An inverse scattering approach for geometric body generation: a machine learning perspective

TL;DR

This paper introduces a novel inverse scattering-based machine learning method for generating 2D and 3D geometric shapes, especially human bodies, by mapping characteristic parameters to shapes via far-field patterns.

Contribution

It pioneers the integration of inverse scattering techniques with machine learning for geometric body generation, enabling stable and efficient shape synthesis from characteristic values.

Findings

Method effectively generates 3D human body shapes with prescribed features.

The approach demonstrates stability and efficiency in shape reconstruction.

Theoretical and numerical validation confirms the method's robustness.

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. 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 governed by the Helmholtz system. It in turn enables us to establish a 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. 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 study is the first attempt to introduce inverse scattering approaches in combination with machine learning to the geometric body generation and it opens up many opportunities for further developments.