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Unsupervised classification of children’s bodies using currents

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Abstract

Object classification according to their shape and size is of key importance in many scientific fields. This work focuses on the case where the size and shape of an object is characterized by a current. A current is a mathematical object which has been proved relevant to the modeling of geometrical data, like submanifolds, through integration of vector fields along them. As a consequence of the choice of a vector-valued reproducing kernel Hilbert space (RKHS) as a test space for integrating manifolds, it is possible to consider that shapes are embedded in this Hilbert Space. A vector-valued RKHS is a Hilbert space of vector fields; therefore, it is possible to compute a mean of shapes, or to calculate a distance between two manifolds. This embedding enables us to consider size-and-shape clustering algorithms. These algorithms are applied to a 3D database obtained from an anthropometric survey of the Spanish child population with a potential application to online sales of children’s wear.

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References

  • Allen B, Curless B, Popović Z (2003) The space of human body shapes: reconstruction and parameterization from range scans. ACM Trans Graph TOG 22:587–594

    Article  Google Scholar 

  • Aronszajn N (1950) Theory of reproducing kernels. Trans Am Math Soc 68:337–404

    Article  MathSciNet  MATH  Google Scholar 

  • Baek SY, Lee K (2012) Parametric human body shape modeling framework for human-centered product design. Comput Aided Des 44(1):56–67

    Article  Google Scholar 

  • Bauer M, Harms P, Michor PW (2011) Sobolev metrics on shape space of surfaces. J Geom Mech 3(4):389–438

    MathSciNet  MATH  Google Scholar 

  • Bock HH (2007) Clustering methods: a history of k-means algorithms. In: Brito P, Bertrand P, Cucumel G, de Carvalho F (eds) Selected contributions in data analysis and classification. Springer, Berlin, pp 161–172

  • Caponnetto A, Micchelli CA, Pontil M, Ying Y (2008) Universal multi-task kernels. J Mach Learn Res 9:1615–1646

    MathSciNet  MATH  Google Scholar 

  • Carmeli C, De Vito E, Toigo A (2006) Vector valued reproducing kernel hilbert spaces of integrable functions and mercer theorem. Anal Appl 4(04):377–408

    Article  MathSciNet  MATH  Google Scholar 

  • Chung M, Lina H, Wang MJJ (2007) The development of sizing systems for taiwanese elementary- and high-school students. Int J Ind Ergon 37:707–716

    Article  Google Scholar 

  • Conway JB (2013) A course in functional analysis, vol 96. Springer, Science & Business Media

  • Cox TF, Cox MA (2000) Multidimensional scaling. CRC press

  • Do Carmo MP (2012) Differential forms and applications. Springer, Science & Business Media

  • Durrleman S (2010) Statistical models of currents for measuring the variability of anatomical curves, surfaces and their evolution. PhD thesis, Université Nice Sophia Antipolis

  • Durrleman S, Pennec X, Trouvé A, Ayache N (2009) Statistical models of sets of curves and surfaces based on currents. Med Image Anal 13(5):793–808

    Article  Google Scholar 

  • European Committee for Standardization (2002) European Standard EN 13402-2: Size system of clothing. Primary and secondary dimensions. http://esearch.cen.eu/esearch/Details.aspx?id=5430955

  • Glaunès J (2005) Transport par difféomorphismes de points, de mesures et de courants pour la comparaison de formes et l’anatomie numérique. PhD thesis, Université Paris 13. http://cis.jhu.edu/joan/TheseGlaunes.pdf. Accessed Sept 2005

  • Glaunes JA, Joshi S (2006) Template estimation form unlabeled point set data and surfaces for computational anatomy. In: 1st MICCAI workshop on mathematical foundations of computational anatomy: geometrical, statistical and registration methods for modeling biological shape variability

  • Gual-Arnau X, Herold-García S, Simó A (2015) Geometric analysis of planar shapes with applications to cell deformations. Image Anal Stereol 34(3):171–182

    Article  MathSciNet  MATH  Google Scholar 

  • Hsing T, Eubank R (2015) Theoretical foundations of functional data analysis, with an introduction to linear operators. Wiley

