Case Study - Technology Solution - Quasi-Invariant Features

Invariants have been used successfully in computer vision to extrapolate from the existing information in an image to fill in the missing or obscured information. In computer vision, an invariant is a quantity that can be computed on a view of an object, which is the same for all views of that object . Standard invariants can, in principle, be a powerful tool for object recognition, particularly as keys to index into a database of object models, because they can be computed for any view and then matched to the 3-D object that produces that view. However, standard invariants are all mathematically unstable, changing values with large variation based on only minute changes in observational geometry. For this reason, standard invariants can only be used for recognition in extremely constrained image/signal-capture situations that do not pertain in battlefield conditions.

IET researchers asked the question "Can the theory of invariants from computer vision be adapted to non-computer vision domains?" For example, could this theory be extended to support the biometric challenge of correctly associating human identification with measurements taken under a wide range of distortions (dust, smudges, etc.)? If so, the potential for this technology is tremendous. Answering this question over the last several years, IET has extended the theory of invariants from computer vision to non-computer vision domains through a combination of observational quasi-invariants and hierarchical Bayesian inferencing.

True invariants of an object under the action of a group of transformations compute sets of numerical values that are exactly equal for that object regardless of the transformation. Invariants are very powerful quantities to use for matching whenever they can be robustly computed. However, they are very rare in images and are unstable under small changes of imaging geometry. Thus distortions, blurs, and incomplete or partial occlusions of biometric signatures will introduce errors in extraction of minutiae points, and, because of instability of invariant computations, any invariants subsequently computed from those minutiae will not match the reference biometric signature.

Quasi-invariants overcome the limitation of traditional invariants; they are plentiful in images and robustly computed whenever they are observed. This is because quasi-invariants are "slowly changing" with respect to various sorts of likely transformations. Quasi-invariants occur in all imagery and other sensor-derived signals, and are robustly computed, being insensitive to small changes in the relative observational geometry between an object and the sensor.

Furthermore, the way a quasi-invariant changes with respect to alterations in viewpoint can be used in conjunction with computational Bayesian inference methods to create pattern-matching algorithms that optimize use of available evidence.

Case Study - Biometrics for Identification
Current fingerprint, retina and iris biometric authentication techniques rely on extraction of certain features of the captured biometric signature/image, called minutiae points, and on matching them to corresponding features of reference fingerprints, retinas or irises. Minutiae points associated to fingerprints typically include points where ridges end or where bifurcations start or end; orientation of the ridge or bifurcation at the point may also be included. Current algorithms that use minutiae points rely on matching up the orientation of the print, and then attempting to match points together. In one-to-many authentication matching, or in cases where minutiae are missing or out of place, straightforward matching algorithms can be subject to combinatorial explosion.

Rather than attempting to align the individual minutiae and then perform matching, our approach is to use quasi-invariants observations of image features which are not overly sensitive to the "view" of the signature. The goal is to model the capture of a signature and a reference signature as two "views" of the same original fingerprint, iris or retina. Although the implied transformation between the views can include minutiae occlusion or omissions, blurs and other distortions, and thus be more general than just a change in the sensor-to-subject acquisition geometry, the same theories of object recognition can be effectively applied.

A key challenge in biometric identification is suppressing false negatives and false positives at the same time, which means making optimal use of the available evidence. IET's approach are to apply confidence measures in the form of probabilistic inferences by combining the calculation of multiple quasi-invariants with computational Bayesian inference techniques to aggregate and synthesize the results of the individual computations.