Geometric Algorithms in Biometrics: Theory and Recent Developments

1. Geometric Algorithms in Biometrics: Theory and Recent Developments Prof. Marina L. Gavrilova BT Laboratory Dept of Computer Science, University of Calgary, Calgary, AB, Canada, T2N1N4

2. Presentation Overview • Geometric Algorithms Preliminaries • Methodology • Voronoi diagrams - definition • Voronoi diagrams - properties • Dual data structure – Delaunay triangulation • Applications: VD in fingerprint recognition, multi-resolution in iris synthesis, distance transform in facial expression modeling and morphing.

3. Processing Data Collection Decision Pattern matching Reporting Sensors Sensors Data source Sensors Data source Data source Identification/Verification Feature extraction Transmission Storage Data Base Compression module Biometric System

4. Processing Data Collection Decision Feature extraction Pattern matching Data source Data source Sensors Data source Sensors Data pre-processing Reporting Sensors Transmission Storage Data Base Compression module Computational Geometry in Biometrics CG methods

5. Threshold distance • A threshold distance: declare distances less than the threshold as a "match" and those greater to indicate "non-match". • Genuine distribution • Inter-template distribution • Imposter distribution

6. Use of metrics • Regularity of metric allows to measure the distances from some distinct features of the template more precisely, and ignore minor discrepancies originated from noise and imprecise measurement while obtaining the data.

7. Pattern Matching • Aside from a problem of measuring the distance, pattern matching between the template and the measured biometric characteristic is a very serious problem on its own.

8. Template comparison • The most common methods are based on bit-map comparison techniques, scaling, rotating and modifying image to fit the template through the use of linear operators, and extracting template boundaries or skeleton (also called medial axis) for the comparison purposes. • In addition, template comparison methods also differ, being based on either pixel to pixel, important features (such as minutae) positions, or boundary/skeleton comparison.

9. Voronoi methods in biometrics • The methodology is making its way to the core methods of biometrics, such as fingerprint identification, iris and retina matching, face analysis, ear geometry and others [Xiao, Zhang, Burge]. • The methods are using Voronoi diagram to partition the area of a studies image and compute some important features (such as areas of Voronoi region, boundary simplification etc.) and compare with similarly obtained characteristics of other biometric data.

10. Applications of Voronoi Diagrams

11. List of Projects • Methodology • Topology-based Matching Algorithm for Fingerprint Recognition in the Presence of Elastic Distortions • Multi-resolution approach for Iris synthesis • Non photo-realistic rendering of facial expressions and aging

12. Background: Voronoi diagram and Delaunay Tessellation A commonly used term in computational geometry is the Voronoi diagram and Delaunay Tessellation A generalized Voronoi diagram(GVD) for a set of objects in space is the set of generalized Voronoi regions where d(x,P)is a distance function between a point x and a site P in the d-dimensional space.

13. Delaunay Tessellation Ageneralized Delaunay tessellation (triangulation in 2d) is the dual of the generalized Voronoi diagram obtained by joining all pairs of sites whose Voronoi regions share a common Voronoi edge according to some specific rule.

14. Voronoi diagram in 2D

15. Generalized Voronoi diagram A generalized Voronoi diagram for a set of objects in the space is the set of generalized Voronoi regions according to some proximity rule. A generalized Delaunay triangulationis the dual of the generalized Voronoi diagram obtained by joining all pairs of sites whose Voronoi regions share a common Voronoi edge.

16. Example: VD and DT in power metric

17. Distance metrics for Voronoi Diagrams General Lp distance Manhattan Supremum Manalanobis

18. List of Projects in BTLab • Methodology • Topology-based Matching Algorithm for Fingerprint Recognition in the Presence of Elastic Distortions • Multi-resolution approach for Iris synthesis • Non photo-realistic rendering of facial expressions and aging

19. Computation Geometry in Fingerprint Identification • Application of Voronoi diagram and Delaunay triangulation in pattern matching. • Space data interpolation to compensate for elastic distortions. • Image Distance Transform to represent fingerprint ridge shape.

