Fingerprint Analysis and Representation

1
Fingerprint Analysis and Representation

• Handbook of Fingerprint Recognition
• Chapter III Sections 7-10

Direct Gray-Scale Minutiae Detection in
Fingerprints
D. Mario and D. Maltoni, IEEE Transactions on
Pattern Analysis and Machine Intelligence,
vol.19, no.1,pp. 27-39, 1997.
Presentation by Xavier Palathingal
2
Fingerprint Analysis and Representation

• Handbook of Fingerprint Recognition
• Chapter III Sections 7-10

3
Outline

• Enhancement
• Minutiae Detection
• Binarization based methods
• Direct gray-scale extraction
• Minutiae Filtering
• Structural post-processing
• Minutiae filtering in the gray-scale domain
• Estimation of Ridge Count

4
Enhancement

• Performance depends on quality of images
• Ideal fingerprint
• Degradation types ridges are not continuous,
  parallel ridges are not well separated,
  cuts/creases/bruises
• Leads to problems in minutiae extraction

5
Enhancement

• For each fingerprint image, the fingerprint areas
• resulting from segmentation can be divided into

• Well-defined region
• Recoverable region
• Unrecoverable region

6
Enhancement Algorithms

• Goal to improve the clarity of the ridge
  structure in the recoverable regions and mark
  unrecoverable regions as too noisy for further
  processing
• Input a gray-scale image
• Output a gray-scale or binary image depending
  on the algorithm
• Effective initial steps - Contrast stretching,
  Histogram manipulation, Normalization, Wiener
  Filtering

7
Normalization approach Hong, Wan, Jain (1998)

• Determines the new intensity value of each pixel
  as,

m and v - image mean and variance m0 and v0 -
desired values after normalization

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

8
Contextual Filters

• The most widely used technique for fingerprint
  image enhancement
• Conventional image filtering a single filter is
  used for convolution throughout
• Contextual filtering - filter characteristics
  change according to local context
• Several types of contextual filters proposed
• Indented behavior 1)provide a low-pass
  averaging effect along the ridge direction.
  2)perform a band pass differentiating in the
  direction orthogonal to the ridges

9
Method proposed by OGorman and Nickerson

• A mother filter defined based on-minimum and
  maximum ridge width, minimum and maximum valley
  width.
• Filter is bell-shaped, elongated along the ridge
  direction, and cosine tapered in the direction
  normal to the ridges.
• The context is defined only by the local ridge
  orientation
• Once the mother filtered is generated, a set of
  16 rotated versions is derived.
• The image enhancement is performed by convolving
  each point of the image with the filter in the
  set whose orientation best matches the local
  ridge orientation

10
Method proposed by Sherlock, Monro, and Millard

• Performed in Fourier domain
• The filter is defined in the frequency domain by
  the function
• where Hradial depends only on the local ridge
• spacing ? 1/f and Hangle depends only on
  local ridge orientation ?
• Both Hradial and Hangle are defined as band-pass
  filters and are characterized by a mean value and
  a bandwidth
• The Fourier transform Pi,i1,n of the filters is
  pre-computed and stored

11
Method proposed by Sherlock, Monro, and Millard
(cont )

• Filtering of an input fingerprint image I is
  performed as follows
• The FFT(Fast Fourier Transform) F of I is
  computed
• each filter Pi is point-by-point multiplied by F,
  thus obtaining n filtered image transforms PFi,
  i1,n (in the frequency domain)
• Inverse FFT is computed for each PFi resulting in
  n filtered images PIi, i1,n (in the spatial
  domain)
• The enhanced image Ienh is obtained by setting,
  for each pixel x,y,
• Ienhx,y PIkx,y, where k is the index of
  the of the filter whose orientation is the
• closest to ?xy

12
Method proposed by Hong, Wan, and Jain

• Based on Gabor filters
• Gabor filters have both frequency-selective and
  orientation-selective properties and have optimal
  joint resolution in spatial and frequency domains
• A Gabor filter is defined by a sinusoidal plane
  wave tapered by a Gaussian

