Fuzzy Graph-Theoretical Clustering Approach on Spatial Relationship Constrain

In the process of segmentation the traditional graph-theoretical clustering method is sensitive to noise and fuzzy edges, thus false segmentation result is appeared. Further, the large computational complexity also affects its application. Aiming at these deficiencies, the traditional approach is improved in the paper. First, to reduce the computational complexity, we divide the pixels of same grey level into one class when initialization. Then, in the traditional algorithm the information of pixel´s gray and the distance between pixel and clusters´ center is used, but the spatial character distribution between pixel and region is neglected, thus caused data is independent of each other. In fact, image segmentation is not only the target of gray statistics, pixel space between the neighbour relationship to maintain the integrity of the target also plays a key role. So in calculating weight coefficient, we define the neighbours relationship between pixels and regions, through increasing the constraint of spatial relationship to modify the value deviation caused by only considering the pixels´ gray and two-dimensional position relations. Furthermore, we propose to combine the fuzzy theory and graph-theoretical clustering method. By using some parameters such as weight coefficient, fuzzy similarity relationship between each pixel is constructed, then the image may be mapped from space field to fuzzy field. Finally, cluster analysis is done by using the maximal fuzzy supporting tree on the new fuzzy graph. Thus some problems encountered in image processing of the traditional graph-theoretical clustering method may be solved.