Image Transform based on Alpha-Beta Associative Memories

Abstract

In this paper, a new method of alpha-beta associative memories for images (MAABI) is presented. This method results in the alpha-beta transform (TAB) for images. The alpha-beta transform presented in this paper is applied to sub-blocks of a gray-scale image and generates an alpha-beta heteroassociative memory on each sub-block using a given transformation matrix. By means of the inverse alpha-beta transform (TABI), the original image patterns are recovered. The data compression process is divided into three stages: transformation, quantization and coding. Our model is focused on image transformation; we compare it with the morphological transform (TM) based on the morphological associative memories (MAM). In order to measure the number of bits contained in an image, the Shannon's entropy is used. The TM, as well as such traditional transforming methods as the discrete cosine transform (DCT) and the discrete wavelet transform (DWT), cannot perform compression over an image; that is why the main advantage of the AB is a smaller value of the entropy measure of the transformed image compared to the entropy of the original image. In addition, TAB provides a faster processing with a small number of elementary operations such as addition, subtraction, maximum and minimum.