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11th International Conference on Image Analysis and Processing (ICIAP'01)
Digital Geometry Fundaments: Application to Plane Recognition
Palermo, Italy
September 26-September 28
ISBN: 0-7695-1183-X
J.M. Chassery, Domaine Universitaire
F. Dupont, Domaine Universitaire
I. Sivignon, Domaine Universitaire
J. Vittone, Domaine Universitaire
Introduction: Triangulation, quadrangulation problems and more generally 3D objects polyhedrization are an important subject of research. In digital geometry, a 3D object is seen as a set of voxels placed in a representation space only constituted of integers. The objective of the polyhedrization is to obtain a complete description of the object with faces, edges and vertices. The recognition of digital planes is a first step which is very important. We will focus on digital na?ve planes that have been studied through their configurations of tricubes [Sch97, VC97], of (n; m)-cubes [VC99b] and connected or not connected voxels set [VC99a, G_er99 ]. The link between the normal equation of a plane and configuration of voxels set has been studied by the construction of the corresponding Farey net [VC99a]. We can find many references about the recognition of digital planes. Some algorithms were related to the construction of the con- vex hull of the studied voxels set [KS91, KR82]. Other approaches use linear programming [ST91], mean square approximation [BF94] or Fourier-Motzkin transform [FP99, FST96, Vee94]. The first algorithms entirely discrete were to recognize rectangular pieces of naive planes [Deb95, DRR94, VC99b]. In this paper, we describe an incremental algorithm to recognize any coplanar voxels set as a digital naive plane by using Farey nets. Then we propose a polyhedrization method able to give all the digital naive planes of the surface of the 3D object.
Citation:
J.M. Chassery, F. Dupont, I. Sivignon, J. Vittone, "Digital Geometry Fundaments: Application to Plane Recognition," iciap, pp.0622, 11th International Conference on Image Analysis and Processing (ICIAP'01), 2001
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