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Systematic triangulations
COMPUTER
VISION,
GRAPHICS,
AND IMAGE
PROCESSING
22, 3 10-3 11 ( 1983)
Abstracts of Papers Accepted for Publication PAPERS Sdoing Tbree-Dimensional Small-Rotation Motion Equatiom: Vniquenes~ Algorithms, and Numerical Results. J.- Q. FANG AND T. S. HUANG. Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 6 1801. Received February 25, 1983. In the first part of this paper, we present a theorem on the uniqueness of the solution to a set of overdetermined nonlinear equations obtained by Huang and Tsai for approximately determining 3-D motion parameters when the rotation angle is small. Our main result is that if we correspondingly select nine points, which are not on a second order surface passing through the viewing point, from two sequential images of a moving object, then we can uniquely determine the solution of the motion equations. In the second part, we discuss the practical aspects of solving these overdetermined nonlinear equations. We propose a modified Newton method for solving nonlinear equations and a modified Levenberg-Marquardt method for solving the nonlinear least square problem, which are better than the original Newton and Levenger-Marquardt methods when applied to the problem of motion estimation. We also studied experimentally the effects on convergence and solution accuracy of the number of corresponding image point pairs, the geometrical configuration of the points in object space, the distance of the object from the image plane, the initial guess solution, and image resolution. A Frost Recursiw Algori?hm for Bbuay Valued Two-Dimemionai Filters. LEONARD A. FERRARI AND JACK SKLANSKY. University of California, Irvine, California 927 17. Received April 13, 1982; revised March II. 1983. We describe an efficient ,algorithm for computing the response of a linear spatially varying digital image filter to an arbitrary digital input image. This response is the superposition summation of the input image with a digital point spread function (PSF). We assume here that the PSF is binary valued. Our approach to this computation is based on the Principle of Inclusion and Exclusion. This approach leads us to a new efficient algorithm. This algorithm is also efficient when the PSF is spatially invariant.
SURVEY Systematk Triangukieus. D. F. WATSON AND G. M. PHILIP. Department of Geology and Geophysics, University of Sydney, Sydney, New South Wales 2006, Australia. Received January 18, 1983; revised March 2, 1983. Efficient and objective interpretation of spatial data depends upon the evaluation of local variation in the adjacency relationships of the data set. For scattered data, this in turn relies upon the systematic triangulation of the locational information. The Optimal, Greedy, and Delaunay triangulations are discussed and some differences illustrated by a simple example which also displays the “most equiangular” property of the Dclaunay triangulation. This property makes the Delaunay triangulation the most appropriate for triangle-based interpolation because it is a result of nearest neighbor spatial ordering of the data. Of the three approaches, only the Delaunay triangulation has efficient published algorithms.
NOTES Connected Pictnres Are Not Recognizable by Determinivtic Tw-Dimemionai On-Line TessetWon Acceptom. KATSJSHI INOUE AND ITSUO TAKANAMI, Department of Electronics, Faculty of Engineering, Yamaguchi University, Ube, 755 Japan; AND Arrra~ NAKAMUIU, Department of Applied Mathe310 0734-I 89X/83 $3.00 Copyright 0 1983 by Academic Press, Inc. All rights of reproduction in any form reselved.
VISION,
GRAPHICS,
AND IMAGE
PROCESSING
22, 3 10-3 11 ( 1983)
Abstracts of Papers Accepted for Publication PAPERS Sdoing Tbree-Dimensional Small-Rotation Motion Equatiom: Vniquenes~ Algorithms, and Numerical Results. J.- Q. FANG AND T. S. HUANG. Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 6 1801. Received February 25, 1983. In the first part of this paper, we present a theorem on the uniqueness of the solution to a set of overdetermined nonlinear equations obtained by Huang and Tsai for approximately determining 3-D motion parameters when the rotation angle is small. Our main result is that if we correspondingly select nine points, which are not on a second order surface passing through the viewing point, from two sequential images of a moving object, then we can uniquely determine the solution of the motion equations. In the second part, we discuss the practical aspects of solving these overdetermined nonlinear equations. We propose a modified Newton method for solving nonlinear equations and a modified Levenberg-Marquardt method for solving the nonlinear least square problem, which are better than the original Newton and Levenger-Marquardt methods when applied to the problem of motion estimation. We also studied experimentally the effects on convergence and solution accuracy of the number of corresponding image point pairs, the geometrical configuration of the points in object space, the distance of the object from the image plane, the initial guess solution, and image resolution. A Frost Recursiw Algori?hm for Bbuay Valued Two-Dimemionai Filters. LEONARD A. FERRARI AND JACK SKLANSKY. University of California, Irvine, California 927 17. Received April 13, 1982; revised March II. 1983. We describe an efficient ,algorithm for computing the response of a linear spatially varying digital image filter to an arbitrary digital input image. This response is the superposition summation of the input image with a digital point spread function (PSF). We assume here that the PSF is binary valued. Our approach to this computation is based on the Principle of Inclusion and Exclusion. This approach leads us to a new efficient algorithm. This algorithm is also efficient when the PSF is spatially invariant.
SURVEY Systematk Triangukieus. D. F. WATSON AND G. M. PHILIP. Department of Geology and Geophysics, University of Sydney, Sydney, New South Wales 2006, Australia. Received January 18, 1983; revised March 2, 1983. Efficient and objective interpretation of spatial data depends upon the evaluation of local variation in the adjacency relationships of the data set. For scattered data, this in turn relies upon the systematic triangulation of the locational information. The Optimal, Greedy, and Delaunay triangulations are discussed and some differences illustrated by a simple example which also displays the “most equiangular” property of the Dclaunay triangulation. This property makes the Delaunay triangulation the most appropriate for triangle-based interpolation because it is a result of nearest neighbor spatial ordering of the data. Of the three approaches, only the Delaunay triangulation has efficient published algorithms.
NOTES Connected Pictnres Are Not Recognizable by Determinivtic Tw-Dimemionai On-Line TessetWon Acceptom. KATSJSHI INOUE AND ITSUO TAKANAMI, Department of Electronics, Faculty of Engineering, Yamaguchi University, Ube, 755 Japan; AND Arrra~ NAKAMUIU, Department of Applied Mathe310 0734-I 89X/83 $3.00 Copyright 0 1983 by Academic Press, Inc. All rights of reproduction in any form reselved.