Commun. Res. Lab., McMaster Univ., Hamilton, Ont.
IEEE Trans Image Process. 1995;4(10):1358-70. doi: 10.1109/83.465101.
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.
用于对图像进行编码的最佳线性分块变换是众所周知的 Karhunen-Loeve 变换（KLT）。然而，最优条件中的平稳性假设对于图像来说远远不成立。图像是由局部统计信息在图像中可能有很大差异的区域组成的。虽然自适应可以带来性能的提高，但对于自适应所基于的准则的最优性的研究却很少。在本文中，我们提出了一种新的变换编码方法，其中自适应是最优的。该系统是模块化的，由与输入数据的不同类对应的多个模块组成。每个模块都由一个线性变换组成，其基在初始训练期间计算。给定输入向量的适当类别由子空间分类器确定。所得到的自适应系统的性能优于最优的非自适应线性变换。该方法也可用作分段器。它执行的分段与光照变化无关。此外，所得到的类别表示类似于视觉皮层中方向敏感柱的排列。
