Rank 1 Weighted Factorization for 3D Structure Recovery: Algorithms and Performance Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Geometrical recovery of missing data for shape from motion
International Journal of Computer Mathematics
Rank Constraints for Homographies over Two Views: Revisiting the Rank Four Constraint
International Journal of Computer Vision
Pose estimation from multiple cameras based on Sylvester's equation
Computer Vision and Image Understanding
Geometrical fitting of missing data for shape from motion under noise distribution
ICNC'06 Proceedings of the Second international conference on Advances in Natural Computation - Volume Part II
A novel recovery algorithm of incomplete observation matrix for converting 2-d video to 3-d content
IWICPAS'06 Proceedings of the 2006 Advances in Machine Vision, Image Processing, and Pattern Analysis international conference on Intelligent Computing in Pattern Analysis/Synthesis
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This paper presents the surface-based factorization method to recover three-dimensional (3-D) structure, i.e., the 3-D shape and 3-D motion, of a rigid object from a two-dimensional (2-D) video sequence. The main ingredients of our approach are as follows: 1) we describe the unknown shape of the 3-D rigid object by polynomial patches; 2) projections of these patches in the image plane move according to parametric 2-D motion models; 3) we recover the parameters describing the 3-D shape and 3-D motion from the 2-D motion parameters by factorizing a matrix that is rank 1 in a noiseless situation. Our method is simultaneously an extension and a simplification of the original factorization method of Tomasi and Kanade (1992). We track regions where the 2-D motion in the image plane is described by a single set of parameters, avoiding the need to track a large number of pointwise features, in general, a difficult task. Then our method estimates the parameters describing the 3-D structure by factoring a rank 1 matrix, not rank 3 as in Tomasi and Kanade. This allows the use of fast iterative algorithms to compute the 3-D structure that best fits the data. Experimental results with real-life video sequences illustrate the good performance of our approach