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 language||English (US)|
|Title of host publication||2012 25th SIBGRAPI Conference on Graphics, Patterns and Images|
|Publisher||Institute of Electrical and Electronics Engineers (IEEE)|
|Number of pages||8|
|State||Published - Aug 2012|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: We would like to thank PierreWeiss and Jean-Marie Morvanfor nice discussions. We also would like to thank Aim@Shapefor providing us with relevant 3D scanned models, and thereviewers for some suggestions that helped us improving thetext. This work was partially done at King Abdullah Universityof Science and Technology, which we would like to thank forthe support.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.