20. Outline • 1. Why and how we use Delaunay triangulation to represent fingerprint feature—local matching • 2. How to solve the finger deformation problem - Apply RBF to match the deformed fingerprint. • 3. Apply nearest neighbor approach (Voronoi diagram) for the global matching.

21. a: original image b: orientation field Terminology (1) • Fingerprint image • Ridge, Valley • Orientation field

22. a: Endpoint b: Bifurcation Bifurcation point and end point ([2]) Terminology (2) • Minutiae points • Bifurcation • End • Singular Points

23. Fingerprint Verification Flowchart of fingerprint verification system

24. (c) Our task (a) (b) (a) Input fingerprint image, (b) Template fingerprint image, (c) Result of registration

25. Singular-point detection • In many biometric problems, such as detecting singular points in fingerprint images, the quality of the result and false detection rates depend directly on the quality of the data (image, print, recording etc). • To improve the result, pre-processing can be used. • Many cases of false detection happen at the boundary of an image or at place where lines are of irregular shape. • Extending the ridge lines beyond the boundary so that the false minutiae point is not detected or topology-based method to smooth the irregularity (including the interpolation techniques) are used [Maltony, Jain, Zhan].

26. Singular point detection Singular point detection example.

27. DT for minutiae point extraction (a) Thinned Image (b) Minutia Extracted

28. DT for minutiae point extraction (a) Purified minutia (b) DT constructed based on (a)

29. DT for matching Delaunay Triangulation can be used for Matching For each Delaunay triangle, the length of three edges, the three angles and the ridge numbers between each edge are recorded to construct a 9 dimensional local vector to find the best-matched local structure in two fingerprints.

30. A A’ θ2 θ’2 θ1 θ'1 B B’ Triangle edge comparison in minutiae matching

31. Delaunay Triangulation of Minutiae Points

32. 2. Modeling Deformation using Radial Basis Functions • What we assume in the global matching is that very point pairs in input fingerprint image and template image have the same transformation , which is a rigid transformation. In fact this is not true due to the elasticity of finger.

33. Rigid Transformation &Non-rigid Transformation (a) Original grid b) Rigid Transformation (c) Non-rigid Transformation Property of rigid Transformation (b): (1) Every point share the same transformation (2) The distance and angle of points are unchanged.

34. Spatial Interpolation using RBF(Radial Basis Functions) Deformation in 2D and 3D

35. Modelling Fingerprint Distortion Region a: a close-contact region Region b: a transitional region Region c: external region Distortions of a square mesh obtained by applying left model

36. Nonlinear deformation on fingerprint • Apply deformation model

37. Apply RBF to solve the deformation function

38. 3. Global matching (Count the number of matching minutiae points)

39. Nearest Neighbor Approach

40. Additional information for matching • So far, we only used the number of matching minutiae points as the matching criterion. We can also add matching score and singular points to verify match under certain transformation

41. List of Projects • Methodology • Topology-based Matching Algorithm for Fingerprint Recognition in the Presence of Elastic Distortions • Multi-resolution approach for Iris synthesis • Non photo-realistic rendering of facial expressions and aging

42. Goals • Synthesis Of Biometric Databases • Iris Database Augmentation • Testing Recognition Methods • Minimal User Input

43. Previous Work • Iris Recognition - [Wildes 94, Daugman 04] • Biometric Synthesis - [Yanushkevich et al. 04] • Iris Synthesis - [Lefohn et al. 03, Cui et al. 04]

44. Iris Synthesis • An Ocularists Approach to Human Iris Synthesis. • [ Lefohn et. al. 03] • An Iris image synthesis method based on PCA and Super-Resolution. • [Cui et. al. 04]

45. Our Approach • Capture Characteristics • Combine Characteristics

46. Organization

47. Ocularists Approach • Uses: 30-70 Layers • Great Results. • Domain Specific Knowledge An ocularist's approach to human iris synthesis. Lefohn et. al. 2003. Used with permission.

48. Method • First step: Isolate the iris. • Polar Transform • Iris Stretching

49. Multiresolution • Data has many resolutions • Levels of resolution have different meanings • Reverse Subdivision • Details

50. Decomposition