Grey level thresholding using second-order statistics

This letter describes algorithms for global thresholding of grey-tone images which use second-order grey level statistics. Two measures of interaction between classes of intensity levels are defined on simple co-occurance matrices and are used to evaluate and select thresholds. One of these measures is seen to be independent of the grey level histogram and effective in selecting thresholds for images with unimodal grey level distributions. The algorithms are also used for multithresholding without modifications. Grey level thresholding for the purpose of image segmentation is essentially a classification pro­ blem. The intensity (grey) levels are to be subdivid­ ed into bands so as to provide classes of intensity levels corresponding to regions of similar attribute. Various threshold selection techniques have been derived based on the grey level histogram or 'improved' versions of such histograms (using edge strength information) (Weszka (1978), Pal et al. (to appear». These techniques follow the simple heuristic of threshold selection at the minimum between histogram peaks (valleys). Weszka and Rosenfeld (1978) suggested a cost function based on the joint probability matrices of grey levels which can be used for threshold evaluation and selection. Unlike grey level histograms, such co­ occurrence matrices (or grey tone spatial dependency matrices (Haralick et al. (1973») con­ tain information about the spatial relationship bet­ ween the intensity levels and can therefore be the basis of more meaningful criteria for grey level classification. However, the 'business' measure of Weszka and Rosenfeld (1978) as a function of the threshold level is essentially an improved histogram and in this respect is similar to other methods aimed at using second-order statistics to define improved histograms. This paper describes two 'interaction measures' for the selection of thresholds based on similar second-order grey level statistics as those mention­ ed above. The measures are defined on simple joint frequency matrices for grey levels occurring in horizontal and vertical nearest neighbour relative positions. The relationship between grey levels at these relative displacements is here referred to as 'intensity transition' and the corresponding co­ occurance matrix is referred to as a transition matrix. The interaction measures are defined to represent the 'cost' of a threshold in terms of the probabilities of transition between the intensity classes which the threshold defines. Therefore the optimum threshold is chosen so as to minimise the interaction measures. One of the measures is similar to the 'business'