The computation of structure from fixed-axis motion: Rigid structures
Biological Cybernetics
A homotopy for solving general polynomial systems that respects m-homogenous structures
Applied Mathematics and Computation
The complexity of robot motion planning
The complexity of robot motion planning
Interpretation of visual motion: a computational study
Interpretation of visual motion: a computational study
Coefficient-parameter polynomial continuation
Applied Mathematics and Computation
Finding all isolated solutions to polynomial systems using HOMPACK
ACM Transactions on Mathematical Software (TOMS)
Motion Estimation with More than Two Frames
IEEE Transactions on Pattern Analysis and Machine Intelligence
Camera calibration problem: some new results
CVGIP: Image Understanding
A criterion for detecting unnecessary reductions in the construction of Groebner bases
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Motion Capture of Arm from a Monocular Image Sequence
VISUAL '99 Proceedings of the Third International Conference on Visual Information and Information Systems
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Much of the dynamic computer vision literature deals with thedetermination of motion and structure by observing two frames captured at twoinstants of time. Motion prediction and understanding can be improvedsignificantly, particularly in the presence of noise, by analyzing an imagesequence containing more than two frames. In this paper, we assume knowledgeof correspondence of points on the surface of an object which is moving withconstant motion, i.e., constant translation and constant rotation around anunknown center. We give a new formulation of the problem and prove that thefollowing results hold in general for the number of solutions to motion andstructure values (i.e., values of translation, rotation, and depth): (a) For three point correspondences over three views, there are at mosttwo solutions, only one of which has all positive depth values; (b) For two point correspondences over four views, there is a uniquesolution; (c) For one point correspondence over five views, there can be up to tensolutions; (d) For one point correspondence over six views, there is a uniquesolution. The method of solution for each of the above formulations requires thesolving of a system of multivariate polynomials, whose coefficients arefunctions of the observed data. In order to determine the number of solutionsto these systems, we use theorems from algebraic geometry which imply thatunder a few mild conditions, the number of solutions at one set of datapoints provides an upper bound on the number of solutions for almost all setsof data points.Thus a bound on the number of solutions is obtained when asingle system is solved by a method such as homotopy continuation, which weuse here.