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Computational Surface Flattening: A Voxelbased Approach
 IEEE Trans. PAMI
, 2002
"... A voxelbased method for flattening a surface in 3D space into 2D while best preserving distances is presented. Triangulation or polyhedral approximation of the voxel data are not required. The problem is divided into two main parts: Voxelbased calculation of the minimal geodesic distances bet ..."
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Cited by 17 (11 self)
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A voxelbased method for flattening a surface in 3D space into 2D while best preserving distances is presented. Triangulation or polyhedral approximation of the voxel data are not required. The problem is divided into two main parts: Voxelbased calculation of the minimal geodesic distances between points on the surface, and finding a configuration of points in 2D that has Euclidean distances as close as possible to these distances. The method suggested combines an efficient voxelbased hybrid distance estimation method, that takes the continuity of the underlying surface into account, with classical multidimensional scaling (MDS) for finding the 2D point configuration.
Length Estimation in 3D Using Cube Quantization
 Proc. SPIE Vision Geometry III
, 1998
"... Estimators for the original length of a continuous 3D curve given its digital representation are developed. The 2D case has been extensively studied. The few estimators that have been suggested for 3D curves suffer from serious drawbacks, partly due to incomplete understanding of the characterist ..."
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Cited by 11 (3 self)
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Estimators for the original length of a continuous 3D curve given its digital representation are developed. The 2D case has been extensively studied. The few estimators that have been suggested for 3D curves suffer from serious drawbacks, partly due to incomplete understanding of the characteristics of digital representation schemes for 3D curves. The selection and thorough understanding of the digital curve representation scheme is crucial to the design of 3D length estimators. A comprehensive study on the digitization of 3D curves was recently carried out. It was shown that grid intersect quantization and other 3D curve discretization schemes that lead to 26directional chain codes do not satisfy several fundamental requirements, and that cube quantization, that leads to 6directional chain codes, should be preferred. The few 3D length estimators that have been suggested are based on 26directional chain coding that naturally provides a classification of the chain links which is necessary for accurate length estimation. Cube quantization is mathematically wellbehaved but the symmetry and uniformity of the 6directional digital chain elements create a challenge in their classification for length estimation. In this paper length estimators for 3D curves digitized using cube quantization are developed. Simple but powerful link classification criteria for 6directional digital curves are presented. They are used to obtain unbiased length estimators, with RMS errors as low as 0:57% for randomly oriented straight lines, about five times better than in the best estimators that have been so far available.
An Elementary Algorithm for Digital Arc Segmentation
"... . This paper concerns the digital circle recognition problem and more precisely the circular separating algorithm. It tries to go further in implementation details, giving pseudocode algorithms for the main points, and using classical tools. After recalling the geometrical meaning of the separa ..."
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Cited by 10 (4 self)
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. This paper concerns the digital circle recognition problem and more precisely the circular separating algorithm. It tries to go further in implementation details, giving pseudocode algorithms for the main points, and using classical tools. After recalling the geometrical meaning of the separating circle problem, we present an incremental algorithm to segment a discrete curve into digital arc. Keywords: digital arc recognition, arc separability, digital circle, digital curvature. 1
2D and 3D Visibility in Discrete Geometry: an application to discrete geodesic paths
"... In this article, we present a discrete definition of the classical visibility in computational geometry based on digital straight lines. We present efficient algorithms to compute the set of pixels in a nonconvex domain that are visible from a source pixel. Based on these definitions, we define dis ..."
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Cited by 6 (2 self)
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In this article, we present a discrete definition of the classical visibility in computational geometry based on digital straight lines. We present efficient algorithms to compute the set of pixels in a nonconvex domain that are visible from a source pixel. Based on these definitions, we define discrete geodesic paths in discrete domain with obstacles. This allows us to introduce a new geodesic metric in discrete geometry.
Digital Plane Preimage Structure
, 2003
"... In digital geometry, digital straightness is an important concept both for practical motivations and theoretical interests. Concerning the digital straightness in dimension 2, many digital straight line characterizations exist and the digital straight segment preimage is well known. In this article, ..."
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Cited by 6 (4 self)
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In digital geometry, digital straightness is an important concept both for practical motivations and theoretical interests. Concerning the digital straightness in dimension 2, many digital straight line characterizations exist and the digital straight segment preimage is well known. In this article, we investigate the preimage associated to digital planes. More precisely, we present structure theorems that describe the preimage of a digital plane. Furthermore, we present a bound on the number of preimage faces.
Visibility in Discrete Geometry: an application to discrete geodesic paths
, 2002
"... In this article, we present a discrete definition of the classical visibility in computational geometry. We present algorithms to compute the set of pixels in a nonconvex domain that are visible from a source pixel. Based on these definitions, we define discrete geodesic paths in discrete domain ..."
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Cited by 2 (0 self)
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In this article, we present a discrete definition of the classical visibility in computational geometry. We present algorithms to compute the set of pixels in a nonconvex domain that are visible from a source pixel. Based on these definitions, we define discrete geodesic paths in discrete domain with obstacles. This allows us to introduce a new geodesic metric in discrete geometry.
On digital plane preimage structure
"... In digital geometry, digital straightness is an important concept both for practical motivations and theoretical interests. Concerning the digital straightness in dimension 2, many digital straight line characterizations exist and the digital straight segment preimage is well known. In this article, ..."
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In digital geometry, digital straightness is an important concept both for practical motivations and theoretical interests. Concerning the digital straightness in dimension 2, many digital straight line characterizations exist and the digital straight segment preimage is well known. In this article, we investigate the preimage associated to digital planes. More precisely, we present first structure theorems that describe the preimage of a digital plane. Furthermore, we present a bound on the number of preimage faces under some given hypotheses. Key words: digital plane preimage, digital straight line, dual transformation. 1
The Encoding and Fourier Descriptors of Arbitrary Curves in 3Dimensional Space
, 2000
"... v CHAPTERS 1 ..."
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, 2007
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. On digital plane preimage structure