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Shape and Motion from Image Streams: a Factorization Method - Full Report on the Orthographic Case (1992) [148 citations — 13 self]

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@TECHREPORT{Tomasi92shapeand,
    author = {Carlo Tomasi and Takeo Kanade},
    title = {Shape and Motion from Image Streams: a Factorization Method - Full Report on the Orthographic Case},
    institution = {International Journal of Computer Vision},
    year = {1992}
}

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Abstract:

Inferring scene geometry and camera motion from a stream of images is possible in principle, but is an ill-conditioned problem when the objects are distant with respect to their size. We have developed a factorization method that can overcome this difficulty by recovering shape and motion without computing depth as an intermediate step. An image stream can be represented by the 2F \Theta P measurement matrix of the image coordinates of P points tracked through F frames. We show that under orthographic projection this matrix is of rank 3. Using this observation, the factorization method uses the singular value decomposition technique to factor the measurement matrix into two matrices which represent object shape and camera motion respectively. The method can also handle and obtain a full solution from a partially filled-in measurement matrix, which occurs when features appear and disappear in the image sequence due to occlusions or tracking failures. The method gives accurate results, ...

Citations

1063	An Iterative Image Registration Technique with an Application to Stereo Vision – Lucas, Kanade - 1981
252	Uniqueness and estimation of three-dimensional motion parameters of rigid objects with curved surface – Tsai, Huang - 1984
205	Determining three-dimensional motion and structure from optical flow generated by several moving objects – ADIV - 1985
116	Direct methods for recovering motion – Horn, Weldon - 1988
72	Singular value decomposition and least squares solutions – Golub, Reinsch - 1970
21	Shape and motion without depth – Tomasi, Kanade - 1990
18	Visual perception of three-dimensional motion – Heeger, Jepson - 1989
18	A rational algebraic formulation of the problem of relative orientation – Thompson - 1959
6	Egomotion and Relative Depth from Optical Flow – Prazdny - 1980
3	Egomotion and relative depth from optical ow – Prazdny - 1980
1	Tsai et al – Tsai, Huang, et al. - 1984