Fast Graph Partitioning Active Contours for Image Segmentation Using Histograms

We present a method to improve the accuracy and speed, as well as significantly reduce the memory requirements, for the recently proposed Graph Partitioning Active Contours (GPACs) algorithm for image segmentation in the work of Sumengen and Manjunath (2006). Instead of computing an approximate but still expensive dissimilarity matrix of quadratic size, $$ , for a 2D image of size N ×M and regular image tiles of size n ×m , we use fixed length histograms and an intensity-based symmetric-centrosymmetric extensor matrix to jointly compute terms associated with the complete N × N dissimilarity matrix. This computationally efficient reformulation of GPAC using a very small memory footprint offers two distinct advantages over the original implementation. It speeds up convergence of the evolving active contour and seamlessly extends performance of GPAC to multidimensional images.