Fingerprint Analysis and Fingerprint Analysis and RepresentationRepresentation

Handbook of Fingerprint RecognitionHandbook of Fingerprint Recognition

Chapter III Sections 7-10Chapter III Sections 7-10

Direct Gray-Scale Minutiae Detection in Fingerprints

D. Mario and D. Maltoni, IEEE Transactions on Pattern D. Mario and D. Maltoni, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.19, no.1,pp. 27-Analysis and Machine Intelligence, vol.19, no.1,pp. 27-

39, 1997.39, 1997.

Presentation by: Xavier PalathingalPresentation by: Xavier Palathingal

Fingerprint Analysis and Fingerprint Analysis and RepresentationRepresentation

Handbook of Fingerprint RecognitionHandbook of Fingerprint Recognition

Chapter III Sections 7-10Chapter III Sections 7-10

OutlineOutline

EnhancementEnhancement Minutiae DetectionMinutiae Detection

Binarization based methodsBinarization based methods Direct gray-scale extractionDirect gray-scale extraction

Minutiae FilteringMinutiae Filtering Structural post-processingStructural post-processing Minutiae filtering in the gray-scale domainMinutiae filtering in the gray-scale domain

Estimation of Ridge CountEstimation of Ridge Count

EnhancementEnhancement

Performance depends on quality of imagesPerformance depends on quality of images Ideal fingerprintIdeal fingerprint Degradation types – ridges are not continuous, parallel Degradation types – ridges are not continuous, parallel

ridges are not well separated, cuts/creases/bruisesridges are not well separated, cuts/creases/bruises Leads to problems in minutiae extractionLeads to problems in minutiae extraction

EnhancementEnhancement

Well-defined regionWell-defined region Recoverable regionRecoverable region Unrecoverable regionUnrecoverable region

For each fingerprint image, the fingerprint areasFor each fingerprint image, the fingerprint areas

resulting from segmentation can be divided into:resulting from segmentation can be divided into:

Enhancement AlgorithmsEnhancement Algorithms

Goal – to improve the clarity of the ridge structure Goal – to improve the clarity of the ridge structure in the recoverable regions and mark unrecoverable in the recoverable regions and mark unrecoverable regions as too noisy for further processingregions as too noisy for further processing

Input – a gray-scale imageInput – a gray-scale image Output – a gray-scale or binary image depending Output – a gray-scale or binary image depending

on the algorithmon the algorithm Effective initial steps - Contrast stretching, Effective initial steps - Contrast stretching,

Histogram manipulation, Normalization, Wiener Histogram manipulation, Normalization, Wiener FilteringFiltering

Normalization approach [Hong, Normalization approach [Hong, Wan, Jain (1998)]Wan, Jain (1998)]

Determines the new intensity value of each pixel Determines the new intensity value of each pixel as,as,

m and v - image mean and variance m and v - image mean and variance

mm00 and v and v00 - desired values after normalization - desired values after normalization

Pixel-wise operation, does not change the ridge and valley Pixel-wise operation, does not change the ridge and valley structuresstructures

Contextual FiltersContextual Filters

The most widely used technique for fingerprint image The most widely used technique for fingerprint image enhancementenhancement

Conventional image filtering – a single filter is used Conventional image filtering – a single filter is used for convolution throughoutfor convolution throughout

Contextual filtering - filter characteristics change Contextual filtering - filter characteristics change according to local contextaccording to local context

Several types of contextual filters proposedSeveral types of contextual filters proposed Indented behavior – 1)provide a low-pass Indented behavior – 1)provide a low-pass

[averaging] effect along the ridge direction. [averaging] effect along the ridge direction. 2)perform a band pass [differentiating] in the 2)perform a band pass [differentiating] in the direction orthogonal to the ridgesdirection orthogonal to the ridges

Method proposed by O’Gorman and Method proposed by O’Gorman and NickersonNickerson

A mother filter defined based on-minimum and maximum A mother filter defined based on-minimum and maximum ridge width, minimum and maximum valley width.ridge width, minimum and maximum valley width.

Filter is bell-shaped, elongated along the ridge direction, Filter is bell-shaped, elongated along the ridge direction, and cosine tapered in the direction normal to the ridges.and cosine tapered in the direction normal to the ridges.

