Representing Surface Curvature Discontinuities

Hiromi T.TANAKA; Daniel T.L.LEE; Fumio KISHINO

Representing Surface Curvature Discontinuities

Hiromi T.TANAKA, Daniel T.L.LEE, Fumio KISHINO

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A representation scheme is presented for shapes of three-dimensional curved objects whose surface curvatures are not continuous at all points, i.e., surfaces with C¹ continuity only. The representation consists of a subset of lines of curvature and their intersections, called surface structure descriptors, organized in a three-layer hierarchy of increasing stringency. From these descriptors, a hierarchical parameterization of C¹ surfaces leading to a global shape representation of the object is obtained in terms of enclosing boundaries of bumps and dents, ridge and valley lines, and peaks and pits (curvature extreme points). To handle the discontinuities of surface curvatures, we introduce a computational scheme in which gradient directions of surface curvatures at the discontinuities can be inferred. Simulation results on the computation of these descriptors from curved surfaces are shown. Potential applications of this representation scheme in computer vision tasks are discussed.

Publication: IEICE TRANSACTIONS on Information Vol.E74-D No.10 pp.3423-3432

Publication Date: 1991/10/25

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Type of Manuscript: Special Section PAPER (Special Issue on Computer Vision and Its Applications)

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Hiromi T.TANAKA
Daniel T.L.LEE
Fumio KISHINO

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Hiromi T.TANAKA, Daniel T.L.LEE, Fumio KISHINO, "Representing Surface Curvature Discontinuities" in IEICE TRANSACTIONS on Information, vol. E74-D, no. 10, pp. 3423-3432, October 1991, doi: .
Abstract: A representation scheme is presented for shapes of three-dimensional curved objects whose surface curvatures are not continuous at all points, i.e., surfaces with C¹ continuity only. The representation consists of a subset of lines of curvature and their intersections, called surface structure descriptors, organized in a three-layer hierarchy of increasing stringency. From these descriptors, a hierarchical parameterization of C¹ surfaces leading to a global shape representation of the object is obtained in terms of enclosing boundaries of bumps and dents, ridge and valley lines, and peaks and pits (curvature extreme points). To handle the discontinuities of surface curvatures, we introduce a computational scheme in which gradient directions of surface curvatures at the discontinuities can be inferred. Simulation results on the computation of these descriptors from curved surfaces are shown. Potential applications of this representation scheme in computer vision tasks are discussed.
URL: https://global.ieice.org/en_transactions/information/10.1587/e74-d_10_3423/_p

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@ARTICLE{e74-d_10_3423,
author={Hiromi T.TANAKA, Daniel T.L.LEE, Fumio KISHINO, },
journal={IEICE TRANSACTIONS on Information},
title={Representing Surface Curvature Discontinuities},
year={1991},
volume={E74-D},
number={10},
pages={3423-3432},
abstract={A representation scheme is presented for shapes of three-dimensional curved objects whose surface curvatures are not continuous at all points, i.e., surfaces with C¹ continuity only. The representation consists of a subset of lines of curvature and their intersections, called surface structure descriptors, organized in a three-layer hierarchy of increasing stringency. From these descriptors, a hierarchical parameterization of C¹ surfaces leading to a global shape representation of the object is obtained in terms of enclosing boundaries of bumps and dents, ridge and valley lines, and peaks and pits (curvature extreme points). To handle the discontinuities of surface curvatures, we introduce a computational scheme in which gradient directions of surface curvatures at the discontinuities can be inferred. Simulation results on the computation of these descriptors from curved surfaces are shown. Potential applications of this representation scheme in computer vision tasks are discussed.},
keywords={},
doi={},
ISSN={},
month={October},}

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TY - JOUR
TI - Representing Surface Curvature Discontinuities
T2 - IEICE TRANSACTIONS on Information
SP - 3423
EP - 3432
AU - Hiromi T.TANAKA
AU - Daniel T.L.LEE
AU - Fumio KISHINO
PY - 1991
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E74-D
IS - 10
JA - IEICE TRANSACTIONS on Information
Y1 - October 1991
AB - A representation scheme is presented for shapes of three-dimensional curved objects whose surface curvatures are not continuous at all points, i.e., surfaces with C¹ continuity only. The representation consists of a subset of lines of curvature and their intersections, called surface structure descriptors, organized in a three-layer hierarchy of increasing stringency. From these descriptors, a hierarchical parameterization of C¹ surfaces leading to a global shape representation of the object is obtained in terms of enclosing boundaries of bumps and dents, ridge and valley lines, and peaks and pits (curvature extreme points). To handle the discontinuities of surface curvatures, we introduce a computational scheme in which gradient directions of surface curvatures at the discontinuities can be inferred. Simulation results on the computation of these descriptors from curved surfaces are shown. Potential applications of this representation scheme in computer vision tasks are discussed.
ER -