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Email Address. Sign In. Access provided by: anon Sign Out. Singularity theory and phantom edges in scale space Abstract: The process of detecting edges in a one-dimensional signal by finding the zeros of the second derivative of the signal can be interpreted as the process of detecting the critical points of a general class of contrast functions that are applied to the signal. It is shown that the second derivative of the contrast function at the critical point is related to the classification of the associated edge as being phantom or authentic.

The contrast of authentic edges decreases with filter scale, while the contrast of phantom edges are shown to increase with scale. As the filter scale increases, an authentic edge must either turn into a phantom edge or join with a phantom edge and vanish.

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## Singularities and Black Holes (Stanford Encyclopedia of Philosophy)

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Geometry of manifolds in the euclidian space and in the Minkowski space Curves in Minkowski space Qualitative theory of differential equations and singularity theory Applications of singularity theory: differential geometry and algebraic geometry Geometry in Minkowski space Symmetries of functions on networks and of mappings on Minkowski spaces Singularities, geometry and differential equations. Please report errors in scientific publications list by writing to: cdi fapesp.

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