Local Culprits of Shape Complexity

© 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.
Citation Formats
M. F. Arslan and Z. S. Tarı, “Local Culprits of Shape Complexity,” presented at the 8th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2021, Virtual, Online, 2021, Accessed: 00, 2021. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85106432643&origin=inward.