## Describing Surfaces (1985)

Venue: | Computer Vision, Graphics, and Image Processing |

Citations: | 51 - 3 self |

### BibTeX

@INPROCEEDINGS{Brady85describingsurfaces,

author = {Michael Brady and Jean Ponce and Alan Yuille and Ttaruo Asada},

title = {Describing Surfaces},

booktitle = {Computer Vision, Graphics, and Image Processing},

year = {1985},

pages = {1--28},

publisher = {MIT Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

This paper continues ou,' work' on vlsuM representations of three-dimensional surfaces [Brady and Yuille 1984b]. The theoretical component o our work is a study of classes of surface curves as a source of constraint on the surface on which they lie, and as a basis for describing it. We analyze bounding contours, sin face intersections, lines of cunature, and asymptotes. Our experimental work hives.igates whether the information suggested by our theoretical study can be computed reliably mid efficiently. We demonstrate algorithms that compute lines of curvature of a (Gaussian smoothed) surface; determine planar patches and umbi!ic regions; extract axes of surfaces of revolution and tube surfaces. We report preliminary results on adapting the curvature primM sketch algorithms of Asada and Brady [1984] to detect and describe surface intersections. () Massachusetts Institute of Technology, 1984 This report describes research done at the Artificial Intelligeice Laboratory of the Massachusetts Institute of Technology. Support for the ]aboratory's Artificial Intelligence reseat.oh is provided in par. by the Adwmced Research Projects Agency of the Department of Defense under Office of Naval Research contract N00014-80-C-0505, the Office of Nax'al Research under contract number N000t4-77-C-0389, ,and the System Development Foundation. This wcrk was done while Haruo Asada was a visiting scientist at MIT on leave from Toshiba Corporation, Japan, and while Jean Ponce was a visking s.ientist on leave from I.'RIA, Paris, Fro,nee. ' Pr't of (t6:7)

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Citation Context ...ules that compute three-dimensional depth, or depth gradients. Such modules include: stereo [Grimson 1981, 1984, Mayhew 1083]; shape from shading [Ikeuchi and Horn 1981, 1984] and photometric stereo [=-=Woodham 1980-=-, 1981]; shape from contour [Brady and Yuille 1984a, Witkin 1981, Barnard 1983, Barnard and Pentland 1983]; shape from motion [Bruss and Horn 1983, Ullman 1978]; and shape from texture [Vilnrotter, Ne... |

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Citation Context ...82, Marr 1082] has centered on the development of modules that compute three-dimensional depth, or depth gradients. Such modules include: stereo [Grimson 1981, 1984, Mayhew 1083]; shape from shading [=-=Ikeuchi and Horn 1981-=-, 1984] and photometric stereo [Woodham 1980, 1981]; shape from contour [Brady and Yuille 1984a, Witkin 1981, Barnard 1983, Barnard and Pentland 1983]; shape from motion [Bruss and Horn 1983, Ullman 1... |

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Citation Context ...to computing the Primal Sketch representation for images [Mart 1976, Haralick et. al. 1983] and the Curvature Primal Sketch representation of the significant changes of curvature along planar curves [=-=Asada and Brady 1984-=-]. In Section 2.3, we show that Joachimsthal's Theorem can, under certain circumstances, be undone by Gaussian smoothing. More precisely, we shall prove that although two surfaces rarely intersect alo... |

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Citation Context ...hading [Ikeuchi and Horn 1981, 1984] and photometric stereo [Woodham 1980, 1981]; shape from contour [Brady and Yuille 1984a, Witkin 1981, Barnard 1983, Barnard and Pentland 1983]; shape from motion [=-=Bruss and Horn 1983-=-, Ullman 1978]; and shape from texture [Vilnrotter, Nevatia, and Price 1981]. In applying vision to robotics, range finding and structured light have been investigated as techniques for recovering dep... |

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Citation Context ...ch modules include: stereo [Grimson 1981, 1984, Mayhew 1083]; shape from shading [Ikeuchi and Horn 1981, 1984] and photometric stereo [Woodham 1980, 1981]; shape from contour [Brady and Yuille 1984a, =-=Witkin 1981-=-, Barnard 1983, Barnard and Pentland 1983]; shape from motion [Bruss and Horn 1983, Ullman 1978]; and shape from texture [Vilnrotter, Nevatia, and Price 1981]. In applying vision to robotics, range fi... |

