On the Reprojection of 3D and 2D Scenes without Explicit Model Selection
It is known that recovering projection matrices from planar configurations is ambiguous, thus, posing the problem of model selection — is the scene planar (2D) or non-planar (3D)? For a 2D scene one would recover a homography matrix, whereas for a 3D scene one would recover the fundamental matrix or trifocal tensor. The task of model selection is especially problematic when the scene is neither 2D nor 3D — for example a “thin” volume in space.
In this paper we show that for certain tasks, such as reprojection, there is no need to select a model. The ambiguity that arises from a 2D scene is orthogonal to the reprojection process, thus if one desires to use multilinear matching constraints for transferring points along a sequence of views it is possible to do so under any situation of 2D, 3D or “thin” volumes.
KeywordsNull Space Fundamental Matrix Estimation Matrix Projection Matrice Reprojection Error
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