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
Presentation Overview
Geometric Algorithms Preliminaries Methodology Voronoi diagrams - definition
Voronoi diagrams - properties
Dual data structure – Delaunay triangulation Applications: VD in fingerprint recognition, multiresolution in iris synthesis, distance transform in facial expression modeling and morphing.
Biometric System
Data Collection
Processing
Decision
Data source
Pattern matching
Identification Data /Verification source
Sensors
Feature extraction
Reporting Sensors
Transmission Compression module
Storage Data Base
Computational Geometry in Biometrics
Data Collection Data source Processing Feature extraction Decision Pattern Data matching source
Sensors
Data preprocessing
Reporting Sensors
Transmission CG methods Compression module
Storage Data Bas e
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
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.
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.
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.
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.
Applications of Voronoi Diagrams
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
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
VorP x d x, P d x, Q, Q S \ {P}
where d(x,P) is a distance function between a point x and a site P in the d-dimensional space.
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.
Voronoi diagram in 2D
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.
Example: VD and DT in power metric
Distance metrics for Voronoi Diagrams
General Lp distance
d d (x, p) xi pi i 1 Manhattan
d i 1
p 1 / p
d ( x, p ) x i p i
Supremum
Manhattan
Euclidean
d (x, p) max xi pi
i 1.. d
Manalanobis
d ( x, p) ( x p)Cov( D) 1 ( x p)
Supremum m
Mahalanobis
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
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.
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.
Terminology (1)
Fingerprint image
Ridge, Valley
Orientation field
a: original image
b: orientation field
Terminology (2)
Minutiae points
Bifurcation End
a: Endpoint b: Bifurcation Bifurcation point and end point ([2])
Singular Points
Fingerprint Verification
Flowchart of fingerprint verification system
Our task
(a)
(b)
(c)
(a) Input fingerprint image, (b) Template fingerprint image,
(c) Result of registration
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].
Singular point detection
Singular point detection example.
DT for minutiae point extraction
(a) Thinned Image
(b) Minutia Extracted
DT for minutiae point extraction
(a) Purified minutia
(b) DT constructed based on (a)
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.
Triangle edge comparison in minutiae matching
A θ1 B θ2
Delaunay Triangulation of Minutiae Points
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 ( , x, y) , which is a rigid transformation. In fact this is not true due to the elasticity of finger.
Rigid Transformation & Non-rigid Transformation
(a) Original grid Transformation
b) Rigid Transformation
(c) Non-rigid
Property of rigid Transformation (b): (1) Every point share the same transformation (2) The distance and angle of points are unchanged.
Spatial Interpolation using RBF(Radial Basis Functions)
Deformation in 2D and 3D
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
Nonlinear deformation on fingerprint
Apply deformation model
Apply RBF to solve the deformation function
3. Global matching (Count the number of matching minutiae points)
Nearest Neighbor Approach
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
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
Goals
●
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Synthesis Of Biometric Databases Iris Database Augmentation
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Testing Recognition Methods Minimal User Input
Previous Work
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Iris Recognition
04] et al. 04]
- [Wildes 94, Daugman
●
Biometric Synthesis
Iris Synthesis
al. 04]
- [Yanushkevich
●
- [Lefohn et al. 03, Cui et
Iris Synthesis
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An Ocularists Approach to Human Iris Synthesis.
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[ Lefohn et. al. 03]
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An Iris image synthesis method based on PCA and Super-Resolution.
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[Cui et. al. 04]
Our Approach
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Capture Characteristics Combine Characteristics
Organization
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.
Method
First step: Isolate the iris.
Polar Transform Iris Stretching
Multiresolution
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Data has many resolutions
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Levels of resolution have different meanings Details
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Reverse Subdivision
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Decomposition
Method
Courtesy of: Michal Dobes and Libor Machala, Iris Database, http://www.inf.upol.cz/iris/
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Capture Details
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Reverse Subdivision All Characteristics
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Details
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Combinations
Classifications
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Frequency of Data Number of Concentric Rings
Courtesy of: Michal Dobes and Libor Machala, Iris Database, http://www.inf.upol.cz/iris/
Database Size
Original Set
Courtesy of: Michal Dobes and Libor Machala, Iris Database, http://www.inf.upol.cz/iris/
Output Irises
Courtesy of: Michal Dobes and Libor Machala, Iris Database, http://www.inf.upol.cz/iris/
Future Work
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Post-Processing
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Multiple samples of each iris
Statistically
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Verification
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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
Presentation Overview
Applications
template matching morphing
Distance Transforms Euclidean Distance Transform Algorithm
algorithm description: Chains, Zen and The Art of Chain Maintenance
Template Matching
Image
Template
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).
Distance Transform as a Temperature Map
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.
L1 Distance Transform Algorithm
Image Morphing
Two steps:
1) 2)
Establish feature correspondences: manually Mapping function: define spatial relationship between all points in both images500
corresponding points
+
=
Examples from the “facial attractiveness” project: www.beautycheck.de
Starting Frame
Ending Frame
Starting Frame
Ending Frame
Starting Frame
Ending Frame
Starting Frame
Ending Frame
Starting Frame
Ending Frame
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.
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