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Volumn PAMI-8, Issue 4, 1986, Pages 413-424

Regularization of Inverse Visual Problems Involving Discontinuities

Author keywords

Controlled continuity constraints; discontinuities; early vision; inverse problems; reconstruction; regularization

Indexed keywords

COMPUTER GRAPHICS; MATHEMATICAL TECHNIQUES - VARIATIONAL TECHNIQUES; PROBABILITY - RANDOM PROCESSES;

EID: 0022756380     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPAMI.1986.4767807     Document Type: Article
Times cited : (579)

References (48)
  • 3
    • 0002309377 scopus 로고
    • Recovering intrinsic scene characteristics from images
    • A. R. Hanson and E. M. Riseman, Eds. New York: Academic
    • H. G. Barrow and J. M. Tenenbaum, “Recovering intrinsic scene characteristics from images,” in Computer Vision Systems, A. R. Hanson and E. M. Riseman, Eds. New York: Academic, 1978, pp. 326.
    • (1978) Computer Vision Systems , pp. 3-26
    • Barrow, H.G.1    Tenenbaum, J.M.2
  • 4
    • 0346473396 scopus 로고
    • Local control of bias and tension in beta-splines
    • B. A. Barsky and J. C. Beatty, “Local control of bias and tension in beta-splines,” ACM Trans. Graphics, vol. 2, pp. 109134, 1983.
    • (1983) ACM Trans. Graphics , vol.2 , pp. 109-134
    • Barsky, B.A.1    Beatty, J.C.2
  • 5
    • 0021020292 scopus 로고
    • The least-disturbance principle and weak constraints
    • A. Blake, “The least-disturbance principle and weak constraints,” Pattern Recognition Lett., vol. 1, pp. 393399, 1983.
    • (1983) Pattern Recognition Lett. , vol.1 , pp. 393-399
    • Blake, A.1
  • 6
    • 0020642302 scopus 로고
    • Rotationally symmetric operators for surface interpolation
    • J. M. Brady and B. K. P. lorn, “Rotationally symmetric operators for surface interpolation,” Comput. Vision, Graphics, Image Processing, vol. 22, pp. 7094, 1983.
    • (1983) Comput. Vision, Graphics, Image Processing , vol.22 , pp. 70-94
    • Brady, J.M.1    Lorn, B.K.P.2
  • 7
    • 0002161735 scopus 로고
    • Machine contouring using minimum curvature
    • I. C. Briggs, “Machine contouring using minimum curvature,” Geophys. phys., vol. 39, pp. 3948, 1974.
    • (1974) Geophys. , vol.39 , pp. 39-48
    • Briggs, I.C.1
  • 8
    • 0016050296 scopus 로고
    • Scalar and planar-valued curve fitting using splines under tension
    • A. K. Cline, “Scalar-and planar-valued curve fitting using splines under tension,” Commun. ACM, vol. 17, pp. 218220, 1974.
    • (1974) Commun. ACM , vol.17 , pp. 218-220
    • Cline, A.K.1
  • 10
    • 49949144652 scopus 로고
    • On numerical differentiation
    • USSR Comp. Math. and Math. Phys.
    • T. F. Dolgopolova and V. K. Ivanov, “On numerical differentiation,” Zh. Vych. Mat. Fiz. (USSR Comp. Math. and Math. Phys.), vol. 6, pp. 570576, 1966.
    • (1966) Zh. Vych. Mat. Fiz. , vol.6 , pp. 570-576
    • Dolgopolova, T.F.1    Ivanov, V.K.2
  • 11
    • 0017216638 scopus 로고
    • Interpolation des fonctions de deux variables suivant le principe de la flexion des plaques minces
    • J. Duchon, “Interpolation des fonctions de deux variables suivant le principe de la flexion des plaques minces,” R.A.I.R. I.R. O. Analyse Numerique, vol. 10, pp. 512, 1976.
    • (1976) R.A.I.R.O. Analyse Numerique , vol.10 , pp. 5-12
    • Duchon, J.1
  • 12
    • 0001935440 scopus 로고
    • Splines minimizing rotation-invariant semi-norms in Sobolev spaces
    • A. Dodd and B. Eckmann, Eds. Berlin: Springer-Verlag
    • J. Duchon, “Splines minimizing rotation-invariant semi-norms in Sobolev spaces,” in Constructive Theory of Functions of Several Variables, A. Dodd and B. Eckmann, Eds. Berlin: Springer-Verlag, 1977, pp. 85100.
