Projective reconstruction with missing data on factorization algorithm

Factorization algorithms are widely used in projective reconstruction, which has an inherent advantage of being able to handle any number of images simultaneously without special treatment for any subgroup of views. However, these algorithms assume that all object points are visible on all images. In order to overcome the limitation, we present an algorithm to estimate projective shape, projection matrices, projective depths and missing data iteratively. Estimation problems of projective shape and projection matrices are solved in terms of singular value decomposition. According to the fact that the sum of linear subspaces, each of which is spanned by the rows of all points in each image, is equal to the linear subspace spanned by the rows of space points, projective depths are estimated. Experimental results with both synthetic data and real images show that the proposed method has small reprojection errors, good convergence property and practicality.