Coping with discontinuities in computer vision: their detection, classification, and measurement

The general principles of detection, classification, and measurement of discontinuities are studied. The following issues are discussed: detecting the location of discontinuities; classifying discontinuities by their degrees; measuring the size of discontinuities; and coping with the random noise and designing optimal discontinuity detectors. An algorithm is proposed for discontinuity detection from an input signal S. For degree k discontinuity detection and measurement, a detector (P,Φ) is used, where P is the pattern and Φ is the corresponding filter. If there is a degree k discontinuity at location t₀, then in the filter response there is a scaled pattern αP at t₀, where α is the size of the discontinuity. This reduces the problem to searching for the scaled pattern in the filter response. A statistical method is proposed for the approximate pattern matching. To cope with the random noise, a study is made of optimal detectors, which minimize the effects of noise