    • (1977) Constructive Theory of Functions of Several Variables , pp. 85-100
    • Duchon, J.1
  • 14
    • 84968515237 scopus 로고
    • Scattered data interpolation: Tests of some methods
    • R. Franke, “Scattered data interpolation: Tests of some methods,” Math. Comput., vol. 38, pp. 181199, 1982.
    • (1982) Math. Comput. , vol.38 , pp. 181-199
    • Franke, R.1
  • 15
    • 0021518209 scopus 로고
    • Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images
    • S. Geman and D. Geman, “Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images,” IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, pp. 721741, 1985.
    • (1985) IEEE Trans. Pattern Anal. Machine Intell , vol.PAMI-6 , pp. 721-741
    • Geman, S.1    Geman, D.2
  • 16
    • 0016136756 scopus 로고
    • B-spline curves and surfaces
    • R. E. Barnhill and R. F. Riesenfeld, Eds. New York: Academic
    • W. J. Gordon and R. F. Riesenfeld, “B-spline curves and surfaces,” in Computer Aided Geometric Design, R. E. Barnhill and R. F. Riesenfeld, Eds. New York: Academic, 1974, pp. 95126.
    • (1974) Computer Aided Geometric Design , pp. 95-126
    • Gordon, W.J.1    Riesenfeld, R.F.2
  • 17
    • 0020642298 scopus 로고
    • An implementation of a computational theory of visual surface interpolation
    • W. E. L. Grimson, “An implementation of a computational theory of visual surface interpolation,” Comput. Vision, Graphics, Image Processing, vol. 22, pp. 3969, 1983.
    • (1983) Comput. Vision, Graphics, Image Processing , vol.22 , pp. 39-69
    • Grimson, W.E.L.1
  • 18
    • 0015291061 scopus 로고
    • Interpolation using surface splines
    • R. L. Harder and R. N. Desmarais, “Interpolation using surface splines,” J. Aircraft, vol. 9, pp. 189191, 1972.
    • (1972) J. Aircraft , vol.9 , pp. 189-191
    • Harder, R.L.1    Desmarais, R.N.2
  • 19
    • 0004469897 scopus 로고
    • Neurons with graded response have collective computational properties like those of two-state neurons
    • USA
    • J. J. Hopfield, “Neurons with graded response have collective Computational properties like those of two-state neurons,” Proc. Nat. Acad. Sci., USA, vol. 81, pp. 30883092, 1984.
    • (1984) Proc. Nat. Acad. Sci. , vol.81 , pp. 3088-3092
    • Hopfield, J.J.1
  • 20
    • 0000406385 scopus 로고
    • A correspondence between Bayesian estimation on stochastic processes and smoothing by splines
    • Kirkpatrick
    • G. Kimeldorf and G. Wahba, “A correspondence between Bayesian estimation on stochastic processes and smoothing by splines,” Ann. Math. Statist., Kirkpatrick, vol. 41, pp. 495502, 1970.
    • (1970) Ann. Math. Statist. , vol.41 , pp. 495-502
    • Kimeldorf, G.1    Wahba, G.2
  • 21
    • 26444479778 scopus 로고
    • Optimization by simulated annealing
    • S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, “Optimization by simulated annealing,” Science, vol. 220, pp. 671680, 1983.
    • (1983) Science , vol.220 , pp. 671-680
    • Kirkpatrick, S.1    Gelatt, C.D.2    Vecchi, M.P.3
  • 22
    • 35048876909 scopus 로고
    • Analog neuronal networks in early vision
    • Cambridge, MA, Al Memo 751
    • C. Koch, J. L. Marroquin, and A. L. Yuille, “Analog neuronal networks in early vision,” M.I.T. A.I. Lab., Cambridge, MA, Al Memo 751, 1985.
    • (1985) M.I.T. A.I. Lab.
    • Koch, C.1    Marroquin, J.L.2    Yuille, A.L.3
  • 24
    • 0003048824 scopus 로고
    • Representing visual information
    • A. R. Hanson and E. M. Riseman, Eds. New York: Academic
    • D. Marr, “Representing visual information,” in Computer Vision Systems, A. R. Hanson and E. M. Riseman, Eds. New York: Academic, 1978.
    • (1978) Computer Vision Systems
