Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

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

2 Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong SAR, China

3 School of Mathematics, Harbin Institute of Technology, Harbin, China

This contribution is part of the Special Issue: Inverse problems in imaging and engineering science
Guest Editors: Lauri Oksanen; Mikko Salo
Link: https://www.aimspress.com/newsinfo/1270.html.

Special Issues: Inverse problems in imaging and engineering science

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.
  Figure/Table
  Supplementary
  Article Metrics

References

1. Levoy M, Pulli K, Curless B, et al. (2000) The digital Michelangelo project: 3D scanning of large statues. Proceedings of the 27th annual conference on computer graphics and interactive techniques, ACM Press 131-144.

2. Hou H, Andrews H (1978) Cubic splines for image interpolation and digital filtering. IEEE Trans Acoust, Speech, Signal Process 26: 508-517.    

3. Mundermann L, Corazza S, Andriacchi TP (2007) Accurately measuring human movement using articulated ICP with soft-joint constraints and a repository of articulated models. 2007 IEEE Conference on Computer Vision and Pattern Recognition 1-6.

4. Anguelov D, Srinivasan P, Koller D, et al. (2005) SCAPE: Shape completion and animation of people. ACM T Graphic 24: 408-416.    

5. Apeagyei PR (2010) Application of 3D body scanning technology to human measurement for clothing Fit. JDCTA 4: 58-68.

6. Ashdown SP, Loker S, Schoenfelder K, et al. (2004) Using 3D scans for fit analysis. JTATM 4: 1-12.

7. Loker S, Ashdown S, Schoenfelder K (2005) Size-specific analysis of body scan data to improve apparel fit. JTATM 4: 1-15.

8. Balan AO, Sigal L, Black MJ, et al. (2007) Detailed human shape and pose from images. 2007 IEEE Conference on Computer Vision and Pattern Recognition 1-8.

9. Guan P, Weiss A, Balan AO, et al. (2009) Estimating human shape and pose from a single image. 2009 IEEE 12th International Conference on Computer Vision 1381-1388.

10. Freifeld O, Black MJ (2012) Lie bodies: A manifold representation of 3D human shape. European Conference on Computer Vision 1-14.

11. Chen F, Brown GM, Song M (2000) Overview of 3-D shape measurement using optical methods. Opt Eng 39: 10-23.    

12. Kart O, Kut A, Vuruskan A, et al. (2012) Web based digital image processing tool for body shape detection. ICT Innovations 2011, Web Proceedings ISSN 1857-7288 139-147.

13. Chen X, Guo Y, Zhao Q, et al. (2012) Clothed and naked human shapes estimation from a single image. International Conference on Computational Visual Media 43-50.

14. Chen Y, Cipolla R (2009) Learning shape priors for single view reconstruction. 2009 IEEE 12th International Conference on Computer Vision Workshops, ICCV Workshops 1425-1432.

15. Chen Y, Cipolla R (2011) Single and sparse view 3d reconstruction by learning shape priors. Comput Vis Image Und 115: 586-602.    

16. Chen Y, Cipolla R, Robertson DP (2011) A practical system for modelling body shapes from single view measurements. The British Machine Vision Conference 1-11.

17. Seo H, Cordier F, Magnenat-Thalmann N (2003) Synthesizing animatable body models with parameterized shape modifications. Proceedings of the 2003 ACM SIGGRAPH/Eurographics Symposium on Computer Animation 120-125.

18. Seitz SM, Curless B, Diebel J, et al. (2006) A comparison and evaluation of multi-view stereo reconstruction algorithms. 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition 1: 519-528.

19. De Boor C (1972) On calculating with B-splines. J Approx Theory 6: 50-62.    

20. Dunn SM, Keizer RL, Yu J (1989) Measuring the area and volume of the human body with structured light. IEEE T Syst Man Cy 19: 1350-1364.    

21. Eskin G (2011) Lectures on Linear Partial Differential Equations, Providence: American Mathematical Society.

22. Esteban CH, Schmitt F (2004) Silhouette and stereo fusion for 3D object modeling. Comput Vis Image Und 96: 367-392.    

23. Zhou S, Fu H, Liu L, et al. (2010) Parametric reshaping of human bodies in images. ACM T Graphic 29: 126.

24. Geng J (2011) Structured-light 3D surface imaging: a tutorial. Adv Opt Photonics 3: 128-160.    

25. Wang X, Guo Y, Li J, et al. (2019) Two gesture-computing approaches by using electromagnetic waves. Inverse Probl Imaging 13: 879-901.    

26. Li J, Liu H, Ma S (2019) Determining a random Schrödinger equation with unknown source and potential. SIAM J Math Anal 51: 3465-3491.    

27. Li J, Liu H, Wang Q (2015) Fast imaging of electromagnetic scatterers by a two-stage multilevel sampling method. Discrete Conts Dyn S 8: 547-561.

28. Li J, Liu H, Zou J (2008) Multilevel linear sampling method for inverse scattering problems. SIAM J Sci Comput 30: 1228-1250.    

29. Li J, Liu H, Zou J (2009) Strengthened linear sampling method with a reference ball. SIAM J Sci Comput 31: 4013-4040.

30. Liu H, Yamamoto M, Zou J (2007) Reflection principle for Maxwell's equations and its application to inverse electromagnetic scattering problem. Inverse Probl 23: 2357-2366.    

31. Liu H, Zou J (2006) Uniqueness in an inverse acoustic obstacle scattering problem for both soundhard and sound-soft polyhedral scatterers. Inverse Probl 22: 515-524.    

32. Kasap M, Magnenat-Thalmann N (2007) Parameterized human body model for real-time applications. 2007 International Conference on Cyberworlds 160-167.

33. Lee SW, Yang HD (2007) Reconstruction of 3D human body pose from stereo image sequences based on top-down learning. Pattern Recognit 40: 3120-3131.    

34. Liu L, Pan Z, Tong J, et al. (2012) Scanning 3d full human bodies using kinects. IEEE T Vis Comput Gr 18: 643-650.    

35. Magnenat-Thalmann N, Seo H (2003) An automatic modeling of human bodies from sizing parameters. Proceedings of the 2003 Symposium on Interactive 3D Graphics 19-26.

36. Schoenberg IJ (1973) Cardinal Spline Interpolation. SIAM.

37. Schoenberg IJ (1946) Contributions to the problem of approximation of equidistant data by analytic functions. Part B. On the problem of osculatory interpolation. A second class of analytic approximation formulae. Q Appl Math 4: 112-141.

38. Treleaven P, Wells J (2007) 3D body scanning and healthcare applications. Comput 40: 28-34.

39. Wang X, Song M, Guo Y, et al. (2019) Fourier method for identifying electromagnetic sources with multi-frequency far-field data. J Comput Appl Math 358: 279-292.    

40. Wang X, Guo Y, Liu H, et al. (2017) Fourier method for recovering acoustic sources from multifrequency far-field data. Inverse Probl 33: 035001.    

41. The World's First Human Visualization Platform, Anatomy, Disease and Treatments-all in interactive 3D, BioDigital, Inc., 2018. Available from: https://www.biodigital.com/.

42. Make Human Community: Open Source tool for making 3D characters. Available from: www.makehumancommunity.org.

© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Article outline

Show full outline
Copyright © AIMS Press All Rights Reserved