Invariance for Single Curved Manifold

Pedro Machado Manhaes de Castro

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

Recently, it has been shown that, for Lambert illumination model, solely scenes composed by developable objects with a very particular albedo distribution produce an (2D) image with isolines that are (almost) invariant to light direction change. In this work, we provide and investigate a more general framework, and we show that, in general, the requirement for such in variances is quite strong, and is related to the differential geometry of the objects. More precisely, it is proved that single curved manifolds, i.e., manifolds such that at each point there is at most one principal curvature direction, produce invariant is surfaces for a certain relevant family of energy functions. In the three-dimensional case, the associated energy function corresponds to the classical Lambert illumination model with albedo. This result is also extended for finite-dimensional scenes composed by single curved objects. © 2012 IEEE.
Original languageEnglish (US)
Title of host publication2012 25th SIBGRAPI Conference on Graphics, Patterns and Images
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Pages158-165
Number of pages8
ISBN (Print)9780769548296
DOIs
StatePublished - Aug 2012
Externally publishedYes

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