    • Marr, D.1
  • 25
    • 0011937444 scopus 로고    scopus 로고
    • Surface reconstruction preserving discontinuities
    • M.I.T. A.I. Lab., Cambridge, MA, Al Memo 792
    • J. L. Marroquin, “Surface reconstruction preserving discontinuities,” M.I.T. A.I. Lab., Cambridge, MA, Al Memo 792, 1984.
    • Marroquin, J.L.1
  • 26
    • 0006498070 scopus 로고
    • An intrinsic approach to multivariate spline interpolation at arbitrary points
    • B. N. Sahney, Ed. Dordrecht, The Netherlands: Reidel
    • J. Meinguet, “An intrinsic approach to multivariate spline interpolation at arbitrary points,” in Polynomial and Spline Approximation: Theory and Applications, B. N. Sahney, Ed. Dordrecht, The Netherlands: Reidel, 1979.
    • (1979) Polynomial and Spline Approximation: Theory and Applications
    • Meinguet, J.1
  • 27
    • 34250265664 scopus 로고
    • Multivariate interpolation at arbitrary points made simple
    • J. Meinguet, “Multivariate interpolation at arbitrary points made simple,” J. Appl. Math. Phys. (ZAMP), vol. 30, pp. 292304, 1979.
    • (1979) J. Appl. Math. Phys. (ZAMP) , vol.30 , pp. 292-304
    • Meinguet, J.1
  • 29
    • 0016141247 scopus 로고
    • Some piecewise polynomial alternatives to splines under tension
    • R. E. Barnhill and R. F. Riesenfeld, Eds. New York: Academic
    • G. M. Nielson, “Some piecewise polynomial alternatives to splines under tension,” in Computer Aided Geometric Design, R. E. Barnhill and R. F. Riesenfeld, Eds. New York: Academic, 1974, pp. 209235. 235.
    • (1974) Computer Aided Geometric Design , pp. 209-235
    • Nielson, G.M.1
  • 30
    • 0016216420 scopus 로고
    • Smooth parametric surfaces
    • R. E. Bamhill and R. F. Riesenfeld, Eds. New York: Academic
    • D. Pilcher, “Smooth parametric surfaces,” in Computer Aided Geometric Design, R. E. Bamhill and R. F. Riesenfeld, Eds. New York: Academic, 1974, pp. 237253.
    • (1974) Computer Aided Geometric Design , pp. 237-253
    • Pilcher, D.1
  • 31
    • 0004331063 scopus 로고
    • Ill-posed problems and regularization analysis in early vision
    • M.I.T. A.I. Lab., Cambridge, MA, Al Memo 773; reprinted New Orleans, LA, L. S. Baumann, Ed.
    • T. Poggio and V. Torre, “Ill-posed problems and regularization analysis in early vision,” M.I.T. A.I. Lab., Cambridge, MA, Al Memo 773; reprinted in Proc. DARPA Image Understanding Workshop, New Orleans, LA, L. S. Baumann, Ed., 1984, pp. 257263.
    • (1984) Proc. DARPA Image Understanding Workshop , pp. 257-263
    • Poggio, T.1    Torre, V.2
  • 33
    • 34250516079 scopus 로고
    • Smoothing by spline functions
    • G. Reinsch, “Smoothing by spline functions,” Numer. Math., vol. 10, pp. 177183, 1967.
    • (1967) Numer. Math. , vol.10 , pp. 177-183
    • Reinsch, G.1
  • 34
    • 0001426609 scopus 로고
    • Spline functions and the problem of graduation
    • I. J. Schoenberg, “Spline functions and the problem of graduation,” Proc. Nat. Acad. Sci., vol. 52, pp. 947950, 1964.
    • (1964) Proc. Nat. Acad. Sci. , vol.52 , pp. 947-950
    • Schoenberg, I.J.1
  • 35
    • 0003085949 scopus 로고
    • Fitting surfaces to scattered data
    • G. G. Lorentz, C. K. Chui, and L. L. Schumaker, Eds. New York: Academic
    • L. L. Schumaker, “Fitting surfaces to scattered data,” in Approximation II, G. G. Lorentz, C. K. Chui, and L. L. Schumaker, Eds. New York: Academic, 1976, pp. 203267.
    • (1976) Approximation II , pp. 203-267
    • Schumaker, L.L.1
  • 37
    • 0000129569 scopus 로고
    • An interpolation curve using a spline in tension
    • D. G. Schweikert, “An interpolation curve using a spline in tension,” J. Math. Phys., vol. 45, pp. 312317, 1966.
