Extracting Boundaries from Images by Comparing Cooccurrence Matrices

This paper describes methods of extracting region boundaries from the frames of an image sequence by combining information from spatial or temporal cooccurrence matrices of the frames. It summarizes past work on the uses of cooccurrence matrices for image segmentation; qualitatively describes the peaks (clusters of high values) that can be expected to occur in cooccurrence matrices when the image(s) contain smooth regions separated by stationary or moving boundaries; and describes methods of extracting stationary or moving region boundaries from an image by combining information from spatial and temporal cooccurrence matrices. 1 Cooccurrence matrices and their uses Cooccurrence matrices, originally called gray-tone spatial dependency matrices, were introduced by Haralick et al. [1], who used them to define textural properties of images. Let I be an image whose pixel gray levels are in the range 0, . . . , 255. Let δ = (u, v) be an integer-valued displacement vector; δ specifies the relative position of the pixels at coordinates (x, y) and (x+ u, y+ v). A spatial cooccurrence matrix Mδ of I is a 256 × 256 matrix whose (i, j) element is the number of pairs of pixels of I in relative position δ such that the first pixel has gray level i and the second one has gray level j. Any δ, or set of δ’s, can be used to define a spatial cooccurrence matrix. In what follows we will usually assume that δ is a set of unit horizontal or vertical displacements, so that Mδ involves counts of pairs of neighboring pixels. In addition to their original use in defining textural properties, cooccurrence matrices have been used for image segmentation. Ahuja and Rosenfeld [2] observed that pairs of pixels in the interiors of smooth regions in I contribute to elements of Mδ near its main diagonal; thus in a histogram of the gray levels Cooccurrence matrices based on smaller numbers of gray levels can also be used, but our method of combining cooccurrence matrices works better for larger matrices. 919 Proc. VIIth Digital Image Computing: Techniques and Applications, Sun C., Talbot H., Ourselin S. and Adriaansen T. (Eds.), 10-12 Dec. 2003, Sydney