The USC Andrew and Erna Viterbi School of Engineering USC Signal and Image Processing Institute USC Ming Hsieh Department of Electrical Engineering University of Southern California

Technical Report USC-SIPI-109

“A Unified Approach for Filtering and Edge Selection in Noisy Images”

by Yi-Tong Zhou, Anand Rangarajan, and Rama Chellappa

January 1988

We consider the problem of enhancement and edge detection on noisy, real images. A unified framework for smoothing and edge detection based on an autoagressive (AR) random field model is presented. An edge is detected, if the first and second directional derivatives and a local estimate of the variance at each point satisfy certain criteria. When noise is present we would like to estimate the directional derivatives from a restored version of the noisy image. We propose a Reduced Update Kalman Filter (RUKF) to perform the restoration. Then we can perform edge detection recursively using a small (4 x 4) window and still be fairly robust in the presence of noise. Since the edge detector operates on the restored image, it follows the RUKF by a fixed lag. A min-max replacement technique is introduced in between the RUKF and the edge detector to improve edge strength. The results compare favorably with those of other edge detectors.

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