Arched foot based on conformal complex neural network testing

Rabha W. Ibrahim

Mathematics and Computers in Simulation (MATCOM), 2020, vol. 174, issue C, 175-182

Abstract: Complex-Valued Neural Networks (CNNs) are the most successful extension of the real-valued neural networks. They play a significant role in deep learning. Following this great fact, CNNs are utilized in computer vision and its critical field Image analysis (IA). Symmetry vision is a theory closely related to assembly and uniformity. More accurately, symmetrical rallies can be categorized as covering self-similarities. In 2D images, the self-similarity comes from rigid transformations (such as operators, polynomials and differential and integral equations) that map one part onto another (in calculus is called an injective map and in the conformal analysis is called a univalent map). In this paper, we define a new style of CNNs called Conformal Neural Networks (CoNNs) based on the concept of conformal theory in the open unit disk. Moreover, we introduce a general symmetric 2D-parameter Beltrami equation (SBE) in a complex domain. The dominant idea is to map the external and inner of the domain conformally to unit disks, using a symmetric differential operator (which is suggested to be the solution of SBE). As an application, we present a new algorithm to obtain the arches of the foot from their marks by training CoNNs. The results prove that the effectiveness of our suggested procedure is a stable form arrangement.

Keywords: Conformal mapping; Univalent function; Complex neural networks; Image analysis; Image processing (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:174:y:2020:i:c:p:175-182

DOI: 10.1016/j.matcom.2020.02.016

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