DOI: 10.1109/34.3908. The computation of visible-surface representations

The computation of visible-surface representations

10.1109/34.3908

Crossref journal-article

Institute of Electrical and Electronics Engineers (IEEE)

IEEE Transactions on Pattern Analysis and Machine Intelligence (263)

Bibliography

Terzopoulos, D. (1988). The computation of visible-surface representations. IEEE Transactions on Pattern Analysis and Machine Intelligence, 10(4), 417â438.

Authors 1

D. Terzopoulos (first)

References 65 Referenced 331

10.1109/TPAMI.1987.4767918
10.1016/0734-189X(84)90033-1
{'key': 'ref33', 'author': 'harris', 'year': '1986', 'journal-title': 'The coupled depth/slope approach to surface reconstruction'} / The coupled depth/slope approach to surface reconstruction by harris (1986)
{'key': 'ref32', 'author': 'hageman', 'year': '1981', 'journal-title': 'Applied Iterative Methods'} / Applied Iterative Methods by hageman (1981)
10.1007/978-3-662-02427-0 / Multi-grid Methods and Applications by hackbusch (1985)
10.1016/0734-189X(85)90163-X / Comput Vision Graphics Image Processing / Discontinuity detection for visual surface reconstruction by grimson (1985)
10.1073/pnas.83.12.4263
{'key': 'ref36', 'first-page': '78', 'author': 'kass', 'year': '1986', 'journal-title': 'From Pixels to Predicates'} / From Pixels to Predicates by kass (1986)
{'key': 'ref35', 'author': 'karplus', 'year': '1958', 'journal-title': 'Analog Simulation Solution of Field Problems'} / Analog Simulation Solution of Field Problems by karplus (1958)
{'key': 'ref34', 'author': 'horn', 'year': '1982', 'journal-title': 'Representation of three-dimensional objects'} / Representation of three-dimensional objects by horn (1982)
{'key': 'ref60', 'first-page': '905', 'author': 'wahba', 'year': '1980', 'journal-title': 'Approximation Theory III'} / Approximation Theory III by wahba (1980)
10.1016/0004-3702(81)90022-9
10.1137/1015003
{'key': 'ref63', 'author': 'zienkiewicz', 'year': '1979', 'journal-title': 'The Finite Element Method'} / The Finite Element Method by zienkiewicz (1979)
10.1016/0734-189X(83)90095-6
10.1109/TC.1977.1674848
10.7551/mitpress/3132.001.0001 / From Images to Surfaces A Computational Study of the Human Early Visual System by grimson (1981)
10.1007/978-3-642-51590-3_14
10.1109/TPAMI.1985.4767615
{'key': 'ref2', 'first-page': '3', 'author': 'barrow', 'year': '1978', 'journal-title': 'Computer Vision Systems'} / Computer Vision Systems by barrow (1978)
{'key': 'ref1', 'year': '1965', 'journal-title': 'Handbook of Mathematical Functions'} / Handbook of Mathematical Functions (1965)
{'key': 'ref20', 'author': 'do carmo', 'year': '1976', 'journal-title': 'Differential Geometry of Curves and Surfaces'} / Differential Geometry of Curves and Surfaces by do carmo (1976)
{'key': 'ref22', 'first-page': '232', 'article-title': 'Description of surfaces from range data', 'author': 'fan', 'year': '1985', 'journal-title': 'Proc DARPA Image Understanding Workshop'} / Proc DARPA Image Understanding Workshop / Description of surfaces from range data by fan (1985)
