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Fingerprint recognition and synthesis – advanced techniques. Biometric Course CPSC 601. Overview. Advanced Matching: Correlation-based techniques Minutiae-based techniques Point-pattern matching Minutiae with pre-alignment Classification Syntactic Structural Statistical Retrieval
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Fingerprint recognition and synthesis – advanced techniques Biometric Course CPSC 601
Overview • Advanced Matching: • Correlation-based techniques • Minutiae-based techniques • Point-pattern matching • Minutiae with pre-alignment • Classification • Syntactic • Structural • Statistical • Retrieval • Synthesis
Correlation-based techniques • Let T and I be the two fingerprint images corresponding to the template and the input fingerprint respectively. A measure of the diversity is the sum of squared differences (SSD) between the intensities of the corresponding pixels: SSD(T, I) = || T – I ||2 = (T – I)T(T – I) = || T ||2 + || I ||2 – 2TTI • If the terms || T ||2 and || I ||2 are constant, the diversity between the two images is minimized when the cross-correlation (CC) between T and I is maximized: CC(T, I) = TTI
Correlation-based techniques • Due to the displacement and rotation that characterize two impressions of a given finger, their similarity cannot be simply computed by superimposing T and I. • Let I(∆x, ∆y, θ) represent a rotation of the input image I by an angle θ around the origin and shifted by ∆x, ∆y pixels in directions x and y respectively. Then the similarity between the two fingerprint images T and I can be measured as: S(T, I) = max∆x, ∆y, θCC(T, I (∆x, ∆y, θ))
Distortions • Non-linear distortion makes impressions of the same finger significantly different in terms of global structure. • Skin condition and finger pressure cause image brightness, contrast and ridge thickness to vary significantly across different impressions. • A direct application of the last equation is computationally very expensive.
Correlation • The correlation theorem states that computing the correlation in the spatial domain is equivalent to performing a point-wise multiplication in the Fourier domain; in particular, Where F(.) is the Fourier transform of an image, F-1(.) is the inverse Fourier transform, “*” denotes the complex conjugate and “X” denotes the point by point multiplication of two vectors. The result is a correlation image whose value at the pixel [x, y] denotes the correlation between T and I when the displacement is ∆x = x and ∆y = y. • Computing the maximum correlation need not necessarily be done in a sequential, exhaustive manner; multi-resolution approaches, space-searching techniques (gradient descent), and other heuristics can be adopted to reduce the number of evaluations. • The Fourier-Mellin transform may be used instead of Fourier transform to achieve rotation invariance in addition to translation invariance. • The approach proposed by Wilson, Watson and Paek partitions both T and I into local regions and computes the maximum correlation (in the Fourier domain) between any pair of regions. This method suffers from “border effects” because of the partial overlapping between the different blocks, but can considerably speed up the matching process. • Correlation between two signals can be computed by an optical system that uses lenses to derive the Fourier transform of the images and a joint transform correlator for their matching.
Minutiae-based Methods Minutiae matching is certainly the most well-known and widely used method for fingerprint matching. Let T and I be the representation of the template and input fingerprint respectively. Each minutia may be described by a number of attributes, including its location in the fingerprint image, orientation, type etc. Most common minutiae matching algorithms consider each minutia as a triplet m = {x, y, θ} that indicates the x, y minutia location coordinates and the minutia angle θ: T = {m1, m2,…,mm}, mi = {xi, yi, θi}, i =1..m I = {m'1, m'2,…,m'n}, m'j = {x'j, y'j, θ'j}, j =1..n, where m and n denote the number of minutiae in T and I respectively. Aligning the two fingerprints is a mandatory step in order to maximize the number of matching minutiae. Correctly aligning two fingerprints certainly requires displacement and rotation to be recovered, and likely involves other geometric transformations: • Scale has to be considered when the resolution of the two fingerprints may vary. • Other distortion-tolerant geometrical transformations could be useful to match minutiae in case one or both of the fingerprints is affected by severe distortions.
