Extraction of rotation invariant signature based on fractal geometry

A new method of feature extraction with a rotation invariant property is presented. One of the main contributions of this study is that a rotation invariant signature of 2D contours is selected based on fractal theory. The rotation invariant signature is a measure of the fractal dimensions, which is rotation invariant based on a series of central projection transform (CPT) groups. As the CPT is applied to a 2D object, a unique contour is obtained. In the unfolding process, this contour is further spread into a central projection unfolded curve, which can be viewed as a periodic function due to the different orientations of the pattern. We consider the unfolded curves to be non-empty and bounded sets in IRⁿ, and the central projection unfolded curves with respect to the box computing dimension are rotation invariant. Some experiments with positive results have been conducted. This approach is applicable to a wide range of areas such as image analysis, pattern recognition etc