By Raynaud M. (Ed), Shioda T. (Ed)
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Extra info for Algebraic Geometry
It is zero for points of the reference plane, increases with height above this plane, and decreases with depth. Remark that the vectors all point towards the epipole in the image, which is near infinity in the direction X. the system of cameras. Correspondences alone can not provide affine information. An affine transformation is a particular projective transformation which preserves the plane at infinity II,. It is easy to see that a transformation A conserves 1 1 ,if, and only if the last row of the matrix of A is of the form [0,O,O, p],with p 0.
Each reconstruction can be transformed into another by an affine transformation of P3. There are shear and different scalings along axes, but parallelism is preserved.
11, it is this requirement is redundant: if , sufficient to specify one epipole to define F and tocomplete the description of affine correspondence. 16, obtained with [0, 0, 0, 1IT. The crucial remark is that the transformation of space is an affine transformation rather than a projective one. This decomposition separatesthe total 22 parameters into two types of parameters: 12 correspond to the affine ambiguity in reconstruction: the arbitrary choice of the affine basis (11 obtained by fixing 'P, 1 is p) 10 describe the affine correspondence: 8 as the infinity homography 2 as the epipole e‘.