    • (1966) J. Math. Phys. , vol.45 , pp. 312-317
    • Schweikert, D.G.1
  • 38
    • 12844256266 scopus 로고
    • Multilevel reconstruction of visual surfaces: Variational principles and finite element representations
    • M.I.T. Lab., Cambridge, MA,Al Memo 671; reprinted in, A. Rosenfeld, Ed. New York: Springer-Verlag
    • D. Terzopoulos, “Multilevel reconstruction of visual surfaces: Variational principles and finite element representations,” M.I.T. Lab., Cambridge, MA, 1982, Al Memo 671; reprinted in Multiresolution Image Processing and Analysis, A. Rosenfeld, Ed. New York: Springer-Verlag, 1984, pp. 237310.
    • (1982) Multiresolution Image Processing and Analysis , vol.1984 , pp. 237-310
    • Terzopoulos, D.1
  • 39
    • 0020970241 scopus 로고
    • Multilevel computational processes for visual surface reconstruction
    • D. Terzopoulos, “Multilevel computational processes for visual surface reconstruction,” Comput. Vision, Graphics, Image Processing, vol. 24, pp.52-96, 1983.
    • (1983) Comput. Vision, Graphics, Image Processing , vol.24 , pp. 52-96
    • Terzopoulos, D.1
  • 40
    • 0020921718 scopus 로고
    • The role of constraints and discontinuities in visible-surface reconstruction
    • AI, Karlsruhe, W. Germany
    • D. Terzopoulos, “The role of constraints and discontinuities in visible-surface reconstruction,” in Proc. 8th Int. Joint Conf. AI, Karlsruhe, W. Germany, 1983, pp. 10731077.
    • (1983) Proc. 8th Int. Joint Conf. , pp. 1073
    • Terzopoulos, D.1
  • 41
    • 0011067081 scopus 로고
    • Multiresolution computation of visible-surface representations
    • Ph.D. dissertation M.I.T., Cambridge, MA
    • D. Terzopoulos, “Multiresolution computation of visible-surface representations,” Ph.D. dissertation, Dep. Elec. Eng. Comput. Sci., M.I.T., Cambridge, MA, 1984.
    • (1984) Dep. Elec. Eng. Comput. Sci.
    • Terzopoulos, D.1
  • 43
    • 0022683168 scopus 로고
    • Image analysis using multigrid relaxation methods
    • Mar.
    • D. Terzopoulos, “Image analysis using multigrid relaxation methods,” IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 129139, Mar. 1986.
    • (1986) IEEE Trans. Pattern Anal. Machine Intell. , vol.PAMI-8 , pp. 129-139
    • Terzopoulos, D.1
  • 44
    • 0001300995 scopus 로고
    • Regularization of incorrectly posed problems
    • A. N. Tikhonov, “Regularization of incorrectly posed problems,” Sov. Math. Dokl., vol. 4, pp. 16241627, 1963.
    • (1963) Sov. Math. Dokl. , vol.4 , pp. 1624-1627
    • Tikhonov, A.N.1
  • 46
    • 0000681041 scopus 로고
    • Some new mathematical methods for variational objective analysis using splines and cross validation
    • G. Wahba and J. Wendelberger, “Some new mathematical methods for variational objective analysis using splines and cross validation,” Monthly Weather Rev., vol. 108, pp. 11221143, 1980.
    • (1980) Monthly Weather Rev. , vol.108 , pp. 1122-1143
    • Wahba, G.1    Wendelberger, J.2
  • 47
    • 0020891393 scopus 로고
    • Scale-space filtering
    • Al, Karlsruhe, W. Germany
    • A. P. Witkin, “Scale-space filtering,” in Proc. 8th Int. Joint Conf., Al, Karlsruhe, W. Germany, 1983, pp. 10191022.
    • (1983) Proc. 8th Int. Joint Conf. , pp. 1019
    • Witkin, A.P.1
  • 48
    • 0017480534 scopus 로고
    • An application of relaxation labeling to line and curve enhancement
    • S. W. Zucker, R. A. Hummel, and A. Rosenfeld, “An application of relaxation labeling to line and curve enhancement,” IEEE Trans. Comput., vol. C-26, pp. 394-403, 1977.
    • (1977) IEEE Trans. Comput. , vol.C-26 , pp. 394-403
    • Zucker, S.W.1    Hummel, R.A.2    Rosenfeld, A.3


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