A STATISTICAL APPROACH TO BUILD 3D PROTOTYPES FROM A

3D ANTHROPOMETRIC SURVEY OF THE SPANISH FEMALE

POPULATION

M.V. Ib´a˜nez

, A. Sim´o

, J. Domingo

, E. Dur´a

, G. Ayala

, S. Alemany

, G. Vinu´e

and C. Solves

Department of Mathematics, Universitat Jaume I, Castell´on, Spain

Dept. of Informatics, University of Valencia, Valencia, Spain

Department of Statistics and O.R., University of Valencia, Valencia, Spain

Biomechanics Institute of Valencia, Universidad Polit´ecnica de Valencia, Valencia, Spain

Keywords:

Random compact sets, 3D-shape, Mean sets.

Abstract:

Fitting cloth is a problem for both the customer and the apparel industry, but analysis of anthropometric data

can be useful to deﬁne better sizing systems. In 2006, the Spanish Ministry of Health coordinated a study

to obtain 3D anthropometric data of the Spanish women. Our aim in this work is to develop a statistical

methodology to deﬁne prototypes based on the 3D clouds of points obtained from 3D scans of a great number

of women and apply it to the 3D anthropometric survey of the Spanish female population. To build the

prototypes, 3D images will be built, and after registration, homologous 2D sections will be averaged, and a

3D ”mean” shape will be reconstructed from them.

1 INTRODUCTION

In 2006, the Spanish Ministry of Health coordinated

a study to obtain anthropometric data of the Spanish

women. Its aim was to provide real and consistent

measures to apparel designers in order to normalize

the sizing system. The ﬁnal purpose is to increase the

protection of consumers and to help in the treatment

of alimentary mental disorders.

A sizing system classiﬁes a speciﬁc population

into homogeneous subgroups based on some corporal

dimensions (Chunga et al., 2007). There are several

local and international standards proposing a regula-

tion of the sizing system based on key anthropomet-

ric measures, but the lack of common criteria is one of

the drawbacksfor their implementation. Most of them

propose size systems by taking into account just a sin-

gle anthropometric dimension, although more elabo-

rated systems use distributions of two