (FVC2000Db1 1_1.bmp) Input (FVC200Db1 100_1.bmp)

Subtraction of image convolved with Gaussian.

Gabor response for filtered image at orientation 0
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Processing steps for Gabor 

Gabor response for filtered image at orientation 1/4 

Gabor response for filtered image at orientation 2/4 

Gabor response for filtered image at orientation 3/4

Gaussian filtered Gabor response for filtered image at orientation 3/4

Standard deviation of Gaussian filtered responses

Table 5-3. Visualization of processing steps in Gabor. 
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6 Local Clarity Score 

Quality Feature Summary 

Origin ISO/IEC TR 29794-4:2010 (ISO/IEC, 2010) – Clause 6.2.2.2 

NFIQ 2.0 Identifier LCS_# 

Acronyms LCS, Ridge-valley Structure 

Table 6-1. Local Clarity Score summary. 

6.1 Feature Description 

Local Clarity Score (LCS) computes the block wise clarity of ridge and valleys by applying linear 

regression to determine a gray-level threshold, classifying pixels as ridge or valley. A ratio of 

misclassified pixels is determined by comparing with the normalized ridge and valley width of that 

block. 

6.2 Variables 

Name Default Description 

 - Input image 

 32 Block height in pixels 

 32 Block width in pixels 

 - Segmentation mask 

Table 6-2. Local Clarity Score input variables. 

6.3 Algorithm 

6.a For each block in the image determine the dominant ridge flow orientation to create an 

orientation line which is perpendicular to the ridge flow. 

6.b Align such that the orientation line is horizontal to create . 

6.c From extract a block which is centered around the orientation line. 

6.d Compute the average profile of . 

6.e Determine a threshold by applying linear regression on . 

6.f Determine the proportion of misclassified pixels and in the ridge and valley regions. 

6.g Determine the normalized ridge width and valley width  and . 

6.h Compute the final quality score . 

6.4 Computing the average profile of a block 

Given the block the average profile is obtained by 

 

 

  

 

 

 

where is the height of the block. 
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6.5 Determining the proportion of misclassified pixels 

For a block there are pixels in the valley region and pixels in the valley region with intensity 

lower than a threshold . Similarly there are pixels in the ridge region and pixels in the ridge 

region with intensity lower than a threshold . and are expressions of these ratios. 

 

 

 

 

 

 

6.6 Determining the normalized ridge and valley width 

The normalized valley width  and the normalized ridge width  are determined 

 

 

 

 

 

 

 

 

 

 

where is the scanner resolution in dpi, is the estimated ridge or valley width for an image 

with 125 dpi resolution, and  and  are the observed valley and ridge widths. According to 

(ISO/IEC, 2010) is reasonable for 125 dpi resolution. 

6.7 Computing the Local Clarity Score 

The final quality score is computed using the average value of and in valid ridge and valley 

regions:

 

 

 

 

 

 

 

 

where 

 and  are the minimum values for the normalized ridge and valley width, and 

 

 and  are the maximum values for the normalized ridge and valley width. 

6.8 Notes 

Particular regions inherent in a fingerprint will negatively affect . For example, ridge endings 

and bifurcations or areas with high curvature such as those commonly found in core and delta 

points. 
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Processing steps 

Processing steps for Local Clarity Score 

Input (FVC2000Db1 1_1.bmp) Input (FVC200Db1 100_1.bmp) 

Input with grid and block marked in blue 

Zoomed view of block 

Block rotated to align ridgelines vertically (block ) 

Extracted section of the block ( ) 

Projected mean gray intensity values ( ) 
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Processing steps for Local Clarity Score 

.

Ridge-valley profile as found by mean values. Red line indicates the threshold for ridge-valley 

separation 

 Ridge-valley separation. Ridges shown in black, valleys in white. The mean intensity values are 

shown above for comparison. 

Ridge areas composed into one block. 

Shown in white are the parts of the fingerprint which were determined to be ridge but do not belong 

to ridge as defined by the threshold.

Valley areas composed into one block. 

Shown in white are the parts of the fingerprint which were determined to be valley but do not 

belong to valley as defined by the threshold. 
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Processing steps for Local Clarity Score 

Map of local clarity scores. High intensity corresponds to high local clarity. 

Table 6-3. Visualization of processing steps in Local Clarity Score. 

7 Mu Mu Block 

Quality Feature Summary 

Origin 

NFIQ 2.0 Identifier MMB_# 

Acronyms MMB

Table 7-1.Summary of Mu Mu Block. 