13
Method proposed by Hong, Wan, and Jain (cont ..)

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

Here, f is the frequency of a sinusoidal plane
wave and sx and sy are the standard deviations
of the Gaussian envelope along the x and y axes

14
Method proposed by Hong, Wan, and Jain (cont ..)
Gabor Filter

• 4 parameters ?,f,sx,sy
• The selection of the values sx and sy involves a
  tradeoff
• A set gij(x,y) i1n0,1..nf of filters are
  priori created and stored , where n0 is the
  number of discrete orientations ?i i1,..n0
  and nf the number of discrete frequencies fj
  j1,..nf
• Each pixel x,y is convolved, with filter
  gij(x,y) such that ?i is the discretized
  orientation closest to ?xy and fj is the
  discretized orientation closest to fxy

15
Method proposed by Hong, Wan, and Jain (cont ..)
Examples

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

16
Minutiae Detection

• Reliable minutiae extraction is extremely
  important
• Enhancement
• Binarization
• Thinning

17
Binarization-based methods

• Simplest method - global threshold
• Local threshold technique
• Fingerprint specific solutions necessary
• FBI minutiae reader by Stock and Swonger
• Composite approach based on a local threshold and
  a slit comparison formula that compares pixel
  alignment along eight discrete directions
• Method proposed by Moayer and Fu
• Based on an iterative application of a Laplacian
  operator and a pair of dynamic thresholds
• At each iteration the image is convolved through
  a Laplacian operator and the pixels whose
  intensity lies outside the range bounded by two
  thresholds are set to 0 and 1 respectively
• The thresholds are progressively moved towards a
  unique value to guarantee convergence

18
Binarization-based methods

• A fuzzy approach by Verma, Majumdar and
  Chatterjee
• Uses an adaptive threshold to preserve the same
  number of 1 and 0 pixels for each neighborhood
• Image is partitioned into small regions
• Each region goes through smoothing, fuzzy
  coding of the pixel intensities, contrast
  enhancement, binarization, 1s and 0s counting,
  fuzzy decoding, and parameter adjusting.
• Repeated until number of 1s approximately equals
  0s
• Method proposed by Coetzee and Botha
• Based 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 and other in the edge
  image
• Gray-scale domain binarization with local
  threshold
• Edge-image a blob-coloring routine is used to
  fill the area delimited by the two ridge edges
• The resulting image is the logical OR of the two
  individual binary images

19
Binarization-based methods

• Approach by Ratha, Chen and Jain
• Based on peak detection in the gray-scale
  profiles along sections orthogonal to the ridge
  orientation
• A 16x16 oriented window is centered around each
  pixel x,y
• The gray-scale profile is obtained by projection
  of the pixel intensities onto the central section

20
Binarization-based methods

• Approach by Ratha, Chen and Jain cont ..
• The profile is smoothed through the local
  averaging the peaks and the two neighboring
  pixels on either side of each peak constitute the
  foreground of the resulting binary image

21
Binarization-based methods

• Domeniconi, Tari and Liang (1998) modeled
  fingerprint ridges and valleys as sequences of
  local maxima and saddle points
• Maxima and saddle points are detected by
  evaluating gradient and the Hessian matrix H at
  each point
• The Hessian of a two-dimensional surface S(x,y)
  is a 2x2 symmetric matrix whose elements are the
  second-order derivatives of S with respect to
  x2,xy and y2
• The eigenvectors of H are the directions along
  which the curvature of S is extremized
• Let p be a stationary point and let ?1 and ?2 be
  the eigenvalues of H in p
• Then p is a local maximum if ?1 ?2 lt 0 and is a
  saddle point if ?1. ?2 lt 0

22
Binarization-based methods

• Approach by Tico and Kuosmanen (1999)
• A slightly different topological approach
• Fingerprint image is treated as a noisy sampling
  of the underlying continuous surface
• Approximated it by Chebyshev polynomials
• Ridge and Valley regions are discriminated by the
  sign of the maximal normal curvature of the
  surface
• The maximal normal curvature along any direction
  d is dTHd
• Abutaleb and Kamel (1999)
• Used Genetic Algorithms to discriminate ridges
  and valleys along the gray-level profile of the
  scanned lines
• The optimization criterion is aimed at increasing
  the correlation between adjacent gray-levels
  along fingerprint sections

23
Results from different methods
24
Thinning

• Reduces the width of the ridges to one pixel
• Skeletons , spikes
• Filling holes, removing small breaks, eliminating
  bridges between ridges etc.

