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PERSISTENCE BARCODES FOR SHAPES.

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Title: PERSISTENCE BARCODES FOR SHAPES.
Authors: CARLSSON, GUNNAR1 gunnar@math.stanford.edu, ZOMORODIAN, AFRA2 afra@cs.stanford.edu, COLLINS, ANNE3 collins@centre.edu, GUIBAS, LEONIDAS J.2 guibas@cs.stanford.edu
Source: International Journal of Shape Modeling. Dec2005, Vol. 11 Issue 2, p149-187. 39p. 20 Diagrams, 2 Charts.
Subjects: Geometric shapes, Tangential coordinates, Homology theory, Topology, Geometry, Interval analysis
Abstract: In this paper, we initiate a study of shape description and classification via the application of persistent homology to tangential constructions on geometric objects. Our techniques combine the differentiating power of geometry with the classifying power of topology. The homology of our first construction, the tangent complex, can distinguish between topologically identical shapes with different "sharp" features, such as corners. To capture "soft" curvature-dependent features, we define a second complex, the filtered tangent complex, obtained by parameterizing a family of increasing subcomplexes of the tangent complex. Applying persistent homology, we obtain a shape descriptor, called a barcode, that is a finite union of intervals. We define a metric over the space of such intervals, arriving at a continuous invariant that reflects the geometric properties of shapes. We illustrate the power of our methods through a number of detailed studies of parameterized families of mathematical shapes. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Shape Modeling is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: PERSISTENCE BARCODES FOR SHAPES.
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  Data: <searchLink fieldCode="AR" term="%22CARLSSON%2C+GUNNAR%22">CARLSSON, GUNNAR</searchLink><relatesTo>1</relatesTo><i> gunnar@math.stanford.edu</i><br /><searchLink fieldCode="AR" term="%22ZOMORODIAN%2C+AFRA%22">ZOMORODIAN, AFRA</searchLink><relatesTo>2</relatesTo><i> afra@cs.stanford.edu</i><br /><searchLink fieldCode="AR" term="%22COLLINS%2C+ANNE%22">COLLINS, ANNE</searchLink><relatesTo>3</relatesTo><i> collins@centre.edu</i><br /><searchLink fieldCode="AR" term="%22GUIBAS%2C+LEONIDAS+J%2E%22">GUIBAS, LEONIDAS J.</searchLink><relatesTo>2</relatesTo><i> guibas@cs.stanford.edu</i>
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Shape+Modeling%22">International Journal of Shape Modeling</searchLink>. Dec2005, Vol. 11 Issue 2, p149-187. 39p. 20 Diagrams, 2 Charts.
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  Data: <searchLink fieldCode="DE" term="%22Geometric+shapes%22">Geometric shapes</searchLink><br /><searchLink fieldCode="DE" term="%22Tangential+coordinates%22">Tangential coordinates</searchLink><br /><searchLink fieldCode="DE" term="%22Homology+theory%22">Homology theory</searchLink><br /><searchLink fieldCode="DE" term="%22Topology%22">Topology</searchLink><br /><searchLink fieldCode="DE" term="%22Geometry%22">Geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Interval+analysis%22">Interval analysis</searchLink>
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  Data: In this paper, we initiate a study of shape description and classification via the application of persistent homology to tangential constructions on geometric objects. Our techniques combine the differentiating power of geometry with the classifying power of topology. The homology of our first construction, the tangent complex, can distinguish between topologically identical shapes with different "sharp" features, such as corners. To capture "soft" curvature-dependent features, we define a second complex, the filtered tangent complex, obtained by parameterizing a family of increasing subcomplexes of the tangent complex. Applying persistent homology, we obtain a shape descriptor, called a barcode, that is a finite union of intervals. We define a metric over the space of such intervals, arriving at a continuous invariant that reflects the geometric properties of shapes. We illustrate the power of our methods through a number of detailed studies of parameterized families of mathematical shapes. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
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  Data: <i>Copyright of International Journal of Shape Modeling is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1142/S0218654305000761
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      – Code: eng
        Text: English
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        PageCount: 39
        StartPage: 149
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      – SubjectFull: Geometric shapes
        Type: general
      – SubjectFull: Tangential coordinates
        Type: general
      – SubjectFull: Homology theory
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      – SubjectFull: Topology
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      – SubjectFull: Geometry
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      – SubjectFull: Interval analysis
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      – TitleFull: PERSISTENCE BARCODES FOR SHAPES.
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            NameFull: CARLSSON, GUNNAR
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            NameFull: COLLINS, ANNE
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            NameFull: GUIBAS, LEONIDAS J.
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            – D: 01
              M: 12
              Text: Dec2005
              Type: published
              Y: 2005
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              Value: 11
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