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

Jinghong Li; Hongyu Liu; Wing-Yan Tsui; Xianchao Wang; Jinghong Li; Hongyu Liu; Wing-Yan Tsui; Xianchao Wang

doi:10.3934/mine.2019.4.800

Mathematics in Engineering

2019, Volume 1, Issue 4: 800-823. doi: 10.3934/mine.2019.4.800

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

1.
School of Science, Qilu University of Technology(Shandong Academy of Sciences), Jinan, Shandong, China

Received: 21 January 2019 Accepted: 17 July 2019 Published: 18 September 2019

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.
- geometric body generation,
- machine learning,
- shape generator,
- inverse source scattering
Citation: Jinghong Li, Hongyu Liu, Wing-Yan Tsui, Xianchao Wang. An inverse scattering approach for geometric body generation: a machine learning perspective[J]. Mathematics in Engineering, 2019, 1(4): 800-823. doi: 10.3934/mine.2019.4.800

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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.

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