25
Thinning

• Coetzee and Botha (1993) identify holes and gaps
  by tracking the ridge line edges through adaptive
  windows and remove them using a simple
  blob-coloring algorithm
• Hung (1993) uses an adaptive filtering technique
  to equalize the width of the ridges
• To remove the spikes, Ratha, Chen and Jain (1995)
  implement a morphological open operator.

26
Thinning

• Fitz and Green (1996) - removes small lines and
  dots both in the ridges and valleys of binary
  images through an application of 4 morphological
  operators on a hexagonal grid
• Luo and Tian (2000) - a two step method.
  skeleton extracted at the end of the first step
  is used to improve the quality of the binary
  image based on a set of structural rules. A new
  skeleton is extracted from this improved binary
  image.
• Ikeda et. al (2002) - use morphological
  operators to enhance ridges and valleys in the
  fingerprint binary image

27
Minutiae detection

• A simple image scan allows the pixel
  corresponding to minutiae to be detected
• crossing number of a pixel p

28
Examples of minutiae extraction
29
Direct gray-scale extraction

• Such methods are used to overcome the problems
  related to fingerprint binarization and thinning
  e.g. spurious minutiae
• Leung, Engeler, and Frank (1990)
• Introduced a neural network-based approach
• A multi-layer perceptron analyzes the output of a
  rank of Gabor filters applied to the gray-scale
  image
• The image is first transformed into frequency
  domain where the filtering takes place
• The resulting magnitude and phase signals
  constitute the input to the neural network
  composed of six sub-networks each of which is
  responsible for detecting minutiae at a specific
  orientation
• A final classifier is employed to combine the
  intermediate responses

30
Direct gray-scale extraction

• Maio and Maltoni (1997)
• Basic idea track the ridge lines in the
  gray-scale image, by sailing according to the
  local orientation of the ridge pattern
• A ridge line is defined as a set of points that
  are local maxima along one direction
• The ridge line extraction algorithm tries to
  locate the local maximum relative to a section
  orthogonal to the ridge direction
• A polygonal approximation of the ridge line can
  be obtained by connecting the consecutive maxima

31
Results of minutiae detection algorithm on a
sample fingerprint
32
Variations of Maio and Maltoni method

• Jiang, Yau, and Ser (1999) proposed µ be
  dynamically adapted
• Liu, Huang, and Chan (2000) instead of tracking
  a single ridge, the algorithm simultaneously
  tracks a central ridge and 2 surrounding valleys
• Chang and Fan (2001) aimed at discriminating
  the true ridge maxima in the sections O obtained
  during ridge line following. For this 2
  thresholds are initially determined.
• Bolle et. al (2002) - provided a formal
  definition of minutiae based on the gray-scale
  image that allows the location and orientation of
  an existing minutia to be more precisely
  determined

33
Minutiae Filtering

• Post-processing stage is useful for removing
  spurious minutiae already present or introduced
  by previous steps
• Two main post-processing types
• Structural post-processing
• Minutiae filtering in the gray-scale domain

34
Structural post-processing

• Xiao and Raafat (1991) identified the most common
  false minutiae structures and introduced an ad
  hoc approach
• The underlying algorithm is rule-based
• Requires as input length of the associated
  ridge(s), the minutia angle, the number of facing
  minutiae in a neighborhood

