Linear modeling and reconstruction of target´s shape from its un-calibrated multiple-view

The constraints on the target shape model are firstly explicitly built up. Then, the relationship between the fundamental matrix and the corresponding homography matrix as well as pole for the inter-frame two-view is also derived. By means of it and the SVD of the skew-symmetric matrix corresponding to the pole direction, the linear self-calibration procedure for multi-view is successfully developed. After it, all the essential matrixes and the 3D inter-frame motion are easily calculated. From them as well as the calibrated multiple-view data set, by means of the orthogonal projection operator theory, a procedure to global-optimally estimate the inter-frame 3D motion and the multi-frame 3D shape is suggested. Then, the SVD of 3q × N multi-frame shape matrix is applied to obtain the shape model and multi-frame 3D motion. The theoretic analysis and experimental demonstration have shown that the developed linear algorithm is fast, accurate, efficient and practical.