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Constraint Networks in Vision
December 1991 (vol. 40 no. 12)
pp. 1359-1367

Applications in machine vision of constraint networks based on an augmented Lagrangian formulation are discussed. Only those applications that have a fundamental significance are addressed. The first of these provides a generalization of the Harris coupled depth-slope analog model of visual reconstruction. Because of the generality of the approach, one can derive many more alternative structures, and the mathematical setting places this approach within the bounds of mixed finite element theory. This offers many advantages in terms of the associated mathematical theory and implementation on digital machines. The second use is in data fusion, which is a crucial task for systems using multiple sensors or methods of analysis of data.

[1] M. Bertero, P. Brianzi, E. R. Pike, and L. Rebolia, "Linear regularizing algorithms for positive solutions of linear inverse problems,"Proc. R. Soc. Lond. A, vol. 425, pp. 257-275, 1988.
[2] T. Poggio and C. Koch, "Ill-posed problems in early vision: From computational theory to analogue networks,"Proc. R. Soc. Lond. B, vol. 226, pp. 303-323, 1985.
[3] D. Terzopoulos, "Regularization of inverse visual problems involving discontinuities,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, no. 4, pp. 413-424, July 1986.
[4] C. A. Mead,Analog VLSI and Neural Systems. Reading, MA: Addison-Wesley, 1989.
[5] J. M. Hutchinson and C. Koch, "Simple analog and hybrid networks for surface interpolation," inAIP Conf. Proc. 151 Neural Networks for Computing, Snowbird, UT. New York: AIP, 1986, pp. 235-240.
[6] J. G. Harris, "A new approach to surface reconstruction: The coupled depth/slope model," inProc. First Int. Conf. Computer Vision, London, 1987, pp. 277-283.
[7] D. Suter, "Co-operative algorithms in machine vision: Models, problem formulation, and neural network implementations," Ph.D. dissertation, Dep. Comput. Sci. and Comput. Eng., Bundoora, Australia, Aug. 1990.
[8] D. Suter, "Coupled derivative/mixed finite element approach to visual reconstruction," inProc. Mini-Conf. Inverse Problems in Partial Differential Equations, Canberra, Australia, ANU Centre for Mathematical Analysis, Aug. 1990.
[9] D. Terzopoulos, "Multi-level reconstruction of visual surfaces: Variational principles and finite element representations," AI Memo 671, MIT, Apr. 1982.
[10] M. Fortin and R. Glowinski,Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems. Amsterdam, The Netherlands: North-Holland, 1983.
[11] P. G. Ciarlet,Introduction to Numerical Linear Algebra and Optimization. Cambridge. Cambridge: Cambridge University Press, 1988.
[12] J. C. Platt and A. H. Barr, "Constrained differential optimization," inProc. 1987 Neural Inform. Processing Syst. Conf., Denver, CO. New York: AIP, Nov. 1987, pp. 612-621.
[13] J. A. Snyman, "A parameter-free multiplier method for constrained minimization problems,"J. Computational Appl. Math., vol. 23, pp. 155-168, 1988.
[14] I.K. Sethi and R. Jain, "Finding trajectories of feature points in a monocular image sequence,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-9, pp. 56-73, Jan. 1987.
[15] A. Tikhonov and A. Goncharsky, Eds.,Ill-Posed Problems in the Natural Sciences. Moscow: MIR, 1987.
[16] F. Girosi and T. Poggio, "Networks and best approximation property," AI Memo 1164, MIT, Oct. 1989.
[17] T. Poggio and F. Girosi, "A theory for approximation and learning," AI Memo 1140, MIT, July 1989.
[18] E. Mjolsness and C. Garret, "Algebraic transformations of objective functions," Tech. Rep. YALEU/DCS/RR-686, Yale Univ., Mar. 1989.
[19] D. P. Bertsekas,Constrained Optimization and Lagrange Multiplier Methods. New York: Academic, 1982.
[20] J. G. Harris, "An analog vlsi chip for thin-plate surface interpolation," inAdvances in Neural Information Processing Systems I, D. S. Touretzky, Ed. San Mateo, CA: Morgan Kaufmann, 1989, pp. 687-694.
[21] J. Harris, C. Koch, J. Luo, and J. Wyatt, "Resistive fuses: Analog hardware for detecting discontinuities in early vision," inAnalog VLSI Implementation of Neural Systems, C. Mead and M. Ismail, Eds. Norwell, MA: Kluwer, 1989, pp. 27-55.
[22] B. K. P. Horn, "Height and gradient from shading," AI Memo 1105, MIT, May 1989.
[23] J. T. Oden and G. F. Carey,Finite Elements: Mathematical Aspects, Vol. IV. Englewood Cliffs, NJ: Prentice-Hall, 1983.
[24] D. Suter and D. Mansor, "Regularization and spline fitting by analog networks,"IEEE Trans. Neural Networks, submitted for publication.
[25] M. Hestenes,Conjugate Direction Methods in Optimization. New York: Springer-Verlag, 1980.
[26] O. Axelsson, "Preconditioning of indefinite problems by regularization,"SIAM J. Numer. Analysis, vol. 16, pp. 58-59, Feb. 1979.
[27] A. Blake, "Comparison of the efficiency of deterministic and stochastic algorithms for visual reconstruction,"IEEE Trans. Pattern Anal. Machine Intell., vol. 11, pp. 2-12, Jan. 1989.
[28] J. Aloimonos and D. Shulman,Integration of Visual Modules: An Extension of the Marr Paradigm. Boston, MA: Academic, 1989.
[29] J. J. Clark and A. L. Yuille,Data Fusion for Sensory Information Processing Systems. Boston, MA: Kluwer, 1990.
[30] D. P. Bertsekas and J. N. Tsitsiklis,Parallel and Distributed Computations. Englewood Cliffs, NJ: Prentice-Hall, 1989.
[31] M. Foxet al., Solving Problems on Concurrent Processors, vol. 1. Englewood Cliffs, NJ: Prentice-Hall, 1988.

Index Terms:
neural networks; machine vision; constraint networks; augmented Lagrangian formulation; Harris coupled depth-slope analog model; visual reconstruction; finite element theory; associated mathematical theory; data fusion; multiple sensors; computer vision; finite element analysis; neural nets.
Citation:
D. Suter, "Constraint Networks in Vision," IEEE Transactions on Computers, vol. 40, no. 12, pp. 1359-1367, Dec. 1991, doi:10.1109/12.106221
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