Persistence Barcodes for Shapes

dc.contributor.authorCarlssony, Gunnaren_US
dc.contributor.authorZomorodian, Afraen_US
dc.contributor.authorCollins, Anneen_US
dc.contributor.authorGuibas, Leonidasen_US
dc.contributor.editorRoberto Scopigno and Denis Zorinen_US
dc.date.accessioned2014-01-29T09:19:50Z
dc.date.available2014-01-29T09:19:50Z
dc.date.issued2004en_US
dc.description.abstractIn this paper, we initiate a study of shape description and classification via the application of persistent homology to two 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 parametrizing 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 parametrized families of mathematical shapes.en_US
dc.description.seriesinformationSymposium on Geometry Processingen_US
dc.identifier.isbn3-905673-13-4en_US
dc.identifier.issn1727-8384en_US
dc.identifier.urihttps://doi.org/10.2312/SGP/SGP04/127-138en_US
dc.publisherThe Eurographics Associationen_US
dc.titlePersistence Barcodes for Shapesen_US
Files
Original bundle
Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
127-138.pdf
Size:
476.39 KB
Format:
Adobe Portable Document Format