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Motion and structure from line correspondences under orthographic projection
Author(s) -
Holt Robert J.,
Netravali Arun N.
Publication year - 1997
Publication title -
international journal of imaging systems and technology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.359
H-Index - 47
eISSN - 1098-1098
pISSN - 0899-9457
DOI - 10.1002/(sici)1098-1098(1997)8:3<301::aid-ima8>3.0.co;2-e
Subject(s) - orthographic projection , rotation (mathematics) , constant (computer programming) , projection (relational algebra) , translation (biology) , line (geometry) , plane (geometry) , parallel , multiplicity (mathematics) , mathematics , instant centre of rotation , geometry , computer vision , computer science , algorithm , biochemistry , chemistry , messenger rna , gene , programming language
In this article we determine the multiplicity of solutions in several cases where line correspondences from orthographic projections over three views are known. We show that in the general case where the motion may vary between frames, seven line correspondences over three views are sufficient to guarantee that in general there is a unique solution for the rotation and directions of the lines, up to a reflection about a plane parallel to the camera plane. There is a three‐parameter infinite family of solutions for the translations and depths of each line in this case. If the object is experiencing constant rotation, then four lines are sufficient to obtain solutions up to the same ambiguities. If the object is moving with constant rotation about a center of rotation which itself is moving in a straight line at constant velocity, then three lines are sufficient, and there is just a one‐parameter infinite family of solutions for the translation and depths of the lines. Several examples are given to illustrate our results. © 1997 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 8, 301–312, 1997