Smooth Mixture Estimation from Multichannel Image Data

Abstract

The following problem arises in computer vision, diagnostic medical imaging and remote sensing: At each pixel in an image a vector of observations is measured. The distribution of these measurements is modeled by a mixture of certain pure class distributions and the goal is to estimate the mixing proportions of the classes by pixel in the image together with any unknown parameters in the pure class distributions. In many problems of this type it is appropriate to incorporate constraints on the mixing proportions. This paper deals with spatial smoothness constraints. An estimation methodology using penalized likelihood with multiple smoothing parameters is applied. Numerical methods for evaluating parameters in the model are developed. We make use of the Expectation Maximization (EM) algorithm. An importance sampling technique for approximating the effective degrees of freedom of the model is also described. The methodology is illustrated with some examples.

The research was supported in part by the Dept. of Energy under FG0685-ER2500 by the National Cancer Institute under 2P01-CA-42045. I am grateful to David Haynor for some valuable discussions.