MEDIAN FILTERS AND THEIR APPLICATIONS TO IMAGE PROCESSING

GEORGE JONGHWA YANG, Purdue University

Abstract

Median filtering is useful in reducing noise while preserving signal jumps. The extent of the noise reduction depends on the noise distribution. The heavier the distribution tail, the better the filter performs in reducing noise. Edge signal is an important feature in images, and is better preserved by median filtering than by average filtering. Images often have spiky noise (binary symmetric channel noise, for example) and median filtering reduces it effectively. We define various median filters and discuss their properties. Among them are the fixed points and some statistical properties. Order statistics were used to describe the effect of ordering image data in reducing noise variance along with its effect in preserving sharp edges. An efficient algorithm for two-dimensional median filtering of images was presented and shown much faster than the conventional sorting method. It requires only approximately (2n + 10) comparisons for a window size of m x n. The algorithm takes advantage of the fact that image signals are in general highly correlated as well as that two neighboring windows have many common elements. The performance evaluation of the median filters was done by measuring its effects on one-dimensional edge location estimation, two-dimensional edge detection, and object shape preservation, and comparing with those of average filter. We looked at Gaussian noise (a light-tailed noise) as well as BSC noise (binary symmetrical channel noise, a heavy-tailed noise). Theoretical performance predictions were derived and computer simulations carried out for edge location estimation by the least square method. Computer simulations using a set of designed test patterns as input were performed to evaluate edge detection and shape preservation. Median filtering was shown superior to average filtering in many cases. In edge location estimation, median filtering preserves step (sharp) edge location better than average filtering, but does not preserve ramp edge location as well for the case of Gaussian noise. For BSC noise, median filtering preserves both step and ramp edge locations better. In edge detection and in terms of the edge distances we defined, median filtering and average filtering are competitive for the case of Gaussian noise. For BSC noise, median filtering performs consistently better than average filtering. In the Euclidean distance measure of Fourier shape descriptors, median filtering preserves shape information better than average filtering for either noise type. Finally applications to various areas in image processing were described for this relatively new and powerful filter.

Degree

Ph.D.

Subject Area

Electrical engineering

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