Minutiae-based Methods Let map(.) be the function that maps a minutia m'j (from I) into m"j according to a given geometrical transformation; for example, by considering a displacement of [∆x, ∆y] and a counterclockwise rotation θ around the origin: map ∆x, ∆y, θ(m'j = {x'j, y'j, θ'j}) = m"j = {x"j, y"j, θ'j + θ}, where
Approaches to point pattern matching Relaxation: The relaxation approach iteratively adjusts the confidence level of each corresponding pair of points based on its consistency with other pairs until a certain criterion is satisfied. At each iteration r, the method computes m . n probabilities pij (probability that point i corresponds to point j): where c(i,j;h,k) is a compatibility measure between the pairing (i, j) and (h, k), which can be defined according to the consistency of the alignments necessary to map point j into i and point k into h. The above equation increases the probability of those pairs that receive substantial support by other pairs and decreases the probability of the remaining ones. At convergence, each point i may be associated with the point j such that pij = maxs{pis}, where s is any other point in the set. Algebraic and operational research solutions: This is based on the restrictive hypothesis that n = m and that an exact alignment may be recovered under an affine transformation.
Approaches to point pattern matching Tree Pruning: It attempts to find the correspondence between the two point sets by searching over a tree of possible matches while employing different tree-pruning methods to reduce the search space. Energy minimization: These methods define a function that associates an energy with each solution of the problem. Optimal solutions are then derived by minimizing the energy function by using a stochastic algorithm such as genetic algorithm or simulated annealing. Hough Transform: This method converts point pattern matching to the problem of detecting peaks in the Hough space of transformation parameters.
Minutiae matching with pre-alignment Storing pre-aligned templates in the database and pre-aligning the input fingerprint before the minutiae matching can speed up the 1:N identification. The two main approaches for pre-alignment are:- • Absolute pre-alignment • Relative pre-alignment
Minutiae matching with pre-alignment The M82 method, developed for minutiae-based fingerprint matching performs a coarse absolute pre-alignment according to the core position (detected through R92 method) and the average orientation of two regions located at the two sides of the core.
Minutiae matching with pre-alignment After the course absolute pre-alignment of both T and I minutiae, M82 determines a list of candidate minutiae pairs by considering the minutiae that are closer than a given distance; the matching degree of each candidate pair is consolidated according to the compatibility with other pairs. The list is sorted with respect to the degree of matching; the top pair is selected as the principal pair and all the remaining minutiae are translated accordingly. In a second stage, a deformation tensor, which allows the matching to tolerate small linear distortion and rotations, is determined.
Minutiae matching with pre-alignment Jain, Hong and Bolle (1997) proposed a minutiae matching approach that exploits ridge features for relative pre-alignment. The relative pre-alignment is based on the observation that minutiae registration can be performed by registering the corresponding ridges. In fact, each minutia is associated with a ridge; during the minutiae extraction stage, when a minutia is detected and recorded, the ridge on which it resides is also recorded. The ridge is represented as a planar curve, with its origin coincident with the minutia and its x-coordinate being in in the same direction as the minutia direction. Also, this planar curve is normalized (in scale) with respect to the average ridge frequency. By matching these ridges, the parameters (∆x, ∆y, θ) may be recovered. The ridge matching task proceeds by iteratively matching pairs of ridges until a pair is found whose matching degree exceeds a certain threshold. The pair is then used for relative pre-alignment.
Avoiding alignment Fingerprint alignment is a critical and time-consuming step. Bazen and Gerez (2001) introduced an intrinsic coordinate system (ICS) whose axes run along hypothetical lines defined by the local orientation of the fingerprint pattern. First, the fingerprint is partitioned in regular regions (i.e. regions that do not contain singular points). In each regular region, the ICS is defined by the orientation field. When using intrinsic coordinates instead of pixel coordinates, minutiae are defined with respect to their position in the orientation field. Translation, displacement and distortion move minutiae with the orientation field they are immersed in and therefore do not change their intrinsic coordinates.
Galton-Henry classification The five most common classes of the Galton-Henry classification scheme are: Arch: An arch fingerprint has ridges that enter from one side, rise to a small bump and go out the opposite side; Arches do not have loops or deltas. Tented Arch: Similar to (plain) arch, except that at least one ridge exhibits a high curvature and one loop and one delta are present. Loop: Has one or more ridges that enter from one side, curve back, and go out the same side they entered. There can be left loops and right loops. Whorl and Whorl with a twin loop: Contains at least one ridge that makes a complete 360-degree path around the center of the fingerprint.
Classification Techniques The features of a fingerprint image used for identification are:- • Ridge line flow • Orientation image • Singular points • Gabor filter responses
Syntactic approaches A syntactic method describes patterns by means of terminal symbols and production rules. A grammar is defined for each class and a parsing process is responsible for classifying each new pattern. The approach introduced by Rao and Black(1980) is based on the analysis of ridge line flow, which is represented by a set of connected lines. These lines are labeled according to the direction changes, thus obtaining a set of strings that are processed through ad hoc grammars or string-matching techniques to derive the final classification.