7.1 Feature Description 

Mu Mu Block is the mean of the block wise mean pixel intensity value in the input image. 

7.2 Variables 

Name Default Description 

 - Input image. 

 32 Block height in pixels. 

 32 Block width in pixels. 

Table 7-2. Mu Mu Block input variables. 

7.3 Algorithm 

7.a For each block in compute the mean pixel intensity. 

7.b Compute the mean of mean pixel intensities. 

8 Mu Mu Sigma Block 

Quality Feature Summary 

Origin 

NFIQ 2.0 Identifier MMSB_# 

Acronyms MMSB 

Table 8-1. Mu Mu Sigma Block summary. 

8.1 Feature Description 

Mu Mu Sigma Block is the mean of the block wise standard deviation pixel intensity value in the 

input image subtracted the block wise standard deviation.
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8.2 Variables 

Name Default Description 

 - Input image. 

 32 Block height in pixels. 

 32 Block width in pixels. 

Table 8-2. Mu Mu Sigma Block input variables. 

8.3 Algorithm 

8.a For each block in compute the mean pixel intensity. 

8.b Compute the mean of the mean pixel intensities. 

8.c Subtract the standard deviation of pixel intensities in . 

9 Mu Sigma Block 

Quality Feature Summary 

Origin 

NFIQ 2.0 Identifier MSB_# 

Acronyms MSB 

Table 9-1. Mu Sigma Block summary. 

9.1 Feature Description 

Mu Sigma Block is the mean of the block wise standard deviation pixel intensity value in the input 

image. 

9.2 Variables 

Name Default Description 

 - Input image. 

 32 Block height in pixels. 

 32 Block width in pixels. 

Table 9-2. Mu Sigma Block input variables. 

9.3 Algorithm 

9.a Compute the standard deviation of blockwise pixel intensities. 

9.b Compute the mean of the standard deviations. 

10 Mu

Quality Feature Summary 

Origin 

NFIQ 2.0 Identifier Mu_# 

Acronyms MUQ 

Table 10-1. Mu summary. 

10.1 Feature Description 

Mu is the mean pixel intensity value in the input image. 
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10.2 Variables 

Name Default Description 

 - Input image. 

Table 10-2. Mu input variables. 

10.3 Algorithm 

10.a Compute the mean intensity of 

10.4 Computing the mean intensity 

 

 

 

 

 

 

 

11 Orientation Flow 

Quality Feature Summary 

Origin ISO/IEC TR 29794-4:2010 (ISO/IEC, 2010) - Clause 6.3.2.1 

NFIQ 2.0 Identifier OF_# 

Acronyms OF

Table 11-1. Orientation Flow summary. 

11.1 Feature Description 

Orientation Flow is a measure of ridge flow continuity which is based on the absolute orientation 

difference between a block and its neighboring blocks. 

11.2 Variables 

Name Default Description 

 - Input image. 

 32 Block height in pixels. 

 32 Block width in pixels. 

 - Segmentation mask. 

 0 Tolerance to angular change in the orientation flow (in 

degrees). 

Table 11-2. Orientation Flow input variables. 

11.3 Algorithm 

11.a For each block in determine the dominant ridge flow orientation. 

11.b Compute the absolute orientation difference for each block . 

11.c Compute the local orientation quality score for . 

11.d Compute the global orientation flow quality score . 

11.4 Block-wise absolute orientation difference 

The ridge flow is determined as a measure of the absolute difference between a block and its 

neighboring blocks. The absolute difference for block is: 

 

 

 

 

 

 
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11.5 Local orientation quality score 

The local orientation quality score for the block orientation difference is determined 

as: 

 

 

 

 

 

where is a threshold for minimum angle difference to consider. 

11.6 Global orientation quality score 

With local orientation quality score blocks the global orientation quality score is computed as: 

 

 

 

 

 

 

 

11.7 Notes 

In ISO/IEC TR 29794-4:2010 is a constant such that the angular tolerance is ( ). The 

local orientation quality score is here assigned such that when the local quality is 

the highest. This is opposite behavior of the ISO/IEC TR 29794-4:2010 definition where 

when the local quality is the highest. 

11.8 Processing steps 

Processing steps for Orientation Flow 

Input (FVC2000Db1 1_1.bmp) Input (FVC200Db1 100_1.bmp) 

Current block marked 
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Processing steps for Orientation Flow 

Zoomed view of current block 

Orientation line shown perpendicular to ridge flow 

Block orientations. Black grey values correspond to zero orientation. 

