Anisotropic Filtering Techniques applied to Fingerprints

Abstract

Noise filtering of images is basically a smoothing process, and it is a subject that has been addressed for many years. The idea of adaptive smoothing is being investigated a long time and many different approaches have been proposed over the years. Mastin (1985) reported superior performance of nonlinear such as medina filtering over linear techniques applied for adaptive image smoothing. Zucker et al. (1977) proposed to perform adaptive smoothing using weighted mask, which is computed by the difference between the value of the center point and its neighbors. Wang et al. (1981) applies a weighting scheme that averages values within a sliding window and changes the weights according to local differential. Instead of basic averaging Davis (Davis & Rozenfeld, 1978) performs iterated local noise cleaning by K-Nearest Neighbour averaging. The main disadvantage of these methods is their difficulty to ensure convergence. Blake (Blake & Zisserman, 1987) proposed a smoothing process, which reconstructs a noisy signal in a piecewise continuous manner by employing weak continuity constraints. Although the convergence behavior was well studied, the computational complexity is extremely high. An anisotropic diffusion scheme was presented by Perona & Malik (1990). They suggested to employ a heat equation in anisotropic medium for edge enhancement. This is done by selectively smoothing regions with low gradient. Another approach, called Forward-and-Backward diffusion, is presented by Smolka et al. (2003) and emphasizes regions with high gradient which are not caused by noise. Almansa (Almansa & Lindeberg, 2000) and Weickert (2001) have used diffusion techniques, which are based on a multi-scale analysis called scale-space representation, and applied an iterative process for local features estimation. Diffusion methods tend to distort sloping edges, while iterative methods slow down the filtering process in images with considerable amount of noise. Steerable filters are a class of filters, in which a filter of arbitrary orientation is synthesized as a linear combination of a set of “basis filters” (Freeman & Adelson, 1991). Steerable filters are used in many image-processing tasks and specifically in image enhancement. Steerablescalable kernels roughly shaped like Gabor functions have the advantage that they can be specified and computed easily (Perona, 1992). However, those filters usually approximate the orientation with low resolution, since they are usually based on angular frequency sampling, and a huge number of basis filters are required in order to approximate orientation steerability with high resolution (Yu et al., 2001). Another kind of structure-