The computation of structure from fixed-axis motion: Rigid structures
type: Item
instance of: scholarly article
title: The computation of structure from fixed-axis motion: Rigid structures
zbMATH Open document ID: 0586.92023
DOI: 10.1007/BF00320477
published in: Biological Cybernetics
publication date: 1986-01-01T00:00:00Z
review text: We show that three distinct orthographic views of three points in a rigid configuration are compatible with at most 64 interpretations of the three-dimensional structure and motion of the points. If, in addition, one assumes that the three points spin about a fixed axis over the three views, then with probability one there is a unique three-dimensional interpretation (plus a reflection). Moreover the probability of false targets is zero. In the special case that the axis of rotation is parallel to the image plane three views of the three points are sufficient to obtain at most two interpretations (plus reflections) - unless one assumes the angular velocity about the axis is constant, in which case three views of two points are sufficient to determine a unique interpretation. Closed form solutions are obtained for each of these cases. The systems of equations studied here are in each case overconstraining (i.e. there are more independent equations than unknowns) and are amenable to solution by nonlinear programming. These two properties make possible the construction of noise insensitive algorithms for computer vision systems. Our uniqueness proofs employ the principle of upper semicontinuity, a principle which underlies a general mathematical framework for the analysis of solutions to overconstraining systems of equations.
Mathematics Subject Classification ID: 91E30
Mathematics Subject Classification ID: 92F05
Mathematics Subject Classification ID: 70B10
zbMATH DE Number: 3941333
zbMATH Keywords: fixed-axis motion
zbMATH Keywords: rigid structures
zbMATH Keywords: three distinct orthographic views of three points
zbMATH Keywords: three-dimensional structure
zbMATH Keywords: Closed form solutions
zbMATH Keywords: nonlinear programming
zbMATH Keywords: noise insensitive algorithms
zbMATH Keywords: computer vision systems
zbMATH Keywords: upper semicontinuity
author: Donald D. Hoffman
author: Bruce M. Bennett
MaRDI profile type: Publication
cites work: Q5563439
cites work: The computation of structure from fixed-axis motion: nonrigid structures
cites work: Q4143433
cites work: The interpretation of biological motion
full work available at URL: https://doi.org/10.1007/bf00320477
OpenAlex ID: W2084308030
description: scientific article; zbMATH DE number 3941333