Map of differences between a block orientation and its 8-neighborhood 

Final flow map 

Table 11-3. Visualization of processing steps in Orientation Flow. 
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12 Orientation Certainty Level 

Quality Feature Summary 

Origin ISO/IEC TR 29794-4:2010 (ISO/IEC, 2010) - Clause 6.2.2.1 

NFIQ 2.0 Identifier OCL_# 

Acronyms OCL 

Table 12-1. Orientation Certainty Level summary. 

12.1 Feature Description 

Orientation Certainty Level is a measure of the strength of the energy concentration along the 

dominant ridge flow orientation. The feature operates in a block-wise manner. 

12.2 Variables 

Name Default Description 

 - Input image. 

 32 Block height in pixels. 

 32 Block width in pixels. 

 - Segmentation mask. 

Table 12-2. Orientation Certainty input variables. 

12.3 Algorithm 

12.a Compute the block wise intensity gradient by applying the 3x3 Sobel operators. 

12.b Compute the covariance matrix. 

12.c Compute the eigen values to obtain for each block. 

12.d Final score is the mean value of the block values. 

12.4 Computing the covariance matrix 

The covariance matrix is computed as: 

 

 

 

 

 

 

 

 

where and represent the intensity gradient at that pixel and is , i.e. the number of 

pixels per block. 

12.5 Computing the eigenvalues and local orientation certainty 

From the covariance matrix the eigenvalues and are computed as: 

 

 

 

 

 

 

 

 

this yields an orientation certainty level OCL: 

 

 

 
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which is a ratio in the interval where 1 is highest certainty level and 0 is lowest. 

12.6 Computing the quality score 

The quality feature is compute using the local orientation certainty levels as: 

 

 

 

 

 

 

where is the number of blocks. 

12.7 Notes 

The computation of the orientation certainty level deviates from ISO/IEC 29794-4:2010 in that we 

subtract the ratio between the eigen values from 1 such that reflects the lowest quality 

and the highest quality. 

12.8 Processing steps 

Processing steps for Orientation Certainty Level 

Input (FVC2000Db1 1_1.bmp) Input (FVC200Db1 100_1.bmp) 

Input with current block marked 

Zoomed view of block 
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Processing steps for Orientation Certainty Level 

Ridge orientation indicated as an ellipse. The eccentricity of the ellipse corresponds to the 

Orientation certainty level in each block. High intensity corresponds to high level of certainty. 

Table 12-3. Visualization of processing steps in Orientation Certainty Level. 

13 Radial Power Spectrum 

Quality Feature Summary 

Origin ISO/IEC TR 29794-4:2010 (ISO/IEC, 2010) - Clause 6.3.2.3 

NFIQ 2.0 Identifier PS_# 

Acronyms RPS, POW, Radial Power Spectrum 

Table 13-1. Radial Power Spectrum summary. 

13.1 Feature Description 

The Radial Power Spectrum is a measure of maximal signal power in a defined frequency band of the 

global radial Fourier spectrum. Ridges can be locally approximated by means of a single sine wave, 

hence high energy concentration a narrow frequency band corresponds to consistent ridge 

structures. 

13.2 Variables 

Name Default Description 

25 Lower bound of frequency band 

84 Upper bound of frequency band 

30

180 Degrees of the spectrum to consider 

Sampling step between annular bands in the frequency 

Table 13-2. Radial Power Spectrum input variables. 

13.3 Algorithm 

13.a Compute the magnitude of the 2D-DFT F(u,v)

13.b Transform F(u,v) into polar coordinates and normalize to the range of [0,1]

13.c Determine the maximum energy to compute Qpow

orientation certainty. 

rmax

rmin

∆r

θ

spectrum 
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13.4 The 2D Discrete Fourier Transform 

The 2D discrete Fourier transform of is: 

 

 

  

 

 

 

 

 

 

 

 

and the magnitude of is: 

 

13.5 Magnitude of frequency bands polar coordinates 

The magnitude of the annular band between and  in the polar Fourier spectrum is 

computed as: 

 

 

 

 

 

 

 

 

 

where is the angle and is the radius. 

13.6 Determine quality score from energy distribution 

The quality feature is found as: 

 

 

 

13.7 Notes 

The Radial Power Spectrum quality feature is resolution dependant. The given defaults assume 

500ppi. 

13.8 Processing steps 

Processing steps for Radial Power Spectrum 

Input (FVC2000Db1 1_1.bmp) Input (FVC200Db1 100_1.bmp) 
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Processing steps for Radial Power Spectrum 

Spectrum with the frequency band of interest located between the 

Polar representation of the spectrum 

Spectrum with marked frequency of interest 

Table 13-3. Visualization of processing steps in Radial Power Spectrum. 

14 Ridge Valley Uniformity 

Quality Feature Summary 

Origin ISO/IEC TR 29794-4:2010 (ISO/IEC, 2010) - Clause 6.2.2.4 

NFIQ 2.0 Identifier RVU_# 

Acronyms RVU 

Table 14-1. Ridge Valley Uniformity summary. 

14.1 Feature Description 

Ridge Valley Uniformity is a measure of the consistency of the ridge and valley widths. 

14.2 Variables 

Name Default Description 

 - Input image 

 32 Block height in pixels 

 32 Block width in pixels 

 - Segmentation mask 

Table 14-2. Ridge Valley Uniformity input variables. 
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14.3 Algorithm 

14.a For each block in the image determine the dominant ridge flow orientation to create an 

orientation line which is perpendicular to the ridge flow 

14.b Align such that the orientation line is horizontal to create 

14.c From extract a block which is centered around the orientation line 

14.d Compute the average profile of to produce a vector 

14.e Determine a threshold by applying linear regression on 

14.f Segment into two levels based on the threshold 

14.g Determine the indexes in where a change from background to foreground or foreground to 

background occurs. If no changes are found then return an empty ratio for that block. 

14.h Remove the first and last parts of to remove incomplete ridge/valleys occurring at the 

border of the original block. Likewise remove the corresponding changes from the change 

index vector. 

14.i If there are no changes after step 8, return an empty ratio for that block 

14.j Calculate the ratios between the width of ridges and valleys for the block. 

14.k Obtain the final quality score as the standard deviation of all ratios. 

14.4 Notes 

The Ridge Valley Uniformity quality feature is resolution dependent. The given defaults assume 

500ppi. 
Development of NFIQ 2.0 Quality Feature Definitions

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14.5 Processing steps 

Processing steps for Ridge Valley Uniformity 

Input (FVC2000Db1 1_1.bmp) Input (FVC200Db1 100_1.bmp) 

Input with block grid and current block marked 

Current block 

Current block with overlap 

Block rotated so ridge lines are vertical 
Development of NFIQ 2.0 Quality Feature Definitions

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Processing steps for Ridge Valley Uniformity 

Cropped section of block 

Projection of mean intensity 

Profile of mean intensity with threshold marked. 

 Segmentation according to thresholding. Ridges marked in black, valleys in white 

Location of ridge-valley edges marked with white 

Cleaned ridge-valley segmentation contains only complete ridges and valleys. 

Table 14-3. Visualization of processing steps in Ridge Valley Uniformity. 

15 Sigma Mu Block 

Quality Feature Summary 

Origin 

NFIQ 2.0 Identifier SMB_# 

Acronyms SMB 

Table 15-1. Sigma Mu Block summary. 

15.1 Feature Description 

Sigma Mu Block is the standard deviation of the block wise mean pixel intensity value in the input 

image. 

15.2 Variables 

Default Description 

 - Input image. 

 

Name 

32 Block height in pixels. 

 32 Block width in pixels. 

Table 15-2. Sigma Mu Block summary. 

15.3 Algorithm 

15.a Compute the mean intensity for each block in . 

15.b Compute the standard deviation of the mean intensities. 
Development of NFIQ 2.0 Quality Feature Definitions

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16 Sigma 

Quality Feature Summary 

Origin 

NFIQ 2.0 Identifier Sigma_# 

Acronyms SIG

Table 16-1. Sigma summary. 

16.1 Feature Description 

Sigma is the standard deviation of pixel intensity values in the input image. 

16.2 Variables 

Name Default Description 

 - Input image. 

Table 16-2. Sigma input variables. 

16.3 Algorithm 

16.a Compute the standard deviation of the pixel intensities in . 

17 References 

Daugman John Uncertainty relation for resolution in space,spatial frequency, and orientation 

optimed by two-dimensional visual cortical filters [Tidsskrift]. - [s.l.] : J. Opt. Soc. Am. A, 1985. - Årg. 

2.

ISO/IEC 29794-4 TR Information technology - Biometric sample quality - Part 4: Finger image data 

[Rapport]. - 2010. 

Olsen Martin Aastrup, Xu Haiyun og Busch Christoph Gabor Filters as Candidate Quality Measure 

for NFIQ 2.0 [Konference] // Proceedings of the 5th IAPR International Conference on Biometrics 

(ICB 2012). - 2012. 

Shen LinLin, Kot Alex ChiChung og Koo Wai Mun Quality measures of fingerprint images 

[Konference] // AVBPA. - 2001.