Computational surface flattening: A voxel-based approach

Ruth Grossmann; Nahum Kiryati; Ron Kimmel

doi:10.1007/3-540-45129-3_17

Computational surface flattening: A voxel-based approach

Ruth Grossmann, Nahum Kiryati^*, Ron Kimmel

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

A voxel-based method for flattening a surface while best preserving the distances is presented. Triangulation or polyhedral approximation of the voxel data are not required. The problem is divided into two main subproblems: Voxel-based calculation of the minimal geodesic distances between the points on the surface, and finding a configuration of points in 2-D that has Euclidean distances as close as possible to the minimal geodesic distances. The method suggested combines an efficient voxel-based hybrid distance estimation method, that takes the continuity of the underlying surface into account, with classical multi-dimensional scaling (MDS) for finding the 2-D point configuration. The proposed algorithm is efficient, simple, and can be applied to surfaces that are not functions. Experimental results are shown.

Original language	English
Title of host publication	Visual Form 2001 - 4th International Workshop on Visual Form, IWVF4, Proceedings
Editors	Carlo Arcelli, Gabriella Sanniti di Baja, Luigi P. Cordella
Publisher	Springer Verlag
Pages	196-204
Number of pages	9
ISBN (Print)	3540421203, 9783540421207
DOIs	https://doi.org/10.1007/3-540-45129-3_17
State	Published - 2001
Event	4th International Workshop on Visual Form, IWVF4 2001 - Capri, Italy Duration: 28 May 2001 → 30 May 2001

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2059
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	4th International Workshop on Visual Form, IWVF4 2001
Country/Territory	Italy
City	Capri
Period	28/05/01 → 30/05/01

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10.1007/3-540-45129-3_17

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Grossmann, R., Kiryati, N., & Kimmel, R. (2001). Computational surface flattening: A voxel-based approach. In C. Arcelli, G. S. di Baja, & L. P. Cordella (Eds.), Visual Form 2001 - 4th International Workshop on Visual Form, IWVF4, Proceedings (pp. 196-204). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2059). Springer Verlag. https://doi.org/10.1007/3-540-45129-3_17

Grossmann, Ruth ; Kiryati, Nahum ; Kimmel, Ron. / Computational surface flattening : A voxel-based approach. Visual Form 2001 - 4th International Workshop on Visual Form, IWVF4, Proceedings. editor / Carlo Arcelli ; Gabriella Sanniti di Baja ; Luigi P. Cordella. Springer Verlag, 2001. pp. 196-204 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "A voxel-based method for flattening a surface while best preserving the distances is presented. Triangulation or polyhedral approximation of the voxel data are not required. The problem is divided into two main subproblems: Voxel-based calculation of the minimal geodesic distances between the points on the surface, and finding a configuration of points in 2-D that has Euclidean distances as close as possible to the minimal geodesic distances. The method suggested combines an efficient voxel-based hybrid distance estimation method, that takes the continuity of the underlying surface into account, with classical multi-dimensional scaling (MDS) for finding the 2-D point configuration. The proposed algorithm is efficient, simple, and can be applied to surfaces that are not functions. Experimental results are shown.",

author = "Ruth Grossmann and Nahum Kiryati and Ron Kimmel",

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year = "2001",

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Grossmann, R , Kiryati, N & Kimmel, R 2001, Computational surface flattening: A voxel-based approach. in C Arcelli, GS di Baja & LP Cordella (eds), Visual Form 2001 - 4th International Workshop on Visual Form, IWVF4, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2059, Springer Verlag, pp. 196-204, 4th International Workshop on Visual Form, IWVF4 2001, Capri, Italy, 28/05/01. https://doi.org/10.1007/3-540-45129-3_17

Computational surface flattening : A voxel-based approach. / Grossmann, Ruth ; Kiryati, Nahum; Kimmel, Ron.

Visual Form 2001 - 4th International Workshop on Visual Form, IWVF4, Proceedings. ed. / Carlo Arcelli; Gabriella Sanniti di Baja; Luigi P. Cordella. Springer Verlag, 2001. p. 196-204 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2059).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - Computational surface flattening

AU - Grossmann, Ruth

AU - Kiryati, Nahum

AU - Kimmel, Ron

N1 - Publisher Copyright: © Springer-Verlag Berlin Heidelberg 2001.

PY - 2001

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N2 - A voxel-based method for flattening a surface while best preserving the distances is presented. Triangulation or polyhedral approximation of the voxel data are not required. The problem is divided into two main subproblems: Voxel-based calculation of the minimal geodesic distances between the points on the surface, and finding a configuration of points in 2-D that has Euclidean distances as close as possible to the minimal geodesic distances. The method suggested combines an efficient voxel-based hybrid distance estimation method, that takes the continuity of the underlying surface into account, with classical multi-dimensional scaling (MDS) for finding the 2-D point configuration. The proposed algorithm is efficient, simple, and can be applied to surfaces that are not functions. Experimental results are shown.

AB - A voxel-based method for flattening a surface while best preserving the distances is presented. Triangulation or polyhedral approximation of the voxel data are not required. The problem is divided into two main subproblems: Voxel-based calculation of the minimal geodesic distances between the points on the surface, and finding a configuration of points in 2-D that has Euclidean distances as close as possible to the minimal geodesic distances. The method suggested combines an efficient voxel-based hybrid distance estimation method, that takes the continuity of the underlying surface into account, with classical multi-dimensional scaling (MDS) for finding the 2-D point configuration. The proposed algorithm is efficient, simple, and can be applied to surfaces that are not functions. Experimental results are shown.

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M3 - פרסום בספר כנס

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SN - 3540421203

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T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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BT - Visual Form 2001 - 4th International Workshop on Visual Form, IWVF4, Proceedings

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Grossmann R , Kiryati N, Kimmel R. Computational surface flattening: A voxel-based approach. In Arcelli C, di Baja GS, Cordella LP, editors, Visual Form 2001 - 4th International Workshop on Visual Form, IWVF4, Proceedings. Springer Verlag. 2001. p. 196-204. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-45129-3_17

Computational surface flattening: A voxel-based approach

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