Invariance for Single Curved Manifold | IEEE Conference Publication | IEEE Xplore

Invariance for Single Curved Manifold


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)...Show More

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.
Date of Conference: 22-25 August 2012
Date Added to IEEE Xplore: 20 December 2012
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Conference Location: Ouro Preto, Brazil
Universidade Federal de Pernambuco, Recife, PE, BR

Universidade Federal de Pernambuco, Recife, PE, BR
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