{'key': 'ref21', 'author': 'ermoliev', 'year': '1982', 'journal-title': 'Progress in Nondifferentiable Optimization'} / Progress in Nondifferentiable Optimization by ermoliev (1982)
{'key': 'ref24', 'first-page': '135', 'author': 'franke', 'year': '1983', 'journal-title': 'Surfaces in Computer Aided Geometric Design'} / Surfaces in Computer Aided Geometric Design by franke (1983)
10.1016/0167-8396(85)90011-1
{'key': 'ref26', 'author': 'gibson', 'year': '1950', 'journal-title': 'The Perception of the Visual World'} / The Perception of the Visual World by gibson (1950)
10.1109/TPAMI.1984.4767596
{'key': 'ref50', 'author': 'szilard', 'year': '1974', 'journal-title': 'Theory and Analysis of Plates Classical and Numerical Methods'} / Theory and Analysis of Plates Classical and Numerical Methods by szilard (1974)
10.1016/0734-189X(83)90020-8
10.1016/0262-8856(86)90029-6
10.1109/TPAMI.1986.4767769
{'key': 'ref57', 'author': 'tikhonov', 'year': '1977', 'journal-title': 'Solutions of Ill-posed Problems'} / Solutions of Ill-posed Problems by tikhonov (1977)
10.1109/TPAMI.1986.4767807
10.1109/TPAMI.1986.4767767
{'key': 'ref54', 'first-page': '156', 'article-title': 'Concurrent multilevel relaxation', 'author': 'terzopoulos', 'year': '1985', 'journal-title': 'Proc DARPA Image Understanding Workshop'} / Proc DARPA Image Understanding Workshop / Concurrent multilevel relaxation by terzopoulos (1985)
{'key': 'ref53', 'author': 'terzopoulos', 'year': '1984', 'journal-title': 'Multiresolution Computation of Visible-Surface Representations'} / Multiresolution Computation of Visible-Surface Representations by terzopoulos (1984)
{'key': 'ref52', 'first-page': '1073', 'article-title': 'The role of constraints and discontinuities in visible-surface reconstruction', 'author': 'terzopoulos', 'year': '1983', 'journal-title': 'Proc 8th Int Joint Conf AI'} / Proc 8th Int Joint Conf AI / The role of constraints and discontinuities in visible-surface reconstruction by terzopoulos (1983)
{'key': 'ref10', 'first-page': '68', 'article-title': 'Visual surface reconstruction using sparse depth data', 'author': 'boult', 'year': '1986', 'journal-title': 'Proc IEEE Conf Computer Vision and Pattern Recognition'} / Proc IEEE Conf Computer Vision and Pattern Recognition / Visual surface reconstruction using sparse depth data by boult (1986)
{'key': 'ref11', 'first-page': '3', 'volume': '8', 'author': 'braddick', 'year': '1978', 'journal-title': 'Perception Handbook of Sensory Physiology'} / Perception Handbook of Sensory Physiology by braddick (1978)
{'key': 'ref40', 'author': 'marr', 'year': '1982', 'journal-title': 'Vision A Computational Investigation into the Human Representation and Processing of Visual Information'} / Vision A Computational Investigation into the Human Representation and Processing of Visual Information by marr (1982)
10.1016/0734-189X(83)90096-8
10.1016/0734-189X(85)90001-5
10.1190/1.1440410
10.1126/science.7367885
