Linear fitting with missing data: applications to structure-from-motion and to characterizing intensity images

A method for generating a complete scene structure from a video sequence that provides incomplete data. The method has a first step of building a first matrix consisting of point locations from a motion sequence by acquiring a sequence of images of a fixed scene using a moving camera; identifying and tracking point features through the sequence; and using the coordinates of the features to build the first matrix with some missing elements where some features are not present in some images. In a second step an approximate solution is built by selecting triples of columns from the first matrix; forming their nullspaces into a second matrix; and taking the three smallest components of the second matrix. In a third step, an iterative algorithm is applied to the three smallest components to build a third matrix and to improve the estimate. Lastly, in a fourth step the third matrix is decomposed to determine the complete scene structure. Another aspect of the present invention are...