Robust Methods for Image Restoration and Edge Detection

Abstract

In this thesis, three separate but related topics are considered. Each topic deals with the problem of noise in various aspects of image processing and computer vision.

Gradient-type edge detectors have long been used for detecting edges in grey-level images. However, the edge-enhancing digital gradient is extremely sensitive to high frequency additive noise. The first topic (chapter two) considers the effect of preprocessing noisy images with moving median filters prior to application of gradient detectors.

The analysis is done by computing error probabilities. Specifically, the probability of detecting psuedo-edges is given as a function of the detector threshold-to-noise ratio (TNR) where it is assumed that no edge is present. Also, the probability of missing an existing edge is computed as a function of the TNR and the signal - (edge height) to-noise ratio. Examples using noisy images are also given. The overall conclusion is that median filtering is superior to both average filtering and not filtering at all.

The second topic (chapter three) deals with the design of inherently robust edge detection schemes, rather than using preprocessing for conventional detectors. Three separate detectors are described. The first uses nonparametric statistics, specifically linear rank sums. The second uses least-square fits of order statistics. The third uses isotonic regression, or order-constrained least-square methods. Examples are given for each method, and are compared favorably with a conventional scheme.

Linear/frequency-domain methods have traditionally been used for removing noise from digital images. However, linear filters tend to blur edges, which may degrade image quality and make further processing difficult. The last topic (chapter four) describes a nonlinear filter based on isotonic regression theory. This filter, called an isotonic edge-sensitive filter (IESF), is novel in that it involves a two-step operation: edge detection and filtering. If an edge is detected, the isotonic regression of the windowed image values is output; otherwise, the local average is. Examples using noisy images are given, and favorable comparisons are made with average and median filters.