Learning, anisotropic diffusion, nonlinear filtering and space-variant vision

Images are frequently corrupted by noise and blurring from various sources. To alleviate these distortions, many vision systems employ filtering to reduce noise and enhance contrast in regions which are presumed to correspond to object borders. The logical extreme of this process is a piecewise constant image with step discontinuities at region boundaries. This goal is unattainable using linear filtering, as it blurs and possibly destroys boundary information.; Anisotropic diffusion provides noise reduction and contrast enhancement by modulating the amount of blurring as a function of local image structure. This approach can produce impressive quality images, but suffers from a number of drawbacks. The most prominent of these are the computational cost of diffusion, coupled with the need for serial integration. These computational concerns make diffusion impractical for most real-time machine vision systems. While nonlinear diffusion models certain human perceptual phenomena well, it remains to be determined how such a process is carried out in vivo. Although complex processing is possible in these situations, the rapid nature of perception relative to neural time constants makes it almost certainly parallel in nature.; These issues are resolved in a number of ways. First, a learning scheme is developed which obviates the need for temporal integration of the anisotropic diffusion equation. This yields an algorithm which is an order of magnitude faster than anisotropic diffusion, while resolving drawbacks such as noise intolerance, instability, seriality, and the need for regularization. A heuristic extension of this approach achieves noise reduction and contrast enhancement comparable to anisotropic diffusion at far less computational cost. An attentional algorithm for license plate detection in an unconstrained visual scene is then developed to quantitatively measure the performance of a variety of nonlinear filters.; A second approach is to reduce the requisite number of serial steps by integrating the anisotropic diffusion equation using an adaptive grid-size algorithm. An investigation of the geometric structure of the mammalian retino-cortical mapping reveals that it implicitly encodes a variable grid-size integration scheme, achieving exponential integration rates in the periphery, and producing large-scale image enhancement in relatively few time steps.