Optimal shape from motion estimation with missing and degenerate data

Reconstructing a 3D scene from a moving camera is one of the most important issues in the field of computer vision. In this scenario, not all points are known in all images (e.g. due to occlusion), thus generating missing data. The state of the art handles the missing points in this context by enforcing rank constraints on the point track matrix. However, quite frequently, close up views tend to capture planar surfaces producing degenerate data. If one single frame is degenerate, the whole sequence will produce high errors on the shape reconstruction, even though the observation matrix verifies the rank 4 constraint. In this paper, we propose to solve the structure from motion problem with degenerate data, introducing a new factorization algorithm that imposes the full scaled orthographic model in one single optimization procedure. By imposing all model constraints, a unique (correct) 3D shape is estimated regardless of the data degeneracies. Experiments show that remarkably good reconstructions are obtained with an approximate models such as orthography.