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Characterizing ∇2G filtered images by their zero crossings

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2 Author(s)
Reimer, J.A. ; University of British Columbia, Vancouver, Canada ; Lawrence, P.

This paper considers the characterization of \nabla ^{2}G filtered images by their zero crossings. It has been suggested that \nabla ^{2}G filtered images might be characterized by their zero crossings [1]. It is shown here that \nabla ^{2}G filtered images, filtered in 1-D or 2-D are not, in general, uniquely given within a scalar by their zero crossing locations. Two theorems in support of such a suggestion are considered. We consider the differences between the requirements of Logan's theorem and \nabla ^{2}G filtering, and show that the zero crossings which result from these two situations differ significantly in number and location. Logan's theorem is therefore not applicable to \nabla ^{2}G filtered images. A recent theorem by Curtis [8] on the adequacy of zero crossings of 2-D functions is also considered. It is shown that the requirements of Curtis' theorem are not satisfied by all \nabla ^{2}G filtered images. An example of two different \nabla ^{2}G filtered images with the same zero crossings is presented.

Published in:

Acoustics, Speech, and Signal Processing, IEEE International Conference on ICASSP '87.  (Volume:12 )

Date of Conference:

Apr 1987