  • Huang H, Wang F, Guibas L (2014) Functional map networks for analyzing and exploring large shape collections. ACM Trans Graph 33(4):1–11

    MATH  Google Scholar 

  • Ibáñez MV, Vinué G, Alemany S, Simó A, Epifanio I, Domingo J, Ayala G (2012) Apparel sizing using trimmed PAM and OWA operators. Expert Syst Appl 29:10512–10520

    Article  Google Scholar 

  • Jain A, Thormählen T, Seidel HP, Theobalt C (2010) Moviereshape: tracking and reshaping of humans in videos. ACM Trans Graph TOG 29:148

    Google Scholar 

  • Jain AK (2010) Data clustering: 50 years beyond k-means. Pattern Recognit Lett 31:651–666

    Article  Google Scholar 

  • Kanungo T, Mount DM, Netanyahu NS, Piatko C, Silverman R, Wu AY (2002) An efficient k-means clustering algorithm: analysis and implementation. IEEE Trans Pattern Anal Mach Intell 24(7):881–892

    Article  MATH  Google Scholar 

  • Kaufman L, Rousseeuw P (1990) Finding groups in data: an introduction to cluster analysis. Wiley, New York

    Book  MATH  Google Scholar 

  • Lang S (1995) Differential and Riemannian manifolds. Springer, New York

    Book  MATH  Google Scholar 

  • Lloyd SP (1957) Least squares quantization in pcm. Bell telephone labs memorandum, Murray Hill, nj. Reprinted in IEEE trans information theory IT-28 (1982) vol 2. pp 129–137

  • MATLAB (2014) version 8.4.0 (R2014b). The MathWorks Inc., Natick

  • Micchelli C, Pontil M (2005) On learning vector-valued functions. Neural Comput 17(1):177–204

    Article  MathSciNet  MATH  Google Scholar 

  • Morgan F (2008) Geometric measure theory: a beginner’s guide. Academic Press, Cambridge

    MATH  Google Scholar 

  • Nazeer KAA, Sebastian MP (2009) Improving the accuracy and efficiency of the k-means clustering algorithm. In: Proceedings of the World Congress on Engineering (London, UK), pp 1–5

  • Ovsjanikov M, Ben-Chen M, Solomon J, Butscher A, Guibas L (2012) Functional maps: a flexible representation of maps between shapes. ACM Trans Graph 31(4):1–11

    Article  Google Scholar 

  • Pennec X (2006) Intrinsic statistics on riemannian manifolds: basic tools for geometric measurements. J Math Imaging Vis 25:127–154

    Article  MathSciNet  Google Scholar 

  • Pishchulin L, Wuhrer S, Helten T, Theobalt C, Schiele B (2015) Building statistical shape spaces for 3d human modeling. arXiv:1503.05860

  • Quang MH, Kang SH, Le TM (2010) Image and video colorization using vector-valued reproducing kernel hilbert spaces. J Math Imaging Vis 37(1):49–65

    Article  MathSciNet  Google Scholar 

  • Steinhaus H (1956) Sur la division des corps matériels en parties. Bull Acad Pol Sci IV(12):801–804

  • Vaillant M, Glaunès J (2005) Surface matching via currents. Biennial international conference on information processing in medical imaging. Springer, Berlin, Heidelberg, pp 381–392

    Chapter  Google Scholar 

  • Vinué G, Simó A, Alemany S (2016) The k-means algorithm for 3d shapes with an application to apparel design. Adv Data Anal Classif 10(1):103–132

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This paper has been partially supported by the Spanish Ministry of Science and Innovation Project DPI2013 – 47279 – C2 – 1 – R. We would also like to thank the Valencian Institute of Biomechanics for providing us with the data set. S.

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Correspondence to Amelia Simó.

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Barahona, S., Gual-Arnau, X., Ibáñez, M.V. et al. Unsupervised classification of children’s bodies using currents. Adv Data Anal Classif 12, 365–397 (2018). https://doi.org/10.1007/s11634-017-0283-0

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  • DOI: https://doi.org/10.1007/s11634-017-0283-0

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