Memory Module Processing

Both from a mathematical as well as a biological perspective, Wavelet transforms present themselves as an attractive means for extracting low-level information from an image. We present a processor-time optimal algorithm to implement wavelet transforms on a VLSI implementable parallel digital architecture. A desirable initial processing step in an artiicial vision system is the identiication of certain attributes in an incoming image. Traditionally, this is done by transforming the image into a domain where these attributes or features emerge as coeecients corresponding to a set of expansion functions. Transforms in computer vision have been used for image analysis, segmentation, feature extraction and representation, data compression and object recognition. Image transforms can be classiied on the basis of the resolution they provide in the visual space domain versus the spatial frequency domain. While the pixel by pixel grey level descripition of the image provides good resolution in the space domain, it gives no information about the spatial frequencies in the image. On the other hand, the Fourier Transform provides excellent resolution in the frequency domain but is spread over all space. It is often desirable to have good localization in both, the spatial as well as the frequency domains. High resolution in space makes the system robust to global distortions while high resolution in frequency makes it robust to high frequency noise. In 1946, Ga-bor 3] proved that no image transform can achieve an arbitrarily high resolution in both the spatial and frequency domains. Gabor deened a family of functions that achieve the minimum joint uncertainty in the two domains. These functions, when used as the expansion functions in a decomposition of a signal, yield a transform that has been called the Gabor Transform. Mallat 6] provides an analysis of the properties of this transform. Daugmann 2] generalized Ga-bor's analysis to two dimensions. His development of 2-D Gabor Functions was motivated by the observation that such functions would closely match experimentally measured two-dimensional visual neural receptive eld prooles 5]. Conceptually, a 2-D Gabor function is a sinusoidal wave (whose orientation and frequency in the two dimensional space is controlled by its two-dimensional wave-vector ~ k) that is modulated by a Gaussian function. Mathematically, this is expressed as: 2 2 exp(j ~ k:~ x) (1) where n k;; is a normalizing constant. 2-D Gabor functions have a constant support (or standard deviation) for all frequencies. This goes against the observed properties of …