IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v174y2020icp175-182.html
   My bibliography  Save this article

Arched foot based on conformal complex neural network testing

Author

Listed:
  • Ibrahim, Rabha W.

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.

Suggested Citation

  • Ibrahim, Rabha W., 2020. "Arched foot based on conformal complex neural network testing," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 174(C), pages 175-182.
  • Handle: RePEc:eee:matcom:v:174:y:2020:i:c:p:175-182
    DOI: 10.1016/j.matcom.2020.02.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475420300550
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2020.02.016?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:174:y:2020:i:c:p:175-182. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.