Reconstruction From Zero Crossings in Scale Space

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Reconstruction From Zero Crossings in Scale Space
R a Hummel
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6, but the rationale for this choice is not the degree of approximation to the Laplacian-of-Gaussian [12].
1. 3. Zero-crossings The zero set of v(x, t) is the point set in (x, t) where v = 0. The set might be empty (for instance, if / is subharmonic or superharmonic; [13]) everything (if /is harmonic; [14]), or a proper subset of (x, t) space. In the latter case, zeros can be isolated points, lines, and surfaces (but never regions). We distinguish components of the zero set which form manifolds
... of codi- mension one: Definition: The zero-crossings ofv(x, t) refers to the point set d{(x, t)\v(x, t)0]. U Zero-crossings have been suggested for segmentation of imagery by edge detection [12], and for stereo matching and motion correspondence between pairs of images (e. G. , [15]). It has also been suggested [10] that the zero-crossings are a nearly complete representation of A/. Marr also sug- gested that the zero-crossings might form a complete representation [1], but also thought that perhaps the zero-crossing information would need to be supplemented with gradient data along the zero-crossings.

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