An inverse scattering approach for geometric body generation: A machine learning perspectivey

Jinghong Li, Hongyu Liu*, Wing Yan Tsui, Xianchao Wang

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

12 Citations (Scopus)

Abstract

In this paper, we are concerned with the 2D and 3D geometric shape generation by prescribing a set of characteristic values of a specific geometric body. One of the major motivations of our study is the 3D human body generation in various applications. We develop a novel method that can generate the desired body with customized characteristic values. The proposed method follows a machine-learning flavour that generates the inferred geometric body with the input characteristic parameters from a training dataset. The training dataset consists of some preprocessed body shapes associated with appropriately sampled characteristic parameters. One of the critical ingredients and novelties of our method is the borrowing of inverse scattering techniques in the theory of wave propagation to the body generation. This is done by establishing a delicate one-to-one correspondence between a geometric body and the far-field pattern of a source scattering problem. It enables us to establish the one-to-one correspondence between the geometric body space and the function space defined by the far-field patterns. Hence, the far-field patterns can act as the shape generators. The shape generation with prescribed characteristic parameters is achieved by first manipulating the shape generators and then reconstructing the corresponding geometric body from the obtained shape generator by a stable multiple-frequency Fourier method. The proposed method is in sharp difference from the existing methodologies in the literature, which usually treat the human body as a suitable Riemannian manifold and the generation is based on non-Euclidean approximation and interpolation. Our method is easy to implement and produces more efficient and stable body generations. We provide both theoretical analysis and extensive numerical experiments for the proposed method. The main goal of the study is to introduce inverse scattering approaches in combination with machine learning to the geometric body generation and it opens up many opportunities for further developments.

Original languageEnglish
Pages (from-to)800-823
Number of pages24
JournalMathematics In Engineering
Volume1
Issue number4
DOIs
Publication statusPublished - 18 Sept 2019

Scopus Subject Areas

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

User-Defined Keywords

  • Geometric body generation
  • Inverse source scattering
  • Machine learning
  • Shape generator

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