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2016 | OriginalPaper | Chapter

3. Apparent Contours for Projections of Smooth Surfaces

Authors : James Damon, Peter Giblin, Gareth Haslinger

Published in: Local Features in Natural Images via Singularity Theory

Publisher: Springer International Publishing

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Abstract

Our goal as described in the overview is to provide a complete analysis of the views of natural scenes involving geometric features, shade/shadow, and apparent contours resulting from viewer movement. Our approach to this will involve progressively adding more detailed structure to simpler situations. The starting point for this is the case where we have a single object whose boundary is a smooth surface \(M \subset \mathbb{R}^{3}\) without geometric features. Hence, for the remainder of this chapter we always assume M is a compact smooth surface without boundary.

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Footnotes
1
In general a smooth function f whose 4-jet at (0, 0) is f 4(x, y) = L 2 + B + C, where L, B, C are linear, cubic and quartic forms in x, y respectively, has type at least A 3 at x = y = 0 if and only if B = LQ for a quadratic form Q and exactly A 3 provided in addition L does not divide Q 2 − 4C.
 
2
We are indebted to Jan Koenderink for this example and for the insight that with some care the general case can be deduced from this very special one.
 
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Metadata
Title
Apparent Contours for Projections of Smooth Surfaces
Authors
James Damon
Peter Giblin
Gareth Haslinger
Copyright Year
2016
Book
Local Features in Natural Images via Singularity Theory

Print ISBN: 978-3-319-41470-6

Electronic ISBN: 978-3-319-41471-3

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-41471-3_3

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