Depth computations from polyhedral images

Sparr, Gunnar

doi:10.1007/3-540-55426-2_43

Cited by 17 publications

(22 citation statements)

References 4 publications

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“…This shape space can be identified with the Grassmannian G m (k − 1) of all m dimensional subspaces of R k−1 , a result of Sparr (1992). For extrinsic analysis on AΣ k m , one embeds it into S(k, R) via an equivariant embedding, as obtained in Dimitric (1996).…”

Section: Introductionmentioning

confidence: 99%

Nonparametric statistics on manifolds with applications to shape spaces

Bhattacharya¹

2008

Institute of Mathematical Statistics Collections

151

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This article presents certain recent methodologies and some new results for the statistical analysis of probability distributions on manifolds. An important example considered in some detail here is the 2-D shape space of k-ads, comprising all configurations of $k$ planar landmarks ($k>2$)-modulo translation, scaling and rotation.Comment: Published in at http://dx.doi.org/10.1214/074921708000000200 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

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Section: Introductionmentioning

confidence: 99%

Nonparametric statistics on manifolds with applications to shape spaces

Bhattacharya¹

2008

Institute of Mathematical Statistics Collections

151

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“…These works are originated from the pioneer work of Koenderink and Van Doom [5] on affine shape representation from restricted camera projection, that is parallel projections and other related works [13,14,8].…”

Section: Introductionmentioning

confidence: 99%

“…Sparr (cf. [13,14]) reconstructs the affine shape using available affine information of objects such as the rectangular patches. Faugeras [1] dealt with the family of affine shapes.…”

Section: Introductionmentioning

confidence: 99%

Affine Stereo Calibration for Relative Affine Shape Reconstruction

Quan¹

1993

Procedings of the British Machine Vision Conference 1993

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It has been shown that relative projective shape, determined up to an unknown projective transformation, with respect to 5 reference points can be obtained from point-to-point correspondences of a pair of images; Affine shape up to an unknown affine transformation with respect to 4 points can be obtained from parallel projection. We show in this paper that afTine shape with respect to 4 reference points can be obtained from two perspective images provided that the pair of images is affinely calibrated. By affine calibration, it means the establishment of a special plane collineation between two image planes, this collineation is the product of two plane collineations each of which establishes a (1,1) correspondence between an image plane and the plane at infinity. Experimental results are also presented.

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“…These three vectors are not required to be orthogonal. The four points may be used to define an affine basis by the addition of a constraint that the sum of the coefficients be constant [5].…”

Section: Calibrating An Orthographic Projectionmentioning

confidence: 99%

“…However, since we know that where A and B are the affine coordinates of point 2 P 3 in the affine basis defined by 2 P 0 , 2 P 1 , 2 P 2 [5]. Alternatively, we can use the correspondence of the 4 points to write 8 simultaneous equations for the 8 unknown coefficients of the correction matrix 1 2 D.…”

Section: Dynamic Re-calibration Of the Projective Transformmentioning

confidence: 99%