Local Culprits of Shape Complexity


8th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2021, Virtual, Online, 16 - 20 May 2021, pp.91-99 identifier

  • Publication Type: Conference Paper / Full Text
  • Volume:
  • Doi Number: 10.1007/978-3-030-75549-2_8
  • City: Virtual, Online
  • Page Numbers: pp.91-99
  • Middle East Technical University Affiliated: Yes


© 2021, Springer Nature Switzerland AG.Quantifying shape complexity is useful in several practical problems in addition to being interesting from a theoretical point of view. In this paper, instead of assigning a single global measure of complexity, we propose a distributed coding where to each point on the shape domain a measure of its contribution to complexity is assigned. We define the shape simplicity as the expressibility of the shape via a prototype shape. To keep discussions concrete we focus on a case where the prototype is a rectangle. Nevertheless, the constructions in the paper is valid in higher dimensions where the prototype is a hyper-cuboid. Thanks to the connection between differential operators and mathematical morphology, the proposed construction naturally extends to the case where diamonds serve as the prototypes.