The context is defined only by the local ridge orientationThe context is defined only by the local ridge orientation Once the mother filtered is generated, a set of 16 rotated Once the mother filtered is generated, a set of 16 rotated

versions is derived.versions is derived. The image enhancement is performed by convolving The image enhancement is performed by convolving

each point of the image with the filter in the set whose each point of the image with the filter in the set whose orientation best matches the local ridge orientationorientation best matches the local ridge orientation

Method proposed by Sherlock, Method proposed by Sherlock, Monro, and MillardMonro, and Millard

Performed in Fourier domainPerformed in Fourier domain The filter is defined in the frequency domain by the The filter is defined in the frequency domain by the

function:function: where Hwhere Hradial radial depends only on the local ridgedepends only on the local ridge spacing ρ = 1/f and Hspacing ρ = 1/f and Hangleangle depends only on local ridge depends only on local ridge

orientation θorientation θ Both HBoth Hradial radial andand HHangle angle areare defined as band-pass filters defined as band-pass filters

and are characterized by a mean value and a and are characterized by a mean value and a bandwidthbandwidth

The Fourier transform PThe Fourier transform P ii,,i=1,…n of the filters is pre-i=1,…n of the filters is pre-computed and storedcomputed and stored

Method proposed by Sherlock, Method proposed by Sherlock, Monro, and Millard (cont …)Monro, and Millard (cont …)

Filtering of an input fingerprint image I is performed as follows:Filtering of an input fingerprint image I is performed as follows: The FFT(Fast Fourier Transform) F of I is computedThe FFT(Fast Fourier Transform) F of I is computed each filter Peach filter Pi i is point-by-point multiplied by F, thus obtaining is point-by-point multiplied by F, thus obtaining nn filtered image filtered image

transforms PFtransforms PFii, , i=1,…n (in the frequency domain)i=1,…n (in the frequency domain) Inverse FFT is computed for each PFInverse FFT is computed for each PF i i resulting in resulting in nn filtered filtered images PIimages PIii, , i=1,…n (in the i=1,…n (in the

spatial domain)spatial domain)

The enhanced image IThe enhanced image Ienh enh is obtained by setting, for each pixel [x,y], is obtained by setting, for each pixel [x,y], IIenhenh[x,y] = PI[x,y] = PIkk[x,y], where k is the index of the of the filter whose orientation is the [x,y], where k is the index of the of the filter whose orientation is the closest to θclosest to θxyxy

Method proposed by Hong, Wan, and Method proposed by Hong, Wan, and JainJain

Based on Gabor filtersBased on Gabor filters Gabor filters have both frequency-selective and Gabor filters have both frequency-selective and

orientation-selective properties and have optimal joint orientation-selective properties and have optimal joint resolution in spatial and frequency domainsresolution in spatial and frequency domains

A Gabor filter is defined by a sinusoidal plane wave A Gabor filter is defined by a sinusoidal plane wave tapered by a Gaussiantapered by a Gaussian

Method proposed by Hong, Wan, and Method proposed by Hong, Wan, and Jain (cont ..)Jain (cont ..)

The even symmetric two-dimensional Gabor filter The even symmetric two-dimensional Gabor filter has the following form: has the following form:

Here, f is the frequency of a sinusoidal plane wave Here, f is the frequency of a sinusoidal plane wave

and σand σxx and σ and σy y are the standard deviations of the are the standard deviations of the

Gaussian envelope along the x and y axesGaussian envelope along the x and y axes

Method proposed by Hong, Wan, and Jain Method proposed by Hong, Wan, and Jain (cont ..) – Gabor Filter(cont ..) – Gabor Filter

4 parameters – θ,f,σ4 parameters – θ,f,σxx,σ,σyy

The selection of the values σThe selection of the values σx x andand σσy y involves a tradeoffinvolves a tradeoff

A set {gA set {gijij(x,y) | i=1…n(x,y) | i=1…n00,1..n,1..nff} of filters are priori created and stored } of filters are priori created and stored

, where n, where n00 is the number of discrete orientations {θ is the number of discrete orientations {θ ii | i=1,..n | i=1,..n00} and } and

nnff the number of discrete frequencies {f the number of discrete frequencies {f jj| j=1,..n| j=1,..nff}}

Each pixel [x,y] is convolved, with filter gEach pixel [x,y] is convolved, with filter g ijij(x,y) such that θ(x,y) such that θ ii is the is the

discretized orientation closest to θdiscretized orientation closest to θxyxy and f and fj j is theis the discretized discretized

orientation closest to forientation closest to fxyxy

Method proposed by Hong, Wan, and Jain Method proposed by Hong, Wan, and Jain (cont ..) – Examples(cont ..) – Examples

Shows the Shows the application of application of Gabor-based Gabor-based contextual contextual filtering on filtering on medium and medium and poor quality poor quality imagesimages

Minutiae DetectionMinutiae Detection

Reliable minutiae extraction is extremely importantReliable minutiae extraction is extremely important EnhancementEnhancement BinarizationBinarization ThinningThinning

