http://worldcat.org/entity/work/id/568781605

Scaling theorems for zero-crossings

The authors 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. They prove that in any dimension the only filter that does not create 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 case of the second derivative along the gradient it is proved that there is no filter that avoids creation of zero-crossings.

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