The optimal linear block transform for coding images is well known to be the Karhunen-Loeve transformation (KLT). However, the assumption of stationarity in the optimality condition is far from valid for images. Images are composed of regions whose local statistics may vary widely across an image. While the use of adaptation can result in improved performance, there has been little investigation into the optimality of the criterion upon which the adaptation is based. In this paper we propose a new transform coding method in which the adaptation is optimal. The system is modular, consisting of a number of modules corresponding to different classes of the input data. Each module consists of a linear transformation, whose bases are calculated during an initial training period. The appropriate class for a given input vector is determined by the subspace classifier. The performance of the resulting adaptive system is shown to be superior to that of the optimal nonadaptive linear transformation. This method can also be used as a segmentor. The segmentation it performs is independent of variations in illumination. In addition, the resulting class representations are analogous to the arrangement of the directionally sensitive columns in the visual cortex.
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