Binarization-based methodsBinarization-based methods Simplest method - global thresholdSimplest method - global threshold Local threshold techniqueLocal threshold technique Fingerprint specific solutions necessaryFingerprint specific solutions necessary

FBI “minutiae reader” – by Stock and Swonger FBI “minutiae reader” – by Stock and Swonger Composite approach based on a local threshold and a “slit Composite approach based on a local threshold and a “slit

comparison” formula that compares pixel alignment along eight comparison” formula that compares pixel alignment along eight discrete directionsdiscrete directions

Method proposed by Moayer and FuMethod proposed by Moayer and Fu Based on an iterative application of a Laplacian operator and a pair of Based on an iterative application of a Laplacian operator and a pair of

dynamic thresholdsdynamic thresholds At each iteration the image is convolved through a Laplacian operator At each iteration the image is convolved through a Laplacian operator

and the pixels whose intensity lies outside the range bounded by two and the pixels whose intensity lies outside the range bounded by two thresholds are set to 0 and 1 respectivelythresholds are set to 0 and 1 respectively

The thresholds are progressively moved towards a unique value to The thresholds are progressively moved towards a unique value to guarantee convergenceguarantee convergence

Binarization-based methodsBinarization-based methodsA fuzzy approach – by Verma, Majumdar and Chatterjee A fuzzy approach – by Verma, Majumdar and Chatterjee Uses an adaptive threshold to preserve the same number of 1 and 0 pixels for Uses an adaptive threshold to preserve the same number of 1 and 0 pixels for

each neighborhoodeach neighborhood Image is partitioned into small regionsImage is partitioned into small regions Each region goes through – smoothing, fuzzy coding of the pixel intensities, Each region goes through – smoothing, fuzzy coding of the pixel intensities,

contrast enhancement, binarization, 1s and 0s counting, fuzzy decoding, and contrast enhancement, binarization, 1s and 0s counting, fuzzy decoding, and parameter adjusting.parameter adjusting.

Repeated until number of 1s approximately equals 0sRepeated until number of 1s approximately equals 0s

Method proposed by Coetzee and BothaMethod proposed by Coetzee and Botha Based on the use of edges in conjunction with the gray-scale imageBased on the use of edges in conjunction with the gray-scale image The ridges are tracked by the two local windows: one in the gray-scale image The ridges are tracked by the two local windows: one in the gray-scale image

and other in the edge imageand other in the edge image Gray-scale domain – binarization with local thresholdGray-scale domain – binarization with local threshold Edge-image – a blob-coloring routine is used to fill the area delimited by the two Edge-image – a blob-coloring routine is used to fill the area delimited by the two

ridge edgesridge edges The resulting image is the logical OR of the two individual binary imagesThe resulting image is the logical OR of the two individual binary images

Binarization-based methodsBinarization-based methodsApproach by Ratha, Chen and JainApproach by Ratha, Chen and Jain

Based on peak detection in the gray-scale profiles along Based on peak detection in the gray-scale profiles along sections orthogonal to the ridge orientationsections orthogonal to the ridge orientation

A 16x16 oriented window is centered around each pixel [x,y]A 16x16 oriented window is centered around each pixel [x,y] The gray-scale profile is obtained by projection of the pixel The gray-scale profile is obtained by projection of the pixel

intensities onto the central sectionintensities onto the central section

Binarization-based methodsBinarization-based methodsApproach by Ratha, Chen and Jain [cont ..]Approach by Ratha, Chen and Jain [cont ..]

The profile is smoothed through the local averaging; the The profile is smoothed through the local averaging; the peaks and the two neighboring pixels on either side of each peaks and the two neighboring pixels on either side of each peak constitute the foreground of the resulting binary imagepeak constitute the foreground of the resulting binary image

Binarization-based methodsBinarization-based methods

Domeniconi, Tari and Liang (1998) modeled fingerprint Domeniconi, Tari and Liang (1998) modeled fingerprint ridges and valleys as sequences of local maxima and ridges and valleys as sequences of local maxima and saddle pointssaddle points

Maxima and saddle points are detected by evaluating Maxima and saddle points are detected by evaluating gradient and the Hessian matrix H at each pointgradient and the Hessian matrix H at each point

The Hessian of a two-dimensional surface S(x,y) is a 2x2 The Hessian of a two-dimensional surface S(x,y) is a 2x2 symmetric matrix whose elements are the second-order symmetric matrix whose elements are the second-order derivatives of S with respect to xderivatives of S with respect to x22,xy and y,xy and y22

The eigenvectors of H are the directions along which the The eigenvectors of H are the directions along which the curvature of S is extremizedcurvature of S is extremized

