December 2022
Volume 22, Issue 14
Open Access
Vision Sciences Society Annual Meeting Abstract  |   December 2022
Automatic detection of shape parts using maximal inscribed disks
Author Affiliations & Notes
  • Morteza Rezanejad
    University of Toronto
  • Kaleem Siddiqi
    McGill University
  • Dirk B. Walther
    University of Toronto
  • Footnotes
    Acknowledgements  Natural Sciences and Engineering Research Council of Canada (NSERC)
Journal of Vision December 2022, Vol.22, 3759. doi:
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      Morteza Rezanejad, Kaleem Siddiqi, Dirk B. Walther; Automatic detection of shape parts using maximal inscribed disks. Journal of Vision 2022;22(14):3759.

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      © ARVO (1962-2015); The Authors (2016-present)

  • Supplements

In this work, we propose a novel method for computing a part representation of 2D shapes using average outward flux (AOF) skeletal representations. In our method, we compute the flux of the gradient of the Euclidean distance function to the object’s boundary through a shrinking region averaged by the area of that region. Each skeletal point is a representation of a maximal inscribed disk bounded within that shape. We trace all skeletal segments, i.e., skeletal contours that connect endpoints to endpoints, endpoints to junction-points, and junction-points to junction-points. We use the traced contours and their connectivity topology to guide how we assemble our representation later. Now, we consider the degree to which the area reconstructed by the maximal disk associated with a skeletal point is unique. Specifically, for each skeletal point, we compute the fraction of area of its maximal disk that does not overlap with the disk of a skeletal point on any other branch. The measure decreases monotonically as one approaches a junction point. We compute this measure for all skeletal points that lie on a skeletal branch that has an endpoint at least on one of its sides. We now remove the regions that can be reconstructed by these skeletal points uniquely and then repeat this process until there are no unique skeletal fragments to be removed. By this process, we achieve a hierarchical representation that uniquely represents shapes in terms of their parts and how they are attached to each other. Our medial representation enables us to make a graph representation of shapes, predict how their part attachments can deform, and allow for top-down analysis of parts. Unlike boundary-to-axis ratio based measures that are delicate to compute, our measure is stable to perturbations to the boundary and offers a robust representation of shapes.


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