Using Isometry to Classify Correct/Incorrect 3D-2D Correspondences

Template-based methods have been successfully used for surface detection and 3D reconstruction from a 2D input image, especially when the surface is known to deform isometrically. However, almost all such methods require that keypoint correspondences be first matched between the template and the input image. Matching thus exists as a current limitation because existing methods are either slow or tend to perform poorly for discontinuous or unsmooth surfaces or deformations. This is partly because the 3D isometric deformation constraint cannot be easily used in the 2D image directly. We propose to resolve that difficulty by detecting incorrect correspondences using the isometry constraint directly in 3D. We do this by embedding a set of putative correspondences in 3D space, by estimating their depth and local 3D orientation in the input image, from local image warps computed quickly and accurately by means of Inverse Composition. We then relax isometry to inextensibility to get a first correct/incorrect classification using simple pairwise constraints. This classification is then efficiently refined using higher-order constraints, which we formulate as the consistency between the correspondences’ local 3D geometry. Our algorithm is fast and has only one free parameter governing the precision/recall trade-off. We show experimentally that it significantly outperforms state-of-the-art.