35
Structural post-processing

• Farina, Kovacs- Vajna, and Leone (1999)
  introduced some optimized variants of some
  previously proposed rules and algorithms
• Spurs and bridges are removed based on the
  observation that in a spurious bifurcation,
  only two branches are generally aligned whereas
  the third one is almost orthogonal to the other
  two
• Short ridges are removed on the basis of the
  relationship between the ridge length and the
  average distance between the ridges
• Terminations and bifurcations are then
  topologically validated they are removed if the
  topological requirements are not fully satisfied

36
Minutiae filtering in gray-scale domain

• A direct minutiae filtering technique reexamines
  the gray-scale image in a spatial neighborhood of
  a detected minutiae with the aim of verifying the
  presence of a real minutia
• Maio and Maltoni used a shared weight neural
  network to verify the minutiae detected by their
  gray-scale algorithm
• The minutiae neighborhoods are normalized with
  respect to their angle and the local ridge
  frequency

37
Minutiae filtering in gray-scale domain

• Then they are passed to a neural network
  classifier, which classifies them as termination,
  bifurcation and non-minutia
• A typical three layer neural network architecture
  has been adopted

38
Estimation of ridge count

• ridge count has often been used to increase
  reliability of analysis
• Ridge count is an abstract measurement of the
  distances between any two points in a fingerprint
  image
• Typically used in forensic matching

39
Summary of the chapter

• Most of the early work was based on
  general-purpose image processing techniques
• Recent developments have 2 important directions
• Focus on optimizing the salient discriminatory
  information in fingerprints
• Algorithms designed specifically for processing
  fingerprints images have been proposed

40
Direct Gray-Scale Minutiae Detection in
Fingerprints
D. Mario and D. Maltoni, IEEE Transactions on
Pattern Analysis and Machine Intelligence,
vol.19, no.1,pp. 27-39, 1997.
41
Outline

• Introduction
• Ridge Line Following
• Sectioning and Maximum Determination
• Tangent Direction Computation
• Stop criteria
• Minutiae Detection
• Performance Evaluation and Comparison
• Conclusion

42
Introduction

• Fingerprints are the most widely used biometric
  features
• Most automatic systems for fingerprint matching
  are based on minutiae matching
• Minutiae classification is based on 4 classes
  terminations, bifurcations, trifurcations
  (crossovers) and undetermined
• This work is based on a two-class minutiae
  classification

43
Introduction

• This work is a direct gray scale minutiae
  detection approach (i.e. without binarization and
  thinning )
• Reasons for not using binarization and thinning
• Loss of information
• Time-consuming
• Unsatisfactory on low-quality images
• Basic idea follow the ridge lines on the gray
  scale image
• A set of starting points is determined
• For each starting point, the algorithm keeps
  following the ridge lines until they terminate or
  intersects other ridge lines

44
Ridge line following basic definitions

• I 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 ,
  i1,,a and j1,,b
• Let z S (i, j) be the discrete surface
  corresponding to the image I S (i, j) gray (i,
  j), i1,a, j1,.b.
• Ridge line is defined as a set of points which
  are local maxima along one direction
• At each step, the algorithm attempts to locate a
  local maximum relative to a section orthogonal to
  the ridge direction
• By connecting the consecutive maxima, a polygonal
  approximation of the ridge line can be obtained

45
Ridge line following algorithm

• Starting point xc,yc and starting direction
  ?c
• Computes a new point xt,yt at each step moving
  µ pixels from the current point xc,yc along
  direction ?c
• Then it computes a section set O as the set of
  points belonging to the section segment lying on
  the xy-plane and having median point xt,yt,
  direction orthogonal to ?c and length 2s 1
• The new point xn,yn, belonging to the ridge
  line, is chosen among the local maxima of an
  enhanced version of the set O
• The point xn,yn becomes the current point
  xc,yc and a new direction ?c is computed

46
Ridge line following algorithm (pseudo-code
version)

• Let (is,js) be a local maximum of a ridge line of
  I
• F0 be the direction of the tangent to the ridge
  line in (is,js)

47
Ridge line following algorithm - steps
48
Sectioning and Maximum Determination

• Sectioning achieved by intersecting S with a
  cutting plane parallel to the z direction
• The section set O( (it, jt), F, s) centered in
  (it, jt), with direction F fc p/2, and length
  2s 1 pixels, is defined as,

