COPING WITH DISCONTINUITIES IN COMPUTER VISION - THEIR DETECTION, CLASSIFICATION, AND MEASUREMENT

The problem of detection, classification, and measurement of discontinuities arises in many applications in science and technology. It is particularly important for computer vision, and the applications include edge detection, visible surface reconstruction, object recognition, etc. The problem is complex because of the noise corrupting the data. It is difficult to distinguish the discontinuities of the underlying structure from the discontinuities caused by the noise. Furthermore, in applications such as edge detection from intensity images, due to the effects of the point spread function of the optic system, the discontinuities of the intensity surface of the underlying scene are not well represented in the intensity image, which is band-limited. This introduces additional complication to the discontinuity detection process. We study discontinuity detection both for functions and from band-limited signals. We propose a discontinuity detector, which consists of a pair of a pattern and a linear filter. We show that for a discontinuity in the signal there is a scaled pattern in the filter response. The location of the pattern is the location of the discontinuity, and the scaling factor of the pattern is the size of the discontinuity. We give a necessary and sufficient condition for the one-to-one correspondence between the discontinuities of the signal and the scaled patterns in the filter response. Therefore, the problem of discontinuity detection and measurement is reduced to searching for the scaled pattern in the filter response. In the presence of noise, the pattern matching is approximate. We propose a statistical approach for the pattern search. We study optimal detectors, which minimize the effects of noise. We show that for white noise the optimal detectors are natural splines. We apply our method to edge detection. Testing results on real data are reported. © 1990 IEEE