{'key': 'ref16', 'article-title': 'Identification of distributed parameters', 'author': 'chavent', 'year': '1973', 'journal-title': 'Proc IFAC Identification System Parameter Estimation'} / Proc IFAC Identification System Parameter Estimation / Identification of distributed parameters by chavent (1973)
{'key': 'ref17', 'author': 'clarke', 'year': '1983', 'journal-title': 'Optimization and Nonsmooth Analysis'} / Optimization and Nonsmooth Analysis by clarke (1983)
10.1098/rspb.1985.0020
{'key': 'ref19', 'author': 'cochran', 'year': '1985', 'journal-title': 'Implementation of a multiresolution surface reconstruction algorithm'} / Implementation of a multiresolution surface reconstruction algorithm by cochran (1985)
10.1016/0004-3702(81)90021-7
{'key': 'ref3', 'first-page': '76', 'article-title': 'Reconstructing smooth surfaces from partial, noisy information', 'author': 'barrow', 'year': '1979', 'journal-title': '?roc DARPA Image Understanding Workshop'} / ?roc DARPA Image Understanding Workshop / Reconstructing smooth surfaces from partial, noisy information by barrow (1979)
10.1016/0167-8655(83)90077-6
10.1016/0734-189X(86)90220-3
{'key': 'ref8', 'first-page': '62', 'article-title': 'Invariant surface reconstruction using weak continuity constraints', 'author': 'blake', 'year': '1986', 'journal-title': 'Proc IEEE Conf Computer Vision and Pattern Recognition'} / Proc IEEE Conf Computer Vision and Pattern Recognition / Invariant surface reconstruction using weak continuity constraints by blake (1986)
{'key': 'ref7', 'first-page': '23', 'article-title': 'Reconstructing a visible surface', 'author': 'blake', 'year': '1984', 'journal-title': 'Proc Nat Conf AI (AAAI-84)'} / Proc Nat Conf AI (AAAI-84) / Reconstructing a visible surface by blake (1984)
{'key': 'ref49', 'author': 'strang', 'year': '1973', 'journal-title': 'An Analysis of the Finite Element Method'} / An Analysis of the Finite Element Method by strang (1973)
10.1190/1.1440688
{'key': 'ref46', 'author': 'rockafellar', 'year': '1981', 'journal-title': 'The Theory of Subgradients and its Application to Problems of Optimization Convex and Nonconvex Functions'} / The Theory of Subgradients and its Application to Problems of Optimization Convex and Nonconvex Functions by rockafellar (1981)
10.1109/PROC.1976.10066
{'key': 'ref48', 'author': 'shiau', 'year': '1985', 'journal-title': 'Smoothing spline estimation with discontinuities'} / Smoothing spline estimation with discontinuities by shiau (1985)
{'key': 'ref47', 'first-page': '203', 'author': 'schumaker', 'year': '1976', 'journal-title': 'Approximation Theory II'} / Approximation Theory II by schumaker (1976)
{'key': 'ref42', 'author': 'marroquin', 'year': '1984', 'journal-title': 'Surface Reconstruction Preserving Discontinuities'} / Surface Reconstruction Preserving Discontinuities by marroquin (1984)
10.1098/rspb.1978.0020
10.1038/317314a0
{'key': 'ref43', 'first-page': '22', 'article-title': 'Boundary detection by minimizing functionals, I', 'author': 'mumford', 'year': '1985', 'journal-title': 'Proc IEEE Conf Computer Vision and Pattern Recognition'} / Proc IEEE Conf Computer Vision and Pattern Recognition / Boundary detection by minimizing functionals, I by mumford (1985)

