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  Direct passive navigation: Analytical solution for planes (1986) [3 citations — 1 self]

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by Shahriar Negahdaripour
In Proceedings of IEEE Conference on Robotics and Automation
ftp://publications.ai.mit.edu/ai-publications/pdf/AIM-863.pdf
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Abstract:

Abstract: In this paper, we derive a closed form solution for recovering the motion of an observer relative to a planar surface directly from image brightness derivatives. We do not compute the optical flow as an intermediate step, only the spatiM and temporal intensity gradients at a minimum of 8 points. We solve a linear matrix equation for the elements of a 3x3 matrix. The eigenvalue decomposition of its symmetric part is then used to compute the motion parameters and the plane orientation.

Citations

1045 Determining optical flow – Horn, Schunck - 1981
483 A computer algorithm for reconstruction of a scene from two projections – Longuet-Higgins - 1981
249 Estimating threedimensional motion parameters of a rigid planar patch, II: Singular value decomposition – Tsai, Huang, et al. - 1982
200 The interpretation of moving retinal images – Longuet-Higgins, Prazdny - 1981
132 Direct passive navigation – Negahdaripour, Horn - 1987
102 The Measurement of Visual Motion – Hildreth - 1984
91 Velocity determination in scenes containing several moving objects – Fennema, Thompson - 1979
63 Determining 3-D motion and structure from optical flow generatedby several moving objects – Adiv - 1985
38 The visual ambiguity of a moving plane – Longuet-Higgins - 1984
38 Determining the movement of objects from a sequence of images – Roach, Aggarwal - 1980
30 Contour evolution, neighborhood deformation, and global image flow: planar surfaces in motion,” Int – Waxman, Wohn - 1985
18 Rigid Body Motion from Depth and Optical Flow – Ballard, Kimball - 1983
16 Surface Structure and 3-D Motion From Image Flow: A Kinematic Analysis – Waxman, Ullman - 1985
15 On the uniqueness of image flow solutions for planar surfaces in motion – Subbarao, Waxman - 1985
11 Detecting the motion of a planar surface by line & surface integrals – Kanatani - 1985
3 Detection of Surface Orientation and Motion from Texture: 1. The Case of Planes – Aloimonos, Chou - 1985
3 On the Derivation of 3D Rigid Point Configurations from Image Sequences – Nagel - 1981
3 Recovery of Rigid Structure from Orthographically Projected Optical Flow – Sugihara, Sugie - 1983
2 Determining 3-D Motion of Planar Objects from Brightness Patterns – Negahdaripour, Horn - 1985
1 et ah, "3D Solution to the Aperature problem – Buxton - 1984