49
Sectioning and Maximum Determination

• Difficulty in determining the local maximum of
  the section set O
• volcano silhouette

50
Sectioning and Maximum Determination

• An approach aimed at regularizing the section
  silhouette
• This makes the determination of the local maxima
  more reliable
• During the ridge line following, each time a new
  section is determined, we regularize its
  silhouette by means of two steps

51
Local regularization step 1
52
Local regularization step 2
53
Local regularization - results
54
Tangent Direction Computation

• The simplest approach based on gradient
  computation
• The gradient phase angle denotes the direction of
  the intensity maximum change
• Therefore, the direction fc of a hypothetical
  edge which crosses the region centered in the
  pixel (ic, jc), is orthogonal to the gradient
  phase angle in (ic, jc)
• This method, while being simple and efficient,
  suffers from non-linearity due to the computation
  of the gradient phase angle

55
Tangent Direction Computation

• Kawagoe and Tojo for each 2x2 pixel
  neighborhood, they make a straight comparison
  against four edge templates to extract a rough
  directional estimate, which is then
  arithmetically averaged over a larger region to
  obtain a more accurate estimate
• Stock and Swonger evaluate the tangent
  direction on the basis of pixel alignments
  relative to a fixed number of reference directions

56
Tangent Direction Computation

• Method used in this work
• Uses a gradient type operator to extract a
  directional estimate from each 2 x 2 pixel
  neighborhood
• Then its averaged over a local window by
  least-squares minimization to control noise

57
Stop Criteria

• Exit from interest area
• Termination
• Intersection
• Excessive bending

58
Minutiae Detection

• The main difficulty is of examining each ridge
  line only once and locating the intersections
  with ridge lines already extracted
• To solve this, an auxiliary image T is used
• T has the same dimension as that of I, and is
  initialized with pixel values set to 0
• Every time a new ridge line is extracted from I,
  the pixels of T corresponding to the ridge line
  are labeled by assigning them an identifier.

59
Minutiae Detection

• The pixels of T corresponding to a ridge line are
  the pixels belonging to the polygonal, e-thick,
  which links the consecutive maximum points (in,
  jn)
• The algorithm find minutia searches for a minutia
  by following the ridge line nearest to the
  starting point

60
Minutia Detection Algorithm
61
Minutia detection

• The algorithm starts by computing a point (ic,
  jc) belonging to the ridge line nearest to the
  starting point (is, js).
• This operation can be carried out as follows

62
Minutia detection

• The computation of tangent direction, the
  sectioning, the regularization and the
  determination of the maximum are performed as in
  the ridge line following algorithm.
• The following figure shows an example

63
Minutia Detectionstop criteria revisited
64
Minutia Detection

• The algorithm find minutia enables all the
  fingerprint minutiae within a window W to be
  detected
• Figure shows the results obtained by applying
  this approach to a sample fingerprint

65
Performance Evaluation and Comparison
66
Performance Evaluation and Comparison

• The technique mentioned in this paper (A) and
  four other schemes based on binarization and
  thinning B, C, D, E
• In all approaches , the minutiae detected have
  been filtered by removing
• The minutiae belonging to regions where the image
  contrast is less than half of the average image
  contrast
• The pairs of termination minutiae which are less
  than k pixels (k6) distant from each other
• The sets of bifurcation minutiae (except one
  minutia for each set) belonging to a neighborhood
  with diameter k pixels (k6)

67
Performance Evaluation and Comparison
68
Performance Evaluation and Comparison
69
Performance Evaluation and Comparison
70
Conclusions - drawn 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.

71
Performance Evaluation and Comparison
72
Computational complexity

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

73
The elementary operations carried out at each
ridge line following step
74
Conclusion

• A new technique is proposed based on ridge
  line following algorithm
• In spite of greater conceptual complexity, this
  technique has less computational complexity than
  the complexity of techniques requiring
  binarization and thinning