ABSTRACT
Image segmentation presents extremely important routine with many applications in image processing (Gonzales and Woods, 2002; Haralick and Shapiro, 1985). The issue of correct image segmentation definition, creation and evaluation still remains unsolved and most often the solution to these problems mainly depends on the predefined goal. High quality and robustness of image segmentation routines is of considerable importance in the practical applications and at the same time contemporary research. Image segmentation makes possible further higher level image processing such as feature extraction, pattern recognition, and classification. Despite the fact that much effort has been put into elaboration of suitable segmentation algorithms the problem is still open in many areas that require particular segmentation characteristics and continuous development of new imagery technologies makes the segmentation quality issue constantly more pressing. Image segmentation presents active research subject in the last decades. High quality
image segmentation routines are of great importance in practical applications owing their
image presents the low-level image transformation routine concerned with image partitioning into distinct disjoint and homogenous regions. Clustering or data grouping describes distinct key procedure in image processing and segmentation. Rough sets have been employed during image analysis routines, see for example (Borkowski and Peters, 2007). The presented research is based on combining the concept of rough sets and entropy measure in the area of image segmentation by means of Rough Entropy Clustering Algorithm. In the previous work (Malyszko and Stepaniuk, 2008), new algorithmic scheme RECA in
the area of rough entropy (Pal, Shankar, and Mitra, 2005) based partitioning routines has been proposed. Proposed entirely novel rough entropy clustering algorithm incorporates the notion of rough entropy into clustering model taking advantage of dealing with some degree of uncertainty in analyzed data. Given predefined number of clusters, with each cluster lower and upper cluster approximations are associated. Image points that are close to the cluster contribute their impact by increasing lower and upper cluster approximation value in case of their proximity only to that cluster or distribute uniformly their impact on some number of upper cluster approximations otherwise. After lower and upper approximation determination for all clusters, their roughness and rough entropy value calculation proceeds. On the base of entropy maximization law, the best segmentation is achieved in case of maximal entropy value. For this purpose, an evolutionary population of separate solutions is maintained with solutions with predefined number of cluster prototypes. For each solution, respective rough entropy measure is calculated and subsequently, new populations are created form parental solutions with high values of this fitness measure. Additionally, an extension of Standard Crisp-Crisp Difference RECA - CCD RECA al-
gorithm into fuzzy domain has been elaborated in the form of Fuzzy RECA algorithms - Fuzzy-Crisp FCD RECA, Fuzzy-Fuzzy Threshold FFT RECA and Fuzzy-Fuzzy Difference FFD RECA. In Fuzzy RECA algorithm setting, the impact of each image point on upper cluster approximations of sufficiently close clusters is not constant and depends upon their distance from these clusters. Upper cluster approximations are increased by fuzzy measure for all image points that are sufficiently close to more than one cluster center relative to distance threshold dist or fuzzy threshold fuzz.
