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Authors: Alejandro Robles ; Mustafa Hajij and Paul Rosen

Affiliation: University of South Florida, United States

ISBN: 978-989-758-290-5

Keyword(s): Mapper, Contour Tree, Topological Data Analysis.

Related Ontology Subjects/Areas/Topics: Computer Vision, Visualization and Computer Graphics ; Image and Video Analysis ; Shape Representation and Matching

Abstract: We study the topological construction called Mapper in the context of simply connected domains, in particular on images. The Mapper construction can be considered as a generalization for contour, split, and joint trees on simply connected domains. A contour tree on an image domain assumes the height function to be a piecewise linear Morse function. This is a rather restrictive class of functions and does not allow us to explore the topology for most real world images. The Mapper construction avoids this limitation by assuming only continuity on the height function allowing this construction to robustly deal with a significantly larger set of images. We provide a customized construction for Mapper on images, give a fast algorithm to compute it, and show how to simplify the Mapper structure in this case. Finally, we provide a simple procedure that guarantees the equivalence of Mapper to contour, join, and split trees on a simply connected domain.

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Paper citation in several formats:
Robles, A.; Hajij, M. and Rosen, P. (2018). The Shape of an Image - A Study of Mapper on Images.In Proceedings of the 13th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 4: VISAPP, ISBN 978-989-758-290-5, pages 339-347. DOI: 10.5220/0006574803390347

@conference{visapp18,
author={Alejandro Robles. and Mustafa Hajij. and Paul Rosen.},
title={The Shape of an Image - A Study of Mapper on Images},
booktitle={Proceedings of the 13th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 4: VISAPP,},
year={2018},
pages={339-347},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0006574803390347},
isbn={978-989-758-290-5},
}

TY - CONF

JO - Proceedings of the 13th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 4: VISAPP,
TI - The Shape of an Image - A Study of Mapper on Images
SN - 978-989-758-290-5
AU - Robles, A.
AU - Hajij, M.
AU - Rosen, P.
PY - 2018
SP - 339
EP - 347
DO - 10.5220/0006574803390347

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