Complexity of Shapes Embedded in Z with a Bias towards Squares

Date

2020-01-01

Author

Arslan, Mazlum Ferhat
Tarı, Zehra Sibel

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Shape complexity is a hard-to-quantify quality, mainly due to its relative nature. Biased by Euclidean thinking, circles are commonly considered as the simplest. However, their constructions as digital images are only approximations to the ideal form. Consequently, complexity orders computed in reference to circle are unstable. Unlike circles which lose their circleness in digital images, squares retain their qualities. Hence, we consider squares (hypercubes in Z(n)) to be the simplest shapes relative to which complexity orders are constructed. Using the connection between L-infinity norm and squares we effectively encode squareness-adapted simplification through which we obtain multi-scale complexity measure, where scale determines the level of interest to the boundary. The emergent scale above which the effect of a boundary feature (appendage) disappears is related to the ratio of the contacting width of the appendage to that of the main body. We discuss what zero complexity implies in terms of information repetition and constructibility and what kind of shapes in addition to squares have zero complexity.

Subject Keywords

Software, Computer Graphics and Computer-Aided Design

URI

https://hdl.handle.net/11511/52368

Journal

IEEE Transactions on Image Processing

DOI

https://doi.org/10.1109/tip.2020.3021316

Collections

Department of Computer Engineering, Article

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Citation Formats

M. F. Arslan and Z. S. Tarı, “Complexity of Shapes Embedded in Z with a Bias towards Squares,” IEEE Transactions on Image Processing, pp. 8870–8879, 2020, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/52368.