Dates

Type	When
Created	22 years, 11 months ago (Aug. 24, 2002, 7:09 p.m.)
Deposited	3 years, 8 months ago (Nov. 29, 2021, 3:06 p.m.)
Indexed	6 hours, 12 minutes ago (Aug. 21, 2025, 1:59 p.m.)
Issued	37 years, 1 month ago (July 1, 1988)
Published	37 years, 1 month ago (July 1, 1988)
Published Print	37 years, 1 month ago (July 1, 1988)

Funders 0

None

BibTeX

@article{Terzopoulos_1988, title={The computation of visible-surface representations}, volume={10}, ISSN={0162-8828}, url={http://dx.doi.org/10.1109/34.3908}, DOI={10.1109/34.3908}, number={4}, journal={IEEE Transactions on Pattern Analysis and Machine Intelligence}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Terzopoulos, D.}, year={1988}, month=jul, pages={417–438} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        21
      ]
    ],
    "date-time": "2025-08-21T17:59:42Z",
    "timestamp": 1755799182715
  },
  "reference-count": 65,
  "publisher": "Institute of Electrical and Electronics Engineers (IEEE)",
  "issue": "4",
  "license": [
    {
      "start": {
        "date-parts": [
          [
            1988,
            7,
            1
          ]
        ],
        "date-time": "1988-07-01T00:00:00Z",
        "timestamp": 583718400000
      },
      "content-version": "vor",
      "delay-in-days": 0,
      "URL": "https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html"
    }
  ],
  "content-domain": {
    "domain": [],
    "crossmark-restriction": false
  },
  "published-print": {
    "date-parts": [
      [
        1988,
        7
      ]
    ]
  },
  "DOI": "10.1109/34.3908",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2002,
        8,
        24
      ]
    ],
    "date-time": "2002-08-24T23:09:11Z",
    "timestamp": 1030230551000
  },
  "page": "417-438",
  "source": "Crossref",
  "is-referenced-by-count": 331,
  "title": "The computation of visible-surface representations",
  "prefix": "10.1109",
  "volume": "10",
  "author": [
    {
      "given": "D.",
      "family": "Terzopoulos",
      "sequence": "first",
      "affiliation": []
    }
  ],
  "member": "263",
  "reference": [
    {
      "key": "ref39",
      "doi-asserted-by": "publisher",
      "DOI": "10.1109/TPAMI.1987.4767918"
    },
    {
      "key": "ref38",
      "doi-asserted-by": "publisher",
      "DOI": "10.1016/0734-189X(84)90033-1"
    },
    {
      "key": "ref33",
      "author": "harris",
      "year": "1986",
      "journal-title": "The coupled depth/slope approach to surface reconstruction"
    },
    {
      "key": "ref32",
      "author": "hageman",
      "year": "1981",
      "journal-title": "Applied Iterative Methods"
    },
    {
      "key": "ref31",
      "doi-asserted-by": "crossref",
      "DOI": "10.1007/978-3-662-02427-0",
      "author": "hackbusch",
      "year": "1985",
      "journal-title": "Multi-grid Methods and Applications"
    },
    {
      "key": "ref30",
      "doi-asserted-by": "crossref",
      "first-page": "316",
      "DOI": "10.1016/0734-189X(85)90163-X",
      "article-title": "Discontinuity detection for visual surface reconstruction",
      "volume": "30",
      "author": "grimson",
      "year": "1985",
      "journal-title": "Comput Vision Graphics Image Processing"
    },
    {
      "key": "ref37",
      "doi-asserted-by": "publisher",
      "DOI": "10.1073/pnas.83.12.4263"
    },
    {
      "key": "ref36",
      "first-page": "78",
      "author": "kass",
      "year": "1986",
      "journal-title": "From Pixels to Predicates"
    },
    {
      "key": "ref35",
      "author": "karplus",
      "year": "1958",
      "journal-title": "Analog Simulation Solution of Field Problems"
    },
    {
      "key": "ref34",
      "author": "horn",
      "year": "1982",
      "journal-title": "Representation of three-dimensional objects"
    },
    {
      "key": "ref60",
      "first-page": "905",
      "author": "wahba",
      "year": "1980",
      "journal-title": "Approximation Theory III"
    },
    {
      "key": "ref62",
      "doi-asserted-by": "publisher",
      "DOI": "10.1016/0004-3702(81)90022-9"
    },
    {
      "key": "ref61",
      "doi-asserted-by": "publisher",
      "DOI": "10.1137/1015003"
    },
    {
      "key": "ref63",
      "author": "zienkiewicz",
      "year": "1979",
      "journal-title": "The Finite Element Method"
    },
    {
      "key": "ref28",
      "doi-asserted-by": "publisher",
      "DOI": "10.1016/0734-189X(83)90095-6"
    },
    {
