Tomasi and Kanade[1] initially developed the Factorization method. Using this robust methodology, one can recover both the shape of the object and its motion from a sequence of images, without having to compute the depth and without any assumption of the model of motion.
The Factorization method applies a singular value decomposition (SVD) to a measurement matrix that consists of tracked feature points. The outcome of this is two submatrices that represent the camera rotation and the object shape. The only drawback of this method is that it makes the assumption that the camera model is orthographic, thus it contains no knowledge of the distance from the camera to the object. Poelman and Kanade [2] described two methods that attempt to solve this problem: the paraperspective projection and scaled orthographic projection. These two methods approximate the perspective projection, while still maintain the linearity to allow the use of the Factorization method in order to recover the scene geometry and camera motion.
In this project, we implemented the Factorization method on a number of real and synthetic image sequences and reconstructed the scene geometry and camera motion. We also explored both the scaled orthographic projection and the paraperspective projection to estimate the distance between the camera and the scene object, comparing the resulting reconstructed shape and motion with that obtained from the orthographic model. We finally attempted to handle the problem of occlusion, which causes some feature points to be lost during the tracking. In this case, we have a measurement matrix only partially filled in.
In this document, we present a brief overview
of the Factorization method, as well as the paraperspective and orthographic
projections. We also describe the problem of occlusion. We then discuss
and summarize the results of our experiments.
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