Complexity of Shapes Embedded in Z with a Bias towards Squares

Date

2020-01-01

Author

Arslan, Mazlum Ferhat
Tarı, Zehra Sibel

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

172
views

0
downloads

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

Suggestions

OpenMETU
Core

On the complexity of shapes embedded in ZN Arslan, Mazlum Ferhat; Tarı, Zehra Sibel; Department of Computer Engineering (2019) Shape complexity is a hard-to-quantify quality, mainly due to its relative nature. In common view, circles are considered to be the simplest shapes. However, when implemented in computer, none of the circularity measures yield the expected scores for the circle. This is because digital domain (Z^n) realizations of circles are only approximations to the ideal form. Consequently, complexity orders computed in reference to circle are unstable. As a remedy, we consider squares to be the simplest shapes relative...
Minimization of Monotonically Levelable Higher Order MRF Energies via Graph Cuts Karci, Mehmet Haydar; Demirekler, Mübeccel (Institute of Electrical and Electronics Engineers (IEEE), 2010-11-01) A feature of minimizing images of submodular binary Markov random field (MRF) energies is introduced. Using this novel feature, the collection of minimizing images of levels of higher order, monotonically levelable multilabel MRF energies is shown to constitute a monotone collection. This implies that these minimizing binary images can be combined to give minimizing images of the multilabel MRF energies. Thanks to the graph cuts framework, the mentioned class of binary MRF energies is known to be minimized ...
Modeling of inelastic behavior of curved members with a mixed formulation beam element Sarıtaş, Afşin (Elsevier BV, 2009-04-01) The curved beam element in this paper is based on Hu-Washizu variational principle. The nonlinear response of the element arises from the integration of stress-strain relations over several control sections along the element length. The finite element approximation for the beam uses shape functions for stress resultants that satisfy equilibrium and discontinuous strains along the beam. No approximation for the beam displacement field is necessary in the formulation. The proposed element is free from membran...
Second-order experimental designs for simulation metamodeling Batmaz, İnci (SAGE Publications, 2002-12-01) The main purpose of this study is to compare the performance of a group of second-order designs such as Box-Behnken, face-center cube, three-level factorial, central composite, minimum bias, and minimum variance plus bias for estimating a quadratic metamodel. A time-shared computer system is used to demonstrate the ability of the designs in providing good fit of the metamodel to the simulation response. First, for various numbers of center runs, these designs are compared with respect to their efficiency, r...
Monte Carlo analysis of ridged waveguides with transformation media Ozgun, Ozlem; Kuzuoğlu, Mustafa (Wiley, 2013-07-01) A computational model is presented for Monte Carlo simulation of waveguides with ridges, by combining the principles of transformation electromagnetics and the finite methods (such as finite element or finite difference methods). The principle idea is to place a transformation medium around the ridge structure, so that a single and easy-to-generate mesh can be used for each realization of the Monte Carlo simulation. Hence, this approach leads to less computational resources. The technique is validated by me...

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.