      "key": "ref64",
      "doi-asserted-by": "publisher",
      "DOI": "10.1109/TC.1977.1674848"
    },
    {
      "key": "ref27",
      "doi-asserted-by": "crossref",
      "DOI": "10.7551/mitpress/3132.001.0001",
      "author": "grimson",
      "year": "1981",
      "journal-title": "From Images to Surfaces A Computational Study of the Human Early Visual System"
    },
    {
      "key": "ref65",
      "doi-asserted-by": "publisher",
      "DOI": "10.1007/978-3-642-51590-3_14"
    },
    {
      "key": "ref29",
      "doi-asserted-by": "publisher",
      "DOI": "10.1109/TPAMI.1985.4767615"
    },
    {
      "key": "ref2",
      "first-page": "3",
      "author": "barrow",
      "year": "1978",
      "journal-title": "Computer Vision Systems"
    },
    {
      "key": "ref1",
      "year": "1965",
      "journal-title": "Handbook of Mathematical Functions"
    },
    {
      "key": "ref20",
      "author": "do carmo",
      "year": "1976",
      "journal-title": "Differential Geometry of Curves and Surfaces"
    },
    {
      "key": "ref22",
      "first-page": "232",
      "article-title": "Description of surfaces from range data",
      "author": "fan",
      "year": "1985",
      "journal-title": "Proc DARPA Image Understanding Workshop"
    },
    {
      "key": "ref21",
      "author": "ermoliev",
      "year": "1982",
      "journal-title": "Progress in Nondifferentiable Optimization"
    },
    {
      "key": "ref24",
      "first-page": "135",
      "author": "franke",
      "year": "1983",
      "journal-title": "Surfaces in Computer Aided Geometric Design"
    },
    {
      "key": "ref23",
      "doi-asserted-by": "publisher",
      "DOI": "10.1016/0167-8396(85)90011-1"
    },
    {
      "key": "ref26",
      "author": "gibson",
      "year": "1950",
      "journal-title": "The Perception of the Visual World"
    },
    {
      "key": "ref25",
      "doi-asserted-by": "publisher",
      "DOI": "10.1109/TPAMI.1984.4767596"
    },
    {
      "key": "ref50",
      "author": "szilard",
      "year": "1974",
      "journal-title": "Theory and Analysis of Plates Classical and Numerical Methods"
    },
    {
      "key": "ref51",
      "doi-asserted-by": "publisher",
      "DOI": "10.1016/0734-189X(83)90020-8"
    },
    {
      "key": "ref59",
      "doi-asserted-by": "publisher",
      "DOI": "10.1016/0262-8856(86)90029-6"
    },
    {
      "key": "ref58",
      "doi-asserted-by": "publisher",
      "DOI": "10.1109/TPAMI.1986.4767769"
    },
    {
      "key": "ref57",
      "author": "tikhonov",
      "year": "1977",
      "journal-title": "Solutions of Ill-posed Problems"
    },
    {
      "key": "ref56",
      "doi-asserted-by": "publisher",
      "DOI": "10.1109/TPAMI.1986.4767807"
    },
    {
      "key": "ref55",
      "doi-asserted-by": "publisher",
      "DOI": "10.1109/TPAMI.1986.4767767"
    },
    {
      "key": "ref54",
      "first-page": "156",
      "article-title": "Concurrent multilevel relaxation",
      "author": "terzopoulos",
      "year": "1985",
      "journal-title": "Proc DARPA Image Understanding Workshop"
    },
    {
      "key": "ref53",
      "author": "terzopoulos",
      "year": "1984",
      "journal-title": "Multiresolution Computation of Visible-Surface Representations"
    },
    {
      "key": "ref52",
      "first-page": "1073",
      "article-title": "The role of constraints and discontinuities in visible-surface reconstruction",
      "author": "terzopoulos",
      "year": "1983",
      "journal-title": "Proc 8th Int Joint Conf AI"
    },
    {
      "key": "ref10",
      "first-page": "68",
      "article-title": "Visual surface reconstruction using sparse depth data",
      "author": "boult",
      "year": "1986",
      "journal-title": "Proc IEEE Conf Computer Vision and Pattern Recognition"
    },
    {
      "key": "ref11",
      "first-page": "3",
      "volume": "8",
      "author": "braddick",
      "year": "1978",
      "journal-title": "Perception Handbook of Sensory Physiology"
    },
    {
      "key": "ref40",
      "author": "marr",
      "year": "1982",
      "journal-title": "Vision A Computational Investigation into the Human Representation and Processing of Visual Information"
    },
    {
      "key": "ref12",
      "doi-asserted-by": "publisher",
      "DOI": "10.1016/0734-189X(83)90096-8"
    },
    {
      "key": "ref13",
      "doi-asserted-by": "publisher",
      "DOI": "10.1016/0734-189X(85)90001-5"
