A Method for Enforcing Integrability in Shape from Shading Algorithms
IEEE Transactions on Pattern Analysis and Machine Intelligence
Equi-areal Catadioptric Sensors
OMNIVIS '02 Proceedings of the Third Workshop on Omnidirectional Vision
A Theory of Catadioptric Image Formation
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Shape from Specular Reflection and Optical Flow
International Journal of Computer Vision
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We present a design technique for realizing given projections as catadioptric sensors. In general, these problems do not have solutions, but approximate solutions may often be found that are visually acceptable. Our approach, which we call the "method of vector fields", reduces the problem to solving a linear system. A given transformation between the image plane object surface is shown to determine a vector field which is normal to the surface in the case where the vector field is a gradient. If the vector field is not a gradient, we present several functionals that may be minimized to give approximate solutions.