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Citation Context ...clude: stereo [Grimson 1981, 1984, Mayhew 1083]; shape from shading [Ikeuchi and Horn 1981, 1984] and photometric stereo [Woodham 1980, 1981]; shape from contour [Brady and Yuille 1984a, Witkin 1981, =-=Barnard 1983-=-, Barnard and Pentland 1983]; shape from motion [Bruss and Horn 1983, Ullman 1978]; and shape from texture [Vilnrotter, Nevatia, and Price 1981]. In applying vision to robotics, range finding and stru... |

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Citation Context ...of the surface. The curves that we have studied are: bounding contours [Koenderinck and van Doom 1982, Koenderinck 1984, Marr 1977, Barrow and Tenenbanm 1978, 1981, Binford 1982]; lines of curvature [=-=Stevens 1982-=-, 1983, Brady and Yuille 1984b]; asymptotes [Brady and Yuille 1984b]; and surface intersections [Binford 1982]. We begin by discuss!rig (extremal) bounding contours of a surface, where the surface nor... |

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Citation Context ...an only be perceived if the curvature in a direction orthogonal to the join changes substantially. Asada mid Brady [1984] discuss the analogous situation for planar curves. A Theorem of Joachimsthal [=-=Weatherburn 1927-=-, page 68] implies that surfaces rarely intersect along their lines of curvature. For example, the htersection of the two cylinders in Figure 2 is not a line of curvature of either surface. The proble... |

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Citation Context ..., Japan, and while Jean Ponce was a visking s.ientist on leave from I.'RIA, Paris, Fro,nee. ' Pr't of (t6:7) Introduction 1 1. Introduction Recent work in Image Understanding [Ballard and Brown 1982, =-=Brady 1982-=-, Marr 1082] has centered on the development of modules that compute three-dimensional depth, or depth gradients. Such modules include: stereo [Grimson 1981, 1984, Mayhew 1083]; shape from shading [Ik... |

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(Show Context)
Citation Context ...[Grimson 1981, 1984, Mayhew 1083]; shape from shading [Ikeuchi and Horn 1981, 1984] and photometric stereo [Woodham 1980, 1981]; shape from contour [Brady and Yuille 1984a, Witkin 1981, Barnard 1983, =-=Barnard and Pentland 1983-=-]; shape from motion [Bruss and Horn 1983, Ullman 1978]; and shape from texture [Vilnrotter, Nevatia, and Price 1981]. In applying vision to robotics, range finding and structured light have been inve... |

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Citation Context ... given over to proving a theorem about generalized cones, a theorem that relates surface curves to a volumetric representation proposed by Maxr [1977]. Mart considered generalized cones [Brooks 1981, =-=Brooks and Binford 1980-=-] with straight axes. He suggested that such a generalized cone is effectively represented by (i) those cross sections, called skeletons, for which the expansion function attainssextreme value; ,'red ... |

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Citation Context ...ace and as a basis for description of the surface. The curves that we have studied are: bounding contours [Koenderinck and van Doom 1982, Koenderinck 1984, Marr 1977, Barrow and Tenenbanm 1978, 1981, =-=Binford 1982-=-]; lines of curvature [Stevens 1982, 1983, Brady and Yuille 1984b]; asymptotes [Brady and Yuille 1984b]; and surface intersections [Binford 1982]. We begin by discuss!rig (extremal) bounding contours ... |

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Citation Context ...orn 1981, 1984] and photometric stereo [Woodham 1980, 1981]; shape from contour [Brady and Yuille 1984a, Witkin 1981, Barnard 1983, Barnard and Pentland 1983]; shape from motion [Bruss and Horn 1983, =-=Ullman 1978-=-]; and shape from texture [Vilnrotter, Nevatia, and Price 1981]. In applying vision to robotics, range finding and structured light have been investigated as techniques for recovering depth directly [... |