    },
    {
      "key": "ref14",
      "doi-asserted-by": "publisher",
      "DOI": "10.1190/1.1440410"
    },
    {
      "key": "ref15",
      "doi-asserted-by": "publisher",
      "DOI": "10.1126/science.7367885"
    },
    {
      "key": "ref16",
      "article-title": "Identification of distributed parameters",
      "author": "chavent",
      "year": "1973",
      "journal-title": "Proc IFAC Identification System Parameter Estimation"
    },
    {
      "key": "ref17",
      "author": "clarke",
      "year": "1983",
      "journal-title": "Optimization and Nonsmooth Analysis"
    },
    {
      "key": "ref18",
      "doi-asserted-by": "publisher",
      "DOI": "10.1098/rspb.1985.0020"
    },
    {
      "key": "ref19",
      "author": "cochran",
      "year": "1985",
      "journal-title": "Implementation of a multiresolution surface reconstruction algorithm"
    },
    {
      "key": "ref4",
      "doi-asserted-by": "publisher",
      "DOI": "10.1016/0004-3702(81)90021-7"
    },
    {
      "key": "ref3",
      "first-page": "76",
      "article-title": "Reconstructing smooth surfaces from partial, noisy information",
      "author": "barrow",
      "year": "1979",
      "journal-title": "?roc DARPA Image Understanding Workshop"
    },
    {
      "key": "ref6",
      "doi-asserted-by": "publisher",
      "DOI": "10.1016/0167-8655(83)90077-6"
    },
    {
      "key": "ref5",
      "doi-asserted-by": "publisher",
      "DOI": "10.1016/0734-189X(86)90220-3"
    },
    {
      "key": "ref8",
      "first-page": "62",
      "article-title": "Invariant surface reconstruction using weak continuity constraints",
      "author": "blake",
      "year": "1986",
      "journal-title": "Proc IEEE Conf Computer Vision and Pattern Recognition"
    },
    {
      "key": "ref7",
      "first-page": "23",
      "article-title": "Reconstructing a visible surface",
      "author": "blake",
      "year": "1984",
      "journal-title": "Proc Nat Conf AI (AAAI-84)"
    },
    {
      "key": "ref49",
      "author": "strang",
      "year": "1973",
      "journal-title": "An Analysis of the Finite Element Method"
    },
    {
      "key": "ref9",
      "doi-asserted-by": "publisher",
      "DOI": "10.1190/1.1440688"
    },
    {
      "key": "ref46",
      "author": "rockafellar",
      "year": "1981",
      "journal-title": "The Theory of Subgradients and its Application to Problems of Optimization Convex and Nonconvex Functions"
    },
    {
      "key": "ref45",
      "doi-asserted-by": "publisher",
      "DOI": "10.1109/PROC.1976.10066"
    },
    {
      "key": "ref48",
      "author": "shiau",
      "year": "1985",
      "journal-title": "Smoothing spline estimation with discontinuities"
    },
    {
      "key": "ref47",
      "first-page": "203",
      "author": "schumaker",
      "year": "1976",
      "journal-title": "Approximation Theory II"
    },
    {
      "key": "ref42",
      "author": "marroquin",
      "year": "1984",
      "journal-title": "Surface Reconstruction Preserving Discontinuities"
    },
    {
      "key": "ref41",
      "doi-asserted-by": "publisher",
      "DOI": "10.1098/rspb.1978.0020"
    },
    {
      "key": "ref44",
      "doi-asserted-by": "publisher",
      "DOI": "10.1038/317314a0"
    },
    {
      "key": "ref43",
      "first-page": "22",
      "article-title": "Boundary detection by minimizing functionals, I",
      "author": "mumford",
      "year": "1985",
      "journal-title": "Proc IEEE Conf Computer Vision and Pattern Recognition"
    }
  ],
  "container-title": "IEEE Transactions on Pattern Analysis and Machine Intelligence",
  "original-title": [],
  "link": [
    {
      "URL": "http://xplorestaging.ieee.org/ielx1/34/219/00003908.pdf?arnumber=3908",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2021,
        11,
        29
      ]
    ],
    "date-time": "2021-11-29T20:06:25Z",
    "timestamp": 1638216385000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "http://ieeexplore.ieee.org/document/3908/"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1988,
        7
      ]
    ]
  },
  "references-count": 65,
  "journal-issue": {
    "issue": "4"
  },
  "URL": "http://dx.doi.org/10.1109/34.3908",
  "relation": {},
  "ISSN": [
    "0162-8828"
  ],
  "subject": [],
  "container-title-short": "IEEE Trans. Pattern Anal. Machine Intell.",
  "published": {
    "date-parts": [
      [
        1988,
        7
      ]
    ]
  }
}