The factorization method developed by Tomasi and Kanade [1] is based on the principle that the measurement matrix has rank 3 when the camera model has an orthographic projection. Poelman and Kanade [2] have shown that this result is also applicable for the scaled orthographic model and the paraperspective model.

In this project, we showed that both perspective approximation models recovered the camera depth up to a scale factor, and recovered the scene object closer to its true shape.  However, the paraperspective is much more difficult to be used in that it is more dependent on good data. This explains the requeriment of using synthetic data in this project. If desired data is obtained, the paraperspective assumption should be more robust for image sequences in which the object translates significantly toward or away from the camera. For our real data experiments, the Factorization method itself performed satisfactorily. This once more proves that this method can effectively be used in many tasks that deal with shape and motion from image sequences.

In this attempt to implement the procedure of occlusion, we recovered around 97-98% of the whole matrix of features and frames (W) when we had 250 points and 160 frames. This implementation still left unknown the rest (around 2%). Better results are obtained when we have a reasonable number of frames and points. Also, a heuristic is needed in order to choose the points that satisfy the reconstruction condition and that are related to a missing point.  The problem of the singularity of the rotation (R) and shape (S) matrices still has to be handled more accurately. Further research is needed in this area in order to be less dependent of the condition that the matrices R and S (and their intermediates) impose in the process of reconstruction.
 

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