Scaling Theorems for Zero Crossings

作者：Alan Yuille, Tomaso Poggio · 发表于：IEEE Transactions on Pattern Analysis and Machine Intelligence · 年份：1986 · DOI：10.1109/tpami.1986.4767748 · 被引用次数：626 · 研究领域：Medical Image Segmentation Techniques、Topological and Geometric Data Analysis、Image and Signal Denoising Methods

We characterize some properties of the zero crossings of the Laplacian of signals¿in particular images¿filtered with linear filters, as a function of the scale of the filter (extending recent work by Witkin [16]). We prove that in any dimension the only filter that does not create generic zero crossings as the scale increases is the Gaussian. This result can be generalized to apply to level crossings of any linear differential operator: it applies in particular to ridges and ravines in the image intensity. In the case of the second derivative along the gradient, there is no filter that avoids creation of zero crossings, unless the filtering is performed after the derivative is applied.