To the Graduate Council: I am submitting herewith a dissertation ...

Chapter 2: Related Work 22A recent research trend focused on un-calibrated cameras and several interestingresults were obtained [Hartley00][Faugeras01]. They show that in several cases andgiven the right set of correspondences the internal parameters of cameras can berecovered in an auto-calibration module, the work is based on projective geometrystratification and invariants. In our implementation of Shape from Motion we assumecalibrated cameras in order to have the highest possible accuracy.Most of the work mentioned previously considered the tasks of motion recovery andstructure reconstruction separately and sequentially. An important exception is theclass of algorithms known as the Factorization methods [Kanade97]. In this approach,a closed form solution of the SFM problem is sought, where shape and motion areobtained simultaneously. It was obtained at the cost of simplified camera models(resulting in approximate reconstructions) such as the orthographic [Tomasi92], andparaperspective models [Poelman94]. The Factorization algorithm was extended tohandle features other than points such as lines and planes [Morris98][Quan96], and tothe case of multiple moving objects [Costeira95]. There is also continuing work onadapting it to perspective camera models, although in these cases iterative techniquesare usually required [Han99].