Adaptive Nonlinear Filtering for Nonlinear Anisotropic Diffusion Approximation in Image Processing

Multi-scale image enhancement and representation is an important part of biological and machine early vision systems. The process of constructing this representation must be both rapid and insensitive to noise, while retaining image structure at all scales. This is a complex task as small scale structure is difficult to distinguish from noise, while larger scale structure requires more computational effort. In both cases good localization can be problematic. Errors can also arise when conflicting results at different scales require cross-scale arbitration. Broadly speaking, multi-scale image analysis has historically been accomplished using two types of techniques: those which are sensitive to image structure and those which are not. Algorithms in the latter category typically use a set of variously sized predefined blurring kernels to produce images each of which retain structure at a different scale (Marr & Hildreth, 1980; Burt & Adelson, 1983; Koenderink, 1984; Hummel, 1986). Koenderink showed that if the kernels are Gaussian, then this process is equivalent to the evolution of the linear heat (or diffusion) equation. He thus transformed the integral equation representing the convolution process into the solution of a partial differential equation (PDE). Structure sensitive multi-scale techniques perform an analysis at a variety of scales within a single image (Klinger, 1971; Perona & Malik, 1987; Nitzberg & Shiota, 1992). Recently, the PDE formalism introduced by Koenderink has been extended to allow structure-sensitive multi-scale analysis (Perona & Malik, 1987, 1990) through the use of a nonlinear conductance function. The end result is a single image representation which contains information at all scales of interest. The Perona and Malik approach produces impressive results, but the numerical integration of a nonlinear PDE is a costly and inherently serial process. In this paper we present a technique Supported in part by the office of naval research (ONR N00014-95-1-0409).