2. 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

3. 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.

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

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

6. 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

7. 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.

8. 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.

9. 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.

10. 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.

11. Applications of Voronoi Diagrams

12. 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

13. 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.

14. Delaunay Tessellation A generalized 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.

15. Voronoi diagram in 2D

16. 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 triangulation is the dual of the generalized Voronoi diagram obtained by joining all pairs of sites whose Voronoi regions share a common Voronoi edge.

17. Example: VD and DT in power metric

18. Distance metrics for Voronoi Diagrams General L p distance Manhattan Supremum Manalanobis

19. 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

20. 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.

21. 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.

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

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

24. Fingerprint Verification Flowchart of fingerprint verification system

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

26. 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].

27. Singular point detection Singular point detection example.

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

29. (a) Purified minutia (b) DT constructed based on (a)

30. 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. 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.

31. Triangle edge comparison in minutiae matching θ2θ2 B θ1θ1 A θ’ 2 B’B’ θ' 1 A’A’

32. Delaunay Triangulation of Minutiae Points

33. 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.

34. 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.

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

36. 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

37. Nonlinear deformation on fingerprint  Apply deformation model

38. Apply RBF to solve the deformation function

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

40. Nearest Neighbor Approach

41. 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

42. 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

43. Goals ● Synthesis Of Biometric Databases ● Iris Database Augmentation ● Testing Recognition Methods ● Minimal User Input

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

45. 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]

46. Our Approach ● Capture Characteristics ● Combine Characteristics

47. Organization

48. Our Approach ● Use Real Iris Sample ● Use sets of Similar Irises ● Capture Characteristics ● Chaikin Reverse Subdivision ● Combine Characteristics ● Multiple Iris Donors

49. 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.

50. Method  First step: Isolate the iris. Polar Transform Iris Stretching

51. Multiresolution ● Data has many resolutions ● Levels of resolution have different meanings ● Reverse Subdivision ● Details

52. Decomposition

53. Method ● Capture Details ● Reverse Subdivision ● Details ● All Characteristics Courtesy of: Michal Dobes and Libor Machala, Iris Database, http://www.inf.upol.cz/iris/http://www.inf.upol.cz/iris/

54. Combinations

55. Classifications ● Frequency of Data ● Number of Concentric Rings Courtesy of: Michal Dobes and Libor Machala, Iris Database, http://www.inf.upol.cz/iris/http://www.inf.upol.cz/iris/

56. Database Size

57. Courtesy of: Michal Dobes and Libor Machala, Iris Database, http://www.inf.upol.cz/iris/http://www.inf.upol.cz/iris/ Original Set

58. Courtesy of: Michal Dobes and Libor Machala, Iris Database, http://www.inf.upol.cz/iris/http://www.inf.upol.cz/iris/ Output Irises

59. Future Work ● Post-Processing ● Multiple samples of each iris ● Verification ● Statistically

60. 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

61. Presentation Overview  Applications template matching morphing  Distance Transforms  Euclidean Distance Transform Algorithm algorithm description: Chains, Zen and The Art of Chain Maintenance

62. Template Matching Image Template

63. What is a Distance Transform? Given an n x m binary image I of white and black pixels, the distance transform of I is a map that assigns to each pixel the distance to the nearest black pixel (a feature).

64. Distance Transform as a Temperature Map

65. What is a Feature Transform? The feature transform of I is a map that assigns to each pixel the feature that is nearest to it.

66. L 1 Distance Transform Algorithm

67. Image Morphing Two steps: 1) Establish feature correspondences: manually 2) Mapping function: define spatial relationship between all points in both images + = Examples from the “facial attractiveness” project: www.beautycheck.dewww.beautycheck.de 500 corresponding points

68. Starting FrameEnding Frame

69. Starting FrameEnding Frame

70. Starting FrameEnding Frame

71. Starting FrameEnding Frame

72. Starting FrameEnding Frame

73. Conclusions  Geometric data structures and methodology based on proximity and topology prove to be useful for emerging field of biometric technologies.  The overview discussed existing computational geometry methods and their recently developed applications in biometrics  We suggest a number of new approaches for investigation of specific biometric problems, including those of synthesis of biometric information.

74. Acknowledgements  CFI Granting Agency  GEOIDE Granting Agency  NSERC Granting Agency  EU Marie Curie Actions  International Center for Voronoi Diagram Research  SPARC and BTLab Collaborators and Students  USBN Grant and Prof. Frank Devai