Nonlinear variance measures in image data

Abstract

The homogeneity of regions in images can be measured in terms of the variation of local image values, or in terms of the local variation of ranks assigned to those image values. Previously proposed measures of nonlinear, or rank variance are shown in this paper to be insufficient measures of rank variation, especially when applied to discrete image data. A more useful measure of rank variance for image analysis, called diversity, is presented and characterised here. The dependence of diversity on the size of the data set involved and on the number of possible data values is discussed. The measure provides a very concise summary of the rank structure about each point and is sensitive to ‘ties’ in the local rank distribution.