II.3 - ASPECTS OF INVARIANT PATTERN AND OBJECT RECOGNITION

Abstract

This chapter discusses the aspects of invariant pattern and object recognition. In a fundamental sense, the problem of invariance is the problem of pattern or object recognition insofar as any system that claims to be capable of recognizing objects or patterns is qualified by its ability to function under, and invariant to, a variety of transformations, whether they be geometric or based on distortions or other types of transformations of data. The chapter describes one particular type of invariance, that is, rigid motions, which, in two dimensions (2D), are restricted to planar translations (x, y) and rotations around the z axis (also including zoom-dilation operations). It also discusses the three-dimensional (3D) six-parameter invariance problem, that is, recognition invariant to three dimensional rigid motions of translations (in X, Y, Z directions) and rotations about all three axes (x, y and z). Three ingredients of invariance, uniqueness, and transformation state are essential for a strong invariant pattern recognition representation. The difference between three-dimensional object recognition and two-dimensional pattern recognition is not only due to the dimensionality differences and the possible rigid motions (specifically four to six parameters invariance) but also in the very nature of object recognition, in comparison to pattern recognition. Object recognition not only involves the registration of object surfaces but also involves understanding the parameters associated with the transition from view-dependent data to the view-independent object surface information. These extra constraints of rendering and camera calibration further complicate invariant object recognition, particularly from the perspective of the inverse optics problem.