LEVEL CROSSINGS AND THE PANUM AREA.

A theorem about level crossings of signals that may be relevant for theories of stereo matching is discussed. It is concerned with the level crossings and the size of the Panum fusional area. The Panum area is the disparity range over which stereo fusion is possible, more precisely is the disparity range over which no false matches occur. Rice's theorem about expected distribution of zero crossings provides a formula on how far to go before a false match can be expected. The probability of false matches decreases with increasing level of level crossings. A generalization for level crossings of the results for zero crossing is obtained and an explicit formula for the level that insures a k-fold increase of Panum fusional area is derived. The formula connects the autocorrelation function of the signal with the probability of a level crossing next to a given one. It is shown that computing level crossing can be useful tool for edge detection.