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Chapter 4.1- 4.3 On-Line Fingerprint Verification Anil Jain, Fellow, IEEE, Lin Hong, and Ruud Bolle, Fellow, IEEE Presented by Chris Miles. Fingerprint Matching. Fingerprint Matching. Compare two given fingerprints T,I Return degree of similarity (0->1) Binary Yes/No
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Chapter 4.1- 4.3 On-Line Fingerprint Verification Anil Jain, Fellow, IEEE, Lin Hong, and Ruud Bolle, Fellow, IEEE Presented by Chris Miles Fingerprint Matching
Fingerprint Matching • Compare two given fingerprints T,I • Return degree of similarity (0->1) • Binary Yes/No • T -> template, acquired during enrollment • I -> Input • Either input images, or feature vectors (minutiae) extracted from them
Issues involved with matching • “extremely difficult problem” • Displacement • Rotation • Partial Overlap • Not completely in image • Distortion (Non-Linear) • Stretches when pushed down
More issues • Pressure and Skin condition • Pressure, dryness, disease, sweat, dirt, grease, humidity • Noise • Dirt on the sensor • Feature Extraction Errors
State of the Art • Many algorithms match high quality images • Challenge is in low-quality and partial matches • 20% of the problems (low quality) at FVC2000 caused 80% of the false non-matches • Many were correctly identified at FVC2002 though
Approaches • Correlation-based matching • Superimpose images – compare pixels • Minutiae-based matching • Classical Technique – Most popular • Compare extracted minutiae • Ridge Feature-based matching • Compare the structures of the ridges • Everything else
Correlation-based Techniques • T and I are images • Sum of squared Differences • SSD(T,I) = ||T-I||2 = (T-I)T(T-I) = ||T||2 + ||I||2 – 2TTI • Difference between pixels • ||T||2 + ||I||2 are constant under transformation • Try to maximize correlation – Minimizes difference • CC(T,I) = TTI • Can't be used because of displacement / rotation
Maximizing Correlation • I(x,y,) • Transformation of I • Rotation around the origin by • Translation by x,y • S(T,I) = max CC(T,I(x,y,)) • Try them all – take max
Doesn't Work • Non-Linear distortion is significant and not accounted for • Skin Condition / Pressure cause brightness / contrast and thickness to vary significantly • Difference correlation • Check max/min correlation values • Matches show greater range • Computationally Expensive (try them all)
Divide and Conquer • Identify local regions in the image • Pieces of the whole • Interesting regions • Match them • Sum correlations to find global correlation • Check difference of transforms for each region • Consolidation
Computation Improvements • Correlation Theorem • Spatial Correlation = point wise mutation in fourier domain • TI = F-1(F *(T) x F(I)) • Resultant image has values = correlation for translating to those points • No rotation • Very large computation improvement
Computational Improvements • Multi resolution hierarchical approaches • Fourier-Mellin • Gives rotational invariance • Other steps reduce accuracy • Divide and Fourier • Partition into local regions • Match them against each other • Border overlap • Much faster
Optical Fingerprint Matching • Lenses to derive the Fourier transform of the images • Joint transform correlator for matching • Very expensive • Complex • Immature
Minutiae-based Methods • Classical Technique • T, I are feature vectors of minutiae • Minutiae = (x,y,) • Two minutiae match if • Euclidean distance < r0 • Difference between angles < • Tolerance Boxes • r0 •
Alignment • Displacement • Rotation • Scale • Distortion-tolerant transformations • More transformations • higher degree of freedom for matcher • More false matches
Formulation • M''j = map(m'j) • Map applies a geometrical transformation • mm(m''j, mi) returns 1 if they match • Matching can be formulated as • maximize mm(mapx, y, )(m'P(i)), mi) • P is an unknown function which pairs the minutiae • Which minutiae in I corresponds to which in T m i=1 • x, y, , P
P • Pairs the minutiae • If P(i) = j • j is i's mate • Most likely pair • If P(i) = null • i, from T has no mate in I • If no i matches a j, that j has no mate • Each minutiae has a maximum of one mate • Trivial if alignment is known
