Nonlinear prediction for Gaussian mixture image models

Prediction is an essential operation in many image processing applications, such as object detection and image and video compression. When the image is modeled as Gaussian, the optimal predictor is linear and easy to obtain. However, image texture and clutter are often non-Gaussian and in such cases, optimal predictors are difficult to find. In this paper, we have derived an optimal predictor for an important class of non-Gaussian image models, the block-based multivariate Gaussian mixture model. This predictor has a special non-linear structure: it is a linear combination of the neighboring pixels but the combination coefficients are also functions of the neighboring pixels, not constants. The efficacy of this predictor is demonstrated in object recognition experiments where the prediction error image is used to identify "hidden" objects. Results indicate that when the background texture is non-linear, i.e., with fast-switching gray-level patches, it performs significantly better than the optimal linear predictor.