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A Simple Method to Recover 3-D Rigid Structure from Motion using SIFT, RANSAC and the Tomasi-Kanade Factorization

Traditionally two frames are used to estimate the 3-D structure, while recent approaches have made use of a long sequence of frames. The latter gives a better recovery of a structure because it amasses temporal information over time. Tomasi-Kanade factorization also assumes all features to be visible throughout the entire image stream. This results in a dense 2-D cloud and therefore allows full recovery of the entire 3-D structure. This paper addresses the problem of 3-D structure reconstruction from motion by using the Tomasi-Kanade factorization method applied to a sequence of frames. Orthographic projection and rigidity is assumed and the singular value decomposition technique is used to factor the measurement matrix (W) into two matrices which correspond to the object’s 3-D structure (S) and camera rotation (R) respectively. To construct W, feature correspondences are established by applying a SIFT tracker following which RANSAC is used to discard the false matches detected by the SIFT tracker. The 3-D point-cloud (S) is converted to a mesh of triangles by connecting the nearest three neighboring points. Finally, the mesh of triangles is rendered by means of the Plyview from CyberWare to achieve the final 3-D structure.