Let p be a stationary point and let λLet p be a stationary point and let λ11 and λ and λ2 2 be the be the eigenvalues of H in peigenvalues of H in p

Then p is a local maximum if λThen p is a local maximum if λ11 ≤ λ ≤ λ2 2 < 0 and is a saddle < 0 and is a saddle point if λpoint if λ11. λ. λ2 2 < 0 < 0

Binarization-based methodsBinarization-based methodsApproach by Tico and Kuosmanen (1999) Approach by Tico and Kuosmanen (1999)

A slightly different topological approachA slightly different topological approach Fingerprint image is treated as a noisy sampling of the underlying continuous Fingerprint image is treated as a noisy sampling of the underlying continuous

surface surface Approximated it by Chebyshev polynomialsApproximated it by Chebyshev polynomials Ridge and Valley regions are discriminated by the sign of the maximal normal Ridge and Valley regions are discriminated by the sign of the maximal normal

curvature of the surfacecurvature of the surface The maximal normal curvature along any direction d is dThe maximal normal curvature along any direction d is dTTHdHd

Abutaleb and Kamel (1999)Abutaleb and Kamel (1999)

Used Genetic Algorithms to discriminate ridges and valleys along the gray-level Used Genetic Algorithms to discriminate ridges and valleys along the gray-level profile of the scanned linesprofile of the scanned lines

The optimization criterion is aimed at increasing the correlation between The optimization criterion is aimed at increasing the correlation between adjacent gray-levels along fingerprint sectionsadjacent gray-levels along fingerprint sections

Results from different methodsResults from different methods

ThinningThinning

Reduces the width of the ridges to one pixelReduces the width of the ridges to one pixel Skeletons , Skeletons , spikesspikes Filling holes, removing small breaks, eliminating Filling holes, removing small breaks, eliminating

bridges between ridges etc.bridges between ridges etc.

ThinningThinning

Coetzee and Botha (1993) identify holes and Coetzee and Botha (1993) identify holes and gaps by tracking the ridge line edges through gaps by tracking the ridge line edges through adaptive windows and remove them using a adaptive windows and remove them using a simple blob-coloring algorithmsimple blob-coloring algorithm

Hung (1993) uses an adaptive filtering technique Hung (1993) uses an adaptive filtering technique to equalize the width of the ridgesto equalize the width of the ridges

To remove the spikes, Ratha, Chen and Jain To remove the spikes, Ratha, Chen and Jain (1995) implement a morphological “open” (1995) implement a morphological “open” operator.operator.

ThinningThinning Fitz and Green (1996) - removes small lines and dots Fitz and Green (1996) - removes small lines and dots

both in the ridges and valleys of binary images through both in the ridges and valleys of binary images through an application of 4 morphological operators on a an application of 4 morphological operators on a hexagonal gridhexagonal grid

Luo and Tian (2000) - a two step method. skeleton Luo and Tian (2000) - a two step method. skeleton extracted at the end of the first step is used to improve extracted at the end of the first step is used to improve the quality of the binary image based on a set of the quality of the binary image based on a set of structural rules. A new skeleton is extracted from this structural rules. A new skeleton is extracted from this improved binary image.improved binary image.

Ikeda et. al (2002) - use morphological operators to Ikeda et. al (2002) - use morphological operators to enhance ridges and valleys in the fingerprint binary enhance ridges and valleys in the fingerprint binary imageimage

Minutiae detection Minutiae detection A simple image scan allows the pixel A simple image scan allows the pixel

corresponding to minutiae to be detectedcorresponding to minutiae to be detected crossing numbercrossing number of a pixel p of a pixel p

Examples of minutiae extractionExamples of minutiae extraction

Direct gray-scale extractionDirect gray-scale extraction Such methods are used to overcome the problems related to Such methods are used to overcome the problems related to

fingerprint binarization and thinning [e.g. spurious minutiae]fingerprint binarization and thinning [e.g. spurious minutiae]

Leung, Engeler, and Frank (1990)Leung, Engeler, and Frank (1990) Introduced a neural network-based approachIntroduced a neural network-based approach A multi-layer perceptron analyzes the output of a rank of A multi-layer perceptron analyzes the output of a rank of

Gabor filters applied to the gray-scale imageGabor filters applied to the gray-scale image The image is first transformed into frequency domain where The image is first transformed into frequency domain where

the filtering takes place;the filtering takes place; The resulting magnitude and phase signals constitute the The resulting magnitude and phase signals constitute the

input to the neural network composed of six sub-networks – input to the neural network composed of six sub-networks – each of which is responsible for detecting minutiae at a each of which is responsible for detecting minutiae at a specific orientationspecific orientation