Structural approaches Structural approaches are based on the relational organization of low-level features into higher-level features. The relational organization is represented by means of symbolic data structures, such as trees and graphs, which allow a hierarchical organization of the information. Maio and Maltoni (1996) partition the orientation image into regions by minimizing a cost function that takes into account the variance of the element orientations within each region. An inexact graph matching technique is then used to compare the relational graphs with class-prototype graphs.
Structural approaches In Chappelli et al. (1999), a template-based matching is performed to guide the partitioning of the orientation images. The main advantage of this approach is that, because it relies only on global structural information, it is able to deal with partial fingerprints, where some singular points are not available, and it can also work on very noisy images.
Statistical approaches • One of the most widely adopted statistical classifiers is the k-nearest neighbor; examples of its application in the fingerprint-classification domain can be found in Fitz and Green(1996), where wedge-ring features obtained from the hexagonal Fourier transform are used as input, and in Jain, Prabhakar and Hong(1999), where the first step of a two-stage classification technique is performed by means of the k-nearest neighbor rule. • Many approaches directly use the orientation image as a feature vector, by simply nesting its rows. By encoding each element of the orientation image with the two components [rcos2θ, rsin2θ], a typical 30 X 30 orientation image results in a vector of 1800 elements. Training a classifier with such high-dimensional vectors would require large amounts of training data, memory and computation time. For this reason, statistical dimensionality reduction techniques are often applied to reduce the dimensionality of the feature vector.
Example of the system A functional scheme of PCASYS (Candela et al., 1995)
Retrieval strategies If an exclusive classification technique is used for indexing, these retrieval strategies can be used: Hypothesized class only Fixed search order Variable search order
Synthetic Fingerprint generation The strategy is to generate a master fingerprint first. Then several synthetic impressions can be derived from the master fingerprint by explicitly tuning displacement, rotation, distortion, skin condition and noise.
Generation of a master fingerprint Creating a master fingerprint involves the following steps: • Fingerprint area generation • Orientation image generation • Frequency image generation • Ridge pattern generation
Generation of a master fingerprint Fingerprint area generation Depending on the finger size, position and pressure against the acquisition sensor, the acquired fingerprint images have different sizes and external shapes.
Generation of a master fingerprint A simple model based on four elliptical arcs and a rectangle and controlled by five parameters can handle most of the variations present in real fingerprint shapes. The following figure shows some examples of fingerprint shapes generated by this model by varying the five parameters.
Generation of a master fingerprint Orientation image generation The orientation model proposed by Sherlock and Monro (1993) allows a consistent orientation image to be computed from the knowledge of the position of the fingerprint singularities (loops and deltas) alone. In this model, the image is located in the complex plane and the local ridge orientation is the phase of the square root of a complex rational function whose singularities (poles and zeros) are located at the same place as the fingerprint singularities (loops and deltas).
Generation of a master fingerprint Frequency image generation The steps are:- • A feasible overall frequency is randomly selected according to the distribution of ridge line frequency in real fingerprints; an average ridge/valley period of nine pixels is used: this simulates a 500 dpi sensor. • The frequency in the above-described regions is slightly decreased according to the positions of the singularities. • The frequency image is randomly perturbed to improve its appearance. • A local smoothing by a 3 X 3 averaging box filter is performed.
Ridge pattern generation • Given an orientation image and a frequency image as an input, a deterministic generation of a ridge line pattern, including consistent minutiae, is not an easy task. One could try to fix a priori the number, the type, and the location of the minutiae, and by means of an explicit model, generate the gray-scale fingerprint image starting from the minutiae neighborhoods and expanding to connect different regions until the whole image is covered.
Ridge pattern generation Gabor filters They are an effective tool for fingerprint enhancement. SFINGE uses equal values for the standard deviations of the Gaussian envelope along the x and y axes: σx = σy = σ The filter applied at each pixel [x, y] has the form:
Perturbation and global translation/rotation Perturbation and global translation/rotation The perturbation phase sequentially performs the following steps: • Isolate the white pixels associated with the valleys into a separate layer. This is simply performed by copying the pixels brighter than a fixed threshold to a temporary image. • Add noise in the form of small white blobs of variable size and shape. The amount of noise increases with the inverse of the fingerprint border distance. • Smooth the resulting image with a 3 X 3 averaging box filter. • Superimpose the valley layer to the resulting image. • Rotate and translate the image.
