Unsupervised classification of children's bodies using currents

TL;DR

This paper introduces an unsupervised method for classifying children's body shapes using a mathematical framework called currents, embedding shapes into a Hilbert space for analysis, with applications in anthropometry and online retail.

Contribution

It develops a novel shape classification approach based on currents and vector-valued RKHS, enabling size and shape analysis of 3D children's bodies.

Findings

Successfully classified children's body shapes from 3D data

Demonstrated potential for online children's wear sizing

Provided a new mathematical framework for shape analysis

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 classification 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.