On robustness of multi fractal spectrum to geometric transformations and illumination

Regular region based segmentation approaches utilize color or intensity information to distinguish between different regions. The performance of such procedures is acceptable for man-made objects, since they mainly consist of regular shapes and smooth surfaces. Most natural objects such as mountains, trees or clouds on the other hand are typically formed of complex, rough and irregular surfaces in 3-D, which are transformed into textured regions on the 2-D image plane through the image formation process. If we want to segment or classify images of such surfaces in an automatic fashion, we need to find a way to capture the essence of their structure succinctly. This can be achieved by making use of the 3-D information in combination with the texture of the corresponding region on the image plane. One possible way to model this relationship is through fractal analysis, which has proven to be a good representation of natural objects. This paper is based on the work of Xu et al. [1]. The aim is to explain a way of efficiently representing natural objects by the use of the multi fractal spectrum (MFS), which is an extension of the regular fractal analysis. Section 1 of this paper will present the concepts of image texture. Then section 2 will briefly introduce the fractal theory and section 3 will elaborate on the concept of fractal dimension (FD). Section 4 is the main part of the paper, which will explain the MFS as a robust and invariant texture descriptor. The final section will present the experimental results obtained by Xu et al. [1] and provide conclusions.