Abstract
The chapter investigates geometrical properties of quasi-perspective projection model in one and two-view geometry. The main results are as follows. (i) Quasi-perspective projection matrix has nine degrees of freedom, and the parallelism alongX andY directions in world system are preserved in images. (ii) Quasi-fundamental matrix can be simplified to a special form with only six degrees of freedom. The fundamental matrix is invariant to any non-singular projective transformation. (iii) Plane induced homography under quasi-perspective model can be simplified to a special form defined by six degrees of freedom. The quasi-homography may be recovered from two pairs of corresponding points with known fundamental matrix. (iv) Any two reconstructions in quasi-perspective space are defined up to a non-singular quasi-perspective transformation.
Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions.
Eric Temple Bell (1883–1960)
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Wang, G., Wu, Q.M.J. (2011). Geometrical Properties of Quasi-Perspective Projection. In: Guide to Three Dimensional Structure and Motion Factorization. Advances in Pattern Recognition. Springer, London. https://doi.org/10.1007/978-0-85729-046-5_3
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