## Two-View Multibody Structure from Motion

Rene Vidal, Yi Ma^{1}, and Stefano Soatto^{2}

(Professor S. Shankar Sastry)

(ONR) N00014-00-1-0621

We present a geometric approach for the analysis of dynamic scenes containing multiple rigidly moving objects seen 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 moving objects. We derive a rank constraint on the image points from which one can estimate the number of independent motions and linearly solve for the multibody fundamental matrix. We prove that the epipoles of each independent motion lie exactly in the intersection of the left null space of the multibody fundamental matrix
with the so-called Veronese surface. We then show that individual epipoles and epipolar lines can be uniformly and efficiently computed by using a novel polynomial factorization technique. Given the epipoles and epipolar lines, the estimation of individual fundamental matrices becomes a linear problem. Then, motion and feature point segmentation is automatically obtained from either the epipoles and epipolar lines or the individual fundamental matrices.

- [1]
- R. Vidal, Y. Ma, S. Soatto, and S. Sastry, "Two-View Multibody Structure from Motion,"
*Int. J. Computer Vision* (submitted).
- [2]
- R. Vidal, S. Soatto, Y. Ma, and S. Sastry, "Segmentation of Dynamic Scenes from the Multibody Fundamental Matrix,"
*ECCV Workshop on Vision and Modeling of Dynamic Scenes,* Copenhagen, Denmark, May 2002.

^{1}Professor, University of Illinois at Urbana Champaign

^{2}Professor, University of California at Los Angeless

More information (http://www.eecs.berkeley.edu/~rvidal/) or

Send mail to the author : (rvidal@eecs.berkeley.edu)

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