Multiresolution Image Analysis Based On Local Symmetries

This report describes two seemingly distinct areas of work. First, there is the derivation of a new multiresolution image restoration algorithm, and secondly there is the development of a new approach to feature extraction. A review of these two areas is presented, the new algorithms outlined, and some results presented. The unifying principle behind this work is the idea of image symmetries. The background of this concept is reviewed, and its applicability to the current work explained. Finally, some speculations and expectations concerning the future direction of this research is included. Contents 1 Introduction 1 1.1 Symmetry In Perception : : : : : : : : : : : : : : : : : : : : : : : : : 1 1.1.1 Invariant Pattern Recognition : : : : : : : : : : : : : : : : : : 1 1.1.2 The Lie Transformation Group Model : : : : : : : : : : : : : : 2 1.2 Symmetry In Representation : : : : : : : : : : : : : : : : : : : : : : : 5 1.2.1 Block Based Fractal Coding : : : : : : : : : : : : : : : : : :..