Extraction of rotation invariant signature based on fractal geometry

In this paper, a new method of feature extraction with rotation invariant property is presented. One of the main contributions of this study is that a rotation invariant signature of 2-D contours is selected based on the fractal theory is proposed. 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 2-D object, a unique contour is obtained. In the unfolding processing, 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 IR, and the central projection unfolded curves with respect to the box computing dimension are rotation invariant. Some experiments with positive results are conducted. This approach is applicable to a wide range of areas such as image analysis, pattern recognition, etc.