Histogram Analysis Using a Scale-Space Approach

A new application of scale-space filtering to the classical problem of estimating the parameters of a normal mixture distribution is described. The technique involves generating a multiscale description of a histogram by convolving it with a series of Gaussians of gradually increasing width (standard deviation), and marking the location and direction of the sign change of zero-crossings in the second derivative. The resulting description, or fingerprint, is interpreted by relating pairs of zero-crossings to modes in the histogram where each mode or component is modeled by a normal distribution. Zero-crossings provide information from which estimates of the mixture parameters are computed. These initial estimates are subsequently refined using an iterative maximum likelihood estimation technique. Varying the scale or resolution of the analysis allows the number of components used in approximating the histogram to be controlled.