Shape recognition using fractal geometry

Abstract

Within this paper fractal transformations are presented as a powerful new shape recognition technique. The motivation behind using fractal transformations is to develop a high speed shape recognition technique which will be scale invariant. A review is given of the most popular existing shape recognition techniques. There then follows a full mathematical analysis of the new technique together with a proof of the authors Fractal Invariance Theorem, the new theorem at the centre of the recognition technique. Through the mathematical analysis it becomes apparent that the fractal recognition technique possesses the remarkable property that it is able to distinguish between similar objects. Details are then given of the practical implementation of the technique together with an algorithm for making the technique rotationally invariant. The technique is then applied to a selection of real world objects and a comparison made with the popular moment invariants technique. This shows that the fractal technique is faster than the technique of moment invariants, and also requires less initial information to be effective. Finally conclusions are drawn and further work detailed.