## An Optimization-Based Approach to the Interpretation of Single Line Drawings as 3-D Wire Frames (1992)

Venue: | International Journal of Computer Vision |

Citations: | 35 - 0 self |

### BibTeX

@ARTICLE{Leclerc92anoptimization-based,

author = {Yvan G. Leclerc and Martin A. Fischler},

title = {An Optimization-Based Approach to the Interpretation of Single Line Drawings as 3-D Wire Frames},

journal = {International Journal of Computer Vision},

year = {1992},

volume = {9},

pages = {113--136}

}

### Years of Citing Articles

### OpenURL

### Abstract

Line drawings provide an effective means of communication about the geometry of 3-D objects. An understanding of how to duplicate the way humans interpret line drawings is extremely important in enabling man-machine communication with respect to images, diagrams, and spatial constructs. In particular, such an understanding could be used to provide the human with the capability to create a line-drawing sketch of a polyhedral object that the machine can automatically convert into the intended 3-D model. A recently published paper (Marill 1991) presented a simple optimization procedure supposedly able to duplicate human judgment in recovering the 3-D "wire frame" geometry of objects depicted in line drawings. Marill provided some impressive examples, but no theoretical justification for his approach. In this paper we introduce our own work by first critically examining Marill's algorithm. We provide an explanation for why Marill's algorithm was able to perform as well as it did on the exa...

### Citations

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Citation Context ...nefficient. One of the better descent algorithms is the conjugate gradient algorithm. To estimate achievable run times, we implemented the conjugate gradient algorithm described in Numerical Recipes (=-=Press et al. 1986-=-). The algorithm requires an objective function (in this case, E()) and the gradient of the objective function (in this case, a function that returns a vector whose i th element is the partial derivat... |

222 | Constructing Simple Stable Descriptions for Image Partitioning
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Citation Context ...lly, we would like to find the orthographic extension of the line drawing 10 with the lowest SDA that has exactly planar faces (i.e., for which DP = 0). To achieve this, we use a continuation method (=-=Leclerc 1989-=-, Witkin et al. 1987), which is a sequence of descent steps applied to E(), for decreasing values of . The sequence begins with the initial condition that Marill suggests (z = 0 for all points) and wi... |

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157 | Impossible Objects as Nonsense Sentences - Huffman - 1971 |

121 |
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Citation Context ...eractive user. A third direction is to explore the relationship between what we have done and previous work in understanding the 3-D shape of curves, such as (Barrow and Tenenbaum 1981, Stevens 1981, =-=Witkin 1981-=-, Barnard and Pentland 1983, Malik and Maydan 1989, Pentland and Kuo 1990). An intriguing relationship between Barrow and Tenenbaum's work on single curves and our work on planar faces is as follows. ... |

83 | Interpreting line drawings as three-dimensional surfaces
- Barrow, Tenenbaum
- 1981
(Show Context)
Citation Context ...possible without intervention from an interactive user. A third direction is to explore the relationship between what we have done and previous work in understanding the 3-D shape of curves, such as (=-=Barrow and Tenenbaum 1981-=-, Stevens 1981, Witkin 1981, Barnard and Pentland 1983, Malik and Maydan 1989, Pentland and Kuo 1990). An intriguing relationship between Barrow and Tenenbaum's work on single curves and our work on p... |

55 | Interpreting pictures of polyhedral scenes - Mackworth - 1973 |

55 |
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Citation Context ...on from an interactive user. A third direction is to explore the relationship between what we have done and previous work in understanding the 3-D shape of curves, such as (Barrow and Tenenbaum 1981, =-=Stevens 1981-=-, Witkin 1981, Barnard and Pentland 1983, Malik and Maydan 1989, Pentland and Kuo 1990). An intriguing relationship between Barrow and Tenenbaum's work on single curves and our work on planar faces is... |

41 | A quantitative approach to figural ‘‘goodness - Hochberg, McAlister - 1953 |

39 |
Emulating the Human Interpretation of Line-Drawings as Three-Dimensional Objects
- Marill
- 1991
(Show Context)
Citation Context ...sed to provide the human with the capability to create a line-drawing sketch of a polyhedral object that the machine can automatically convert into the intended 3-D model. A recently published paper (=-=Marill 1991) presente-=-d a simple optimization procedure supposedly able to duplicate human judgment in recovering the 3-D "wire frame" geometry of objects depicted in line drawings. Marill provided some impressiv... |

