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Fingerprint Matching

Explore the complexities of fingerprint matching, including various issues, state-of-the-art techniques, and computational improvements for accurate verification.

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Fingerprint Matching

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  1. 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

  2. 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

  3. Issues involved with matching • “extremely difficult problem” • Displacement • Rotation • Partial Overlap • Not completely in image • Distortion (Non-Linear) • Stretches when pushed down

  4. More issues • Pressure and Skin condition • Pressure, dryness, disease, sweat, dirt, grease, humidity • Noise • Dirt on the sensor • Feature Extraction Errors

  5. 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

  6. 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

  7. FVC2002

  8. 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

  9. 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

  10. Correlation Results

  11. 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)

  12. 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

  13. Computation Improvements • Correlation Theorem • Spatial Correlation = point wise mutation in fourier domain • TI = F-1(F *(T) x F(I)) • Resultant image has values = correlation for translating to those points • No rotation • Very large computation improvement

  14. 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

  15. Optical Fingerprint Matching • Lenses to derive the Fourier transform of the images • Joint transform correlator for matching • Very expensive • Complex • Immature

  16. 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 • 

  17. Alignment • Displacement • Rotation • Scale • Distortion-tolerant transformations • More transformations • higher degree of freedom for matcher • More false matches

  18. 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(mapx, 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

  19. 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

  20. 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

  21. Matching

  22. 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

  23. 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

  24. 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

  25. 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

  26. 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

  27. Hough Transform

  28. 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

  29. 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 Swith the highest A value • mi1,mj1 are the principle pair and S is the course transformation

  30. 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

  31. 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

  32. 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

  33. 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

  34. 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

  35. 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

  36. Results

  37. Results

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