A final classifier is employed to combine the intermediate A final classifier is employed to combine the intermediate responsesresponses

Direct gray-scale extractionDirect gray-scale extractionMaio and Maltoni (1997) Maio and Maltoni (1997)

Basic idea – track the ridge lines in the gray-scale image, by Basic idea – track the ridge lines in the gray-scale image, by “sailing” according to the local orientation of the ridge pattern“sailing” according to the local orientation of the ridge pattern

A ridge line is defined as a set of points that are local maxima A ridge line is defined as a set of points that are local maxima along one directionalong one direction

The ridge line extraction algorithm tries to locate the local The ridge line extraction algorithm tries to locate the local maximum relative to a section orthogonal to the ridge maximum relative to a section orthogonal to the ridge directiondirection

A polygonal approximation of the ridge line can be obtained A polygonal approximation of the ridge line can be obtained by connecting the consecutive maximaby connecting the consecutive maxima

Results of minutiae detection Results of minutiae detection algorithm on a sample fingerprintalgorithm on a sample fingerprint

Variations of Maio and Maltoni methodVariations of Maio and Maltoni method

Jiang, Yau, and Ser (1999) – proposed μ be dynamically Jiang, Yau, and Ser (1999) – proposed μ be dynamically adaptedadapted

Liu, Huang, and Chan (2000) – instead of tracking a single Liu, Huang, and Chan (2000) – instead of tracking a single ridge, the algorithm simultaneously tracks a central ridge and ridge, the algorithm simultaneously tracks a central ridge and 2 surrounding valleys2 surrounding valleys

Chang and Fan (2001) – aimed at discriminating the true ridge Chang and Fan (2001) – aimed at discriminating the true ridge maxima in the sections Ω obtained during ridge line following. maxima in the sections Ω obtained during ridge line following. For this 2 thresholds are initially determined.For this 2 thresholds are initially determined.

Bolle et. al (2002) - provided a formal definition of minutiae Bolle et. al (2002) - provided a formal definition of minutiae based on the gray-scale image that allows the location and based on the gray-scale image that allows the location and orientation of an existing minutia to be more precisely orientation of an existing minutia to be more precisely determineddetermined

Minutiae FilteringMinutiae Filtering

Post-processing stage is useful for Post-processing stage is useful for removing spurious minutiae [already removing spurious minutiae [already present or introduced by previous steps]present or introduced by previous steps]

Two main post-processing types:Two main post-processing types: Structural post-processing Structural post-processing Minutiae filtering in the gray-scale domainMinutiae filtering in the gray-scale domain

Structural post-processingStructural post-processing Xiao and Raafat (1991) identified the most common false Xiao and Raafat (1991) identified the most common false

minutiae structures and introduced an ad hoc approachminutiae structures and introduced an ad hoc approach The underlying algorithm is rule-basedThe underlying algorithm is rule-based Requires as input – length of the associated ridge(s), the Requires as input – length of the associated ridge(s), the

minutia angle, the number of facing minutiae in a minutia angle, the number of facing minutiae in a neighborhoodneighborhood

Structural post-processingStructural post-processing Farina, Kovacs- Vajna, and Leone (1999) introduced some optimized Farina, Kovacs- Vajna, and Leone (1999) introduced some optimized

variants of some previously proposed rules and algorithmsvariants of some previously proposed rules and algorithms

Spurs and bridges are removed based on the observation that in a Spurs and bridges are removed based on the observation that in a “spurious” bifurcation, only two branches are generally aligned whereas the “spurious” bifurcation, only two branches are generally aligned whereas the third one is almost orthogonal to the other twothird one is almost orthogonal to the other two

Short ridges are removed on the basis of the relationship between the ridge Short ridges are removed on the basis of the relationship between the ridge length and the average distance between the ridgeslength and the average distance between the ridges

Terminations and bifurcations are then topologically validated: they are Terminations and bifurcations are then topologically validated: they are removed if the topological requirements are not fully satisfiedremoved if the topological requirements are not fully satisfied

Minutiae filtering in gray-scale domainMinutiae filtering in gray-scale domain A direct minutiae filtering technique reexamines the gray-scale A direct minutiae filtering technique reexamines the gray-scale

image in a spatial neighborhood of a detected minutiae with the aim image in a spatial neighborhood of a detected minutiae with the aim of verifying the presence of a real minutia of verifying the presence of a real minutia

Maio and Maltoni used a shared weight neural network to verify the Maio and Maltoni used a shared weight neural network to verify the minutiae detected by their gray-scale algorithmminutiae detected by their gray-scale algorithm

The minutiae neighborhoods are normalized with respect to their The minutiae neighborhoods are normalized with respect to their angle and the local ridge frequencyangle and the local ridge frequency

