## Skewed mirror symmetry in the 3D reconstruction of polyhedral models (2003)

Citations: | 2 - 0 self |

### BibTeX

@MISC{Vicent03skewedmirror,

author = {A. Piquer Vicent and P. Company Calleja and R. R. Martin},

title = {Skewed mirror symmetry in the 3D reconstruction of polyhedral models},

year = {2003}

}

### OpenURL

### Abstract

We aim to reconstruct three-dimensional polyhedra from axonometric line drawings. Existence of mirror symmetry in polyhedra can assist the reconstruction process. We present a new approach for determining planes of mirror symmetry of such polyhedral objects based on prior detection of their planar faces and any axes of symmetry of these faces. The axes are obtained from skewed facial symmetries, for which we also give a new method of determination.

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Citation Context ...or each face. Figure 2. Projection of a polyhedron with transparent faces and their detection. Line labelling methods for line drawings can also be used as a precedent to face detection (from Huffman =-=[Huf71]-=- and Clowes [Clo71] to Varley [Var00a], [Var00b]). Relatively little work has been concerned with the detection of faces in line drawings containing hidden edges. Two methods developed by Leclerc [Lec... |

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Citation Context ...ear as oblique or skewed symmetric faces after projection (Figure 1, right). Algorithms exist that detect symmetry or approximate symmetry, either by starting out with a finite set of points like Alt =-=[Alt88]-=- and Mills [Mill01], or by using approaches like Highnam [Hig86], who represents the points by a string of characters, and tests whether it is palindromic. Algorithms have also been devised that stem ... |

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Citation Context ...o not require consideration of the whole contour, which is important when processing drawings with hidden lines removed, for example. However, the skewed symmetry processing method developed by Gross =-=[Gro94]-=- is based on prior knowledge of how many axes of skewed symmetry the contour has, and this number cannot be greater than five. Yip [Yip94] gave a method for finding the axes of skewed symmetry using a... |

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Citation Context ...ch as Grimstead [Gri95], have also followed the steps of Kanade and Friedberg in the search for skewed facial symmetry using gradient space in an attempt to reconstruct three-dimensional drawings. Oh =-=[Oh88] g-=-ave a method for finding the skewed symmetry axes of polygons in order to determine surface orientation. Oh’s method is simple but has the disadvantage of being extremely time-consuming. In [Gro91],... |

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Citation Context ...es from real images in which hidden parts cannot be seen, and for which contour recognition was needed. In such cases there can be a lot of noise in the input data [Gro91], [Sug94], [Cha95], [She01], =-=[Sau01]. -=-Others take measurements from real objects [Zab94], for which certain characteristics are already known. Wen [Wen95] followed largely in Friedberg’s footsteps and gave a simple method for finding wh... |

1 |
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Citation Context .... Marola [Mar89] has focused on detecting axes of symmetry in plane figures obtained from digitized greyscale images, where noise arising during contour detection was important. Other studies such as =-=[She99]-=- analyze how to compute symmetry and measures of the degree of symmetry in polygons. Figure 1. A symmetrical figure and its skewed symmetry after projection We assume that each input drawing is (appro... |