31 | A theory of origami world - Kanade - 1980 |

27 |
Recovering three-dimensional shape from a single image of a curved object
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(Show Context)
Citation Context ...xplore the relationship between what we have done and previous work in understanding the 3-D shape of curves, such as (Barrow and Tenenbaum 1981, Stevens 1981, Witkin 1981, Barnard and Pentland 1983, =-=Malik and Maydan 1989-=-, Pentland and Kuo 1990). An intriguing relationship between Barrow and Tenenbaum's work on single curves and our work on planar faces is as follows. They defined the problem of interpreting curves in... |

21 |
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(Show Context)
Citation Context ...se, only returns the wire frame. But in the case of a Blocks World object, competent algorithms exist for finding all the valid completions of the wire frame as a solid polyhedral object (Strat 1984, =-=Markowsky and Wesley 1981-=-). 19 As noted in Appendix A, we have made some initial progress toward the solution of this problem and have developed an algorithmic procedure that can successfully handle all of the examples discus... |

15 | A necessary and sufficient condition for a picture to represent a polyhedral scene - Sugihara - 1984 |

11 | The Use of Gradient and Dual Space in Line-Drawing Interpretation - Draper - 1981 |

7 |
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Citation Context ...be assessed. Figures that could be coded more simply under a depth interpretation were, in fact, seen in depth; those that could not be simplified in this way were seen to lie in the picture plane.&qu=-=ot; (Pomerantz and Kubovy 1981-=-, pp. 439--440). Barrow and Tenenbaum (1981) suggested ideas similar to Marill's for interpreting line drawings (both for simple closed curves and polyhedra), but did not pursue the ideas in greater d... |

6 | Generating semantic descriptions from line drawings of scenes with shadows - Waltz - 1972 |

3 |
Three-dimensional shape from line drawings
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(Show Context)
Citation Context .... A third direction is to explore the relationship between what we have done and previous work in understanding the 3-D shape of curves, such as (Barrow and Tenenbaum 1981, Stevens 1981, Witkin 1981, =-=Barnard and Pentland 1983-=-, Malik and Maydan 1989, Pentland and Kuo 1990). An intriguing relationship between Barrow and Tenenbaum's work on single curves and our work on planar faces is as follows. They defined the problem of... |

1 |
Three-dimensional line interpretation via local processing
- Pentland, Kuo
- 1990
(Show Context)
Citation Context ... between what we have done and previous work in understanding the 3-D shape of curves, such as (Barrow and Tenenbaum 1981, Stevens 1981, Witkin 1981, Barnard and Pentland 1983, Malik and Maydan 1989, =-=Pentland and Kuo 1990-=-). An intriguing relationship between Barrow and Tenenbaum's work on single curves and our work on planar faces is as follows. They defined the problem of interpreting curves in a manner similar to th... |

1 |
Spatial reasoning from line drawings of polyhedra
- Strat
- 1984
(Show Context)
Citation Context ...ill, of course, only returns the wire frame. But in the case of a Blocks World object, competent algorithms exist for finding all the valid completions of the wire frame as a solid polyhedral object (=-=Strat 1984-=-, Markowsky and Wesley 1981). 19 As noted in Appendix A, we have made some initial progress toward the solution of this problem and have developed an algorithmic procedure that can successfully handle... |

1 | Mathematical structures of line draings of polyhedrons---toward man-machine communication by means of line drawings - Sugihara - 1982 |

1 |
Two algorithms for polyhedral pictures
- Whitely
- 1986
(Show Context)
Citation Context ... More recently, Barnard and Pentland (1983) and Pentland and Kuo (1990) have pursued Barrow and Tenenbaum's approach for 2 Gradient space, originally conceived of by James Clerk Maxwell in 1864 (see (=-=Whitely 1986-=-)) and rediscovered by D. A. Huffman, provides only necessary conditions for planar realizability of general polyhedral objects with hidden lines removed, and thus consistent edge labeling is possible... |