Point Pattern Matching • Alignment is rarely known • Cast as point pattern matching • Angular component is only a small difference • Techniques • Relaxation • Algebraic and operational research solutions • Tree search (pruning) • Search (Energy Minimization) • Hough Transform
Relaxation • Maintain confidence levels between all possible matchings • How likely we think Ia matches Tb • Iteratively • Calculate the consistencies the transformations required for those matches • Adjust the confidence levels of points that agree with other points • Decrease others • Iterative -> slow
Algebraic and Operational Research Solutions • Use algebraic methods • Requires very restrictive assumptions • Exactly aligns under affine transformation • N = M • All minutiae perfectly identified • Assignment problems • Bipartite graph matching
Tree Search (Pruning) • Search the tree of possible matches • If A matches B, then C matches F, then D matches K • More assumptions • M=N • No outliers -> All minutiae must match
Search (Energy Minimization) • Cast as a general search problem • Search towards the optimal set of matches • Fitness is a function of consistency • Can use any general search technique • GA • Simulated Annealing
Hough Transform • Brute force search over possible Pairings / rotations / scalings • Foreach mi in I • Foreach mj in T • Foreach in discretized 's • If I – J < threshold • Foreach scale in discretized scales • dx,dy = mi – map ,scale (mj) • A[dx,dy,theta,scale]++ • Whichever A is highest is the closest transformation • Can then find pairings easily
Improvements • Vote on neighboring bins / smooth the bins, to get more robust answers • Parallelize on custom hardware • Hierarchical discretization • Chang et al 1997 • Find the principle pair and a course transformation with respect to it that matches the most points • Calculate pairing • Use the pairing to calculate exact alignment
Principle Pair • Brute force for the segment, 2 pts, which can be best mapped to a corresponding segment in T • Foreach mi in I • Foreach mj in T • Reset A • Foreach mi2 in I • Foreach mj2 in T • ,S = Transformation required to turn mi1,mi2 into mj1,mj2 • A[,S]++ • Remember the mi1and mj1 and Swith the highest A value • mi1,mj1 are the principle pair and S is the course transformation
Segment Matching • Udupa, Garg, Sharma 2001 • Looking for matching segments of similar lengths • Foreach, determine transforms to match them • Try to match remaining minutiae • Check consistencies of best matches • Final score is a combination of the number of mated pairs, the fraction of consistent alignments, and the topological correspondence
Minutiae match with pre-alignment • Idea – pre-align T before storage in database • Align each I just once against the global orientation • Reduces computation in identification systems • Absolute pre-alignment • Orient everything in a common direction • No reliable system to do this • Difficult to detect core, or even basic orientation • Relative pre-alignent • Align I to for each T seperately • No computation savings
M82 – Fbi • Do course absolute pre-alignment • Center the image around the core location • Orient it with ridges to the left/right averaged facing up • Find principal pairs • Look at minutiae around the center • Find the best matching pair -> Principle • Calculate course transformation, deformation tensor
Avoiding Alignment • Ordinary Person - “You should go to work” • Philosopher - “Why?” • Intrinsic coordinate system • Instead of using global coordinate system orient them with respect to the ridge patterns • Minutiae are defined with respect to this • Transformation / rotation does not change their relative location • Problems partitioning the image into the local coordinate systems
Ridge Relative Pre-alignment • Jain, Hong, Bolle 1997 • Store minutiae along with information about the ridge attached to it • Oriented along minutiae orientation • Normalized to ridge frequency • Compare with other ridges until you find a good match • Take as principle pair
Comparing ridges • Convert minutiae in T,I to polar coordinates with respect to the reference minutiae • Reference minutiae = the one with the ridge • Order them into a list • Check how many insertions / deletions / transformations are necessary to match the lists • Variant • Match distances and relative angles of sampled points