Two-View Multibody Structure from Motion

We present an algebraic geometric approach to 3-D motion estimation and segmentation of multiple rigid-body motions from noise-free point correspondences in two perspective views. Our approach exploits the algebraic and geometric properties of the so-called multibody epipolar constraint and its associated multibody fundamental matrix, which are natural generalizations of the epipolar constraint and of the fundamental matrix to multiple motions. We derive a rank constraint on a polynomial embedding of the correspondences, from which one can estimate the number of independent motions as well as linearly solve for the multibody fundamental matrix. We then show how to compute the epipolar lines from the first-order derivatives of the multibody epipolar constraint and the epipoles by solving a plane clustering problem using Generalized PCA (GPCA). Given the epipoles and epipolar lines, the estimation of individual fundamental matrices becomes a linear problem. The clustering of the feature ...

• Type: Journal
• Year: 2006
• Where: IJCV
• Authors: René Vidal, Yi Ma, Stefano Soatto, Shankar Sastry
• Keywords: IJCV 2006, Individual Fundamental Matrices, Multibody Epipolar Constraint, Multibody Fundamental Matrix