Minutiae filtering in gray-scale domainMinutiae filtering in gray-scale domain

Then they are passed to a neural network Then they are passed to a neural network classifier, which classifies them as termination, classifier, which classifies them as termination, bifurcation and non-minutiabifurcation and non-minutia

A typical three layer neural network architecture A typical three layer neural network architecture has been adoptedhas been adopted

Estimation of ridge countEstimation of ridge count

ridge countridge count has often been used to increase reliability of has often been used to increase reliability of analysisanalysis

Ridge count is an abstract measurement of the distances Ridge count is an abstract measurement of the distances between any two points in a fingerprint imagebetween any two points in a fingerprint image

Typically used in forensic matchingTypically used in forensic matching

Summary [Summary [of the chapterof the chapter]]

Most of the early work was based on general-Most of the early work was based on general-purpose image processing techniquespurpose image processing techniques

Recent developments have 2 important Recent developments have 2 important directions:directions: Focus on optimizing the salient discriminatory Focus on optimizing the salient discriminatory

information in fingerprintsinformation in fingerprints Algorithms designed specifically for processing Algorithms designed specifically for processing

fingerprints images have been proposedfingerprints images have been proposed

Direct Gray-Scale Minutiae Detection in Fingerprints

D. Mario and D. Maltoni, IEEE Transactions on D. Mario and D. Maltoni, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.19, Pattern Analysis and Machine Intelligence, vol.19,

no.1,pp. 27-39, 1997.no.1,pp. 27-39, 1997.

OutlineOutline

IntroductionIntroduction Ridge Line FollowingRidge Line Following

Sectioning and Maximum DeterminationSectioning and Maximum Determination Tangent Direction ComputationTangent Direction Computation Stop criteriaStop criteria

Minutiae DetectionMinutiae Detection Performance Evaluation and ComparisonPerformance Evaluation and Comparison ConclusionConclusion

IntroductionIntroduction Fingerprints are the most widely used biometric featuresFingerprints are the most widely used biometric features Most automatic systems for fingerprint matching are based on Most automatic systems for fingerprint matching are based on

minutiae matchingminutiae matching Minutiae classification is based on 4 classes – terminations, Minutiae classification is based on 4 classes – terminations,

bifurcations, trifurcations (crossovers) and undeterminedbifurcations, trifurcations (crossovers) and undetermined This work is based on a two-class minutiae classificationThis work is based on a two-class minutiae classification

IntroductionIntroduction

This work is a direct gray scale minutiae detection This work is a direct gray scale minutiae detection approach (i.e. without binarization and thinning )approach (i.e. without binarization and thinning )

Reasons for not using binarization and thinning :Reasons for not using binarization and thinning : Loss of informationLoss of information Time-consumingTime-consuming Unsatisfactory on low-quality imagesUnsatisfactory on low-quality images

Basic idea – follow the ridge lines on the gray scale Basic idea – follow the ridge lines on the gray scale imageimage

A set of starting points is determinedA set of starting points is determined For each starting point, the algorithm keeps following the For each starting point, the algorithm keeps following the

ridge lines until they terminate or intersects other ridge ridge lines until they terminate or intersects other ridge lineslines

Ridge line following – basic definitionsRidge line following – basic definitions I be an a x b gray scale image with g gray levelsI be an a x b gray scale image with g gray levels Gray(i,j) be the gray level of pixel(i,j) of I , i=1,…,a and j=1,…,bGray(i,j) be the gray level of pixel(i,j) of I , i=1,…,a and j=1,…,b Let z = S (i, j) be the discrete surface corresponding to the image I: S (i, j) = Let z = S (i, j) be the discrete surface corresponding to the image I: S (i, j) =

gray (i, j), i=1,…a, j=1,….b.gray (i, j), i=1,…a, j=1,….b. Ridge line is defined as a set of points which are local maxima along one Ridge line is defined as a set of points which are local maxima along one

directiondirection At each step, the algorithm attempts to locate a local maximum relative to a At each step, the algorithm attempts to locate a local maximum relative to a

section orthogonal to the ridge directionsection orthogonal to the ridge direction By connecting the consecutive maxima, a polygonal approximation of the By connecting the consecutive maxima, a polygonal approximation of the

ridge line can be obtainedridge line can be obtained

Ridge line following – algorithmRidge line following – algorithm

Starting point : [xStarting point : [xcc,y,ycc] and starting direction : θ] and starting direction : θcc

Computes a new point [xComputes a new point [xtt,y,ytt] at each step moving μ pixels from the current ] at each step moving μ pixels from the current point [xpoint [xcc,y,ycc] along direction θ] along direction θc c

Then it computes a section set Ω as the set of points belonging to the Then it computes a section set Ω as the set of points belonging to the section segment lying on the xy-plane and having median point [xsection segment lying on the xy-plane and having median point [x tt,y,ytt], ], direction orthogonal to θdirection orthogonal to θc c and length 2σ + 1and length 2σ + 1

The new point [xThe new point [xnn,y,ynn], belonging to the ridge line, is chosen among the local ], belonging to the ridge line, is chosen among the local maxima of an enhanced version of the set Ωmaxima of an enhanced version of the set Ω

The point [xThe point [xnn,y,ynn] becomes the current point [x] becomes the current point [xcc,y,ycc] and a new direction θ] and a new direction θcc is is computedcomputed

Ridge line following – algorithm Ridge line following – algorithm (pseudo-code version)(pseudo-code version)

Let (iLet (iss,j,jss) be a local maximum of a ridge line of I) be a local maximum of a ridge line of I ΦΦ00 be the direction of the tangent to the ridge be the direction of the tangent to the ridge

line in (iline in (iss,j,jss))

Ridge line following algorithm - stepsRidge line following algorithm - steps

Sectioning and Maximum Sectioning and Maximum DeterminationDetermination

Sectioning – achieved by intersecting S with a Sectioning – achieved by intersecting S with a cutting plane parallel to the z directioncutting plane parallel to the z direction

The section set Ω( (iThe section set Ω( (itt, j, jtt), Φ, σ) centered in (i), Φ, σ) centered in (itt, j, jtt), ), with direction Φ = φwith direction Φ = φc c ++ π/2, and length 2σ + 1 π/2, and length 2σ + 1 pixels, is defined as,pixels, is defined as,

Sectioning and Maximum Sectioning and Maximum DeterminationDetermination

Difficulty in determining the local maximum of the Difficulty in determining the local maximum of the section set Ωsection set Ω

volcano silhouettevolcano silhouette

Sectioning and Maximum DeterminationSectioning and Maximum Determination

An approach aimed at An approach aimed at regularizing the regularizing the section silhouettesection silhouette

This makes the determination of the local This makes the determination of the local maxima more reliablemaxima more reliable

During the ridge line following, each time a During the ridge line following, each time a new section is determined, we regularize new section is determined, we regularize its silhouette by means of two steps:its silhouette by means of two steps:

Local regularization – step 1Local regularization – step 1

Local regularization – step 2Local regularization – step 2

Local regularization - resultsLocal regularization - results

Tangent Direction ComputationTangent Direction Computation

The simplest approach – based on gradient computationThe simplest approach – based on gradient computation

The gradient phase angle denotes the direction of the The gradient phase angle denotes the direction of the intensity maximum changeintensity maximum change

Therefore, the direction φTherefore, the direction φc c of a hypothetical edge which of a hypothetical edge which crosses the region centered in the pixelcrosses the region centered in the pixel (i(icc, j, jcc), is ), is orthogonal to the gradient phase angle in (iorthogonal to the gradient phase angle in (icc, j, jcc))

This method, while being simple and efficient, suffers This method, while being simple and efficient, suffers from non-linearity due to the computation of the gradient from non-linearity due to the computation of the gradient phase anglephase angle

Tangent Direction ComputationTangent Direction Computation Kawagoe and Tojo – for each 2x2 pixel Kawagoe and Tojo – for each 2x2 pixel

neighborhood, they make a straight comparison neighborhood, they make a straight comparison against four edge templates to extract a rough against four edge templates to extract a rough directional estimate, which is then arithmetically directional estimate, which is then arithmetically averaged over a larger region to obtain a more averaged over a larger region to obtain a more accurate estimateaccurate estimate

Stock and Swonger – evaluate the tangent Stock and Swonger – evaluate the tangent direction on the basis of pixel alignments relative direction on the basis of pixel alignments relative to a fixed number of reference directionsto a fixed number of reference directions

Tangent Direction ComputationTangent Direction Computation

Method used in this work :Method used in this work :

Uses a gradient type operator to extract a Uses a gradient type operator to extract a directional estimate from each 2 x 2 pixel directional estimate from each 2 x 2 pixel neighborhoodneighborhood

Then its averaged over a local window by Then its averaged over a local window by least-squares minimization to control noiseleast-squares minimization to control noise

Stop CriteriaStop Criteria

Exit from interest areaExit from interest area

TerminationTermination

IntersectionIntersection

Excessive bendingExcessive bending

Minutiae DetectionMinutiae Detection The main difficulty is of examining each ridge line only The main difficulty is of examining each ridge line only

once and locating the intersections with ridge lines once and locating the intersections with ridge lines already extractedalready extracted

To solve this, an auxiliary image T is usedTo solve this, an auxiliary image T is used

T has the same dimension as that of I, and is initialized T has the same dimension as that of I, and is initialized with pixel values set to 0with pixel values set to 0

Every time a new ridge line is extracted from I, the pixels Every time a new ridge line is extracted from I, the pixels of T of T correspondingcorresponding to the ridge line are labeled by to the ridge line are labeled by assigning them an identifier.assigning them an identifier.

Minutiae DetectionMinutiae Detection The pixels of T corresponding to a ridge line are the pixels The pixels of T corresponding to a ridge line are the pixels

belonging to the polygonal, ε-thick, which links the belonging to the polygonal, ε-thick, which links the consecutive maximum points (iconsecutive maximum points (inn, j, jnn))

The algorithm The algorithm find minutiafind minutia searches for a minutia by searches for a minutia by following the ridge line nearest to the starting pointfollowing the ridge line nearest to the starting point

Minutia Detection – Algorithm Minutia Detection – Algorithm

Minutia detectionMinutia detection The algorithm starts by computing a point (iThe algorithm starts by computing a point (icc, j, jcc) )

belonging to the ridge line nearest to the starting point (ibelonging to the ridge line nearest to the starting point (iss, ,

jjss). ).

This operation can be carried out as follows:This operation can be carried out as follows:

Minutia detectionMinutia detection The computation of tangent direction, the sectioning, the The computation of tangent direction, the sectioning, the

regularization and the determination of the maximum are regularization and the determination of the maximum are performed as in the ridge line following algorithm.performed as in the ridge line following algorithm.

The following figure shows an example:The following figure shows an example:

Minutia DetectionMinutia Detectionstop criteria revisitedstop criteria revisited

Minutia DetectionMinutia Detection

The algorithm The algorithm find minutia find minutia enables all the fingerprint enables all the fingerprint minutiae within a window W to be detectedminutiae within a window W to be detected

Figure shows the results obtained by applying this Figure shows the results obtained by applying this approach to a sample fingerprintapproach to a sample fingerprint

Performance Evaluation and Performance Evaluation and ComparisonComparison

Performance Evaluation and ComparisonPerformance Evaluation and Comparison

The technique mentioned in this paper (A) and four other The technique mentioned in this paper (A) and four other schemes based on binarization and thinning – B, C, D, Eschemes based on binarization and thinning – B, C, D, E

In all approaches , the minutiae detected have been In all approaches , the minutiae detected have been filtered by removing:filtered by removing:

The minutiae belonging to regions where the image contrast is The minutiae belonging to regions where the image contrast is less than half of the average image contrastless than half of the average image contrast

The pairs of termination minutiae which are less than k pixels (k=6) The pairs of termination minutiae which are less than k pixels (k=6) distant from each otherdistant from each other

The sets of bifurcation minutiae (except one minutia for each set) The sets of bifurcation minutiae (except one minutia for each set) belonging to a neighborhood with diameter k pixels (k=6)belonging to a neighborhood with diameter k pixels (k=6)

Performance Evaluation and ComparisonPerformance Evaluation and Comparison

Performance Evaluation and ComparisonPerformance Evaluation and Comparison

Performance Evaluation and ComparisonPerformance Evaluation and Comparison

Conclusions - Conclusions - drawn from the tablesdrawn from the tables the average error percentage, in terms of dropped and

exchanged minutiae, as produced by proposed approach is comparable to the errors produced by the other approaches, although slightly larger.

the average error percentage, in terms of false minutiae, as produced by proposed approach is considerably lower than the errors produced by the other approaches.

the average computational time of proposed approach is considerably lower than the time of the other approaches.

approach E, whose performance in terms of total error is comparable with that of proposed approach, is one order of magnitude slower than our approach.

Performance Evaluation and ComparisonPerformance Evaluation and Comparison

Computational complexityComputational complexity

We assume, for We assume, for simplicity, that a simplicity, that a fingerprint pattern is fingerprint pattern is made up of a set of made up of a set of straight horizontal straight horizontal segments, which are segments, which are ξ-pixels thick and ξ-ξ-pixels thick and ξ-pixels distant from pixels distant from each othereach other

The elementary operations carried The elementary operations carried out at each ridge line following stepout at each ridge line following step

ConclusionConclusion

A new technique is proposed – based on A new technique is proposed – based on ridge line following algorithm ridge line following algorithm

In spite of greater conceptual complexity, In spite of greater conceptual complexity, this technique has less computational this technique has less computational complexity than the complexity of complexity than the complexity of techniques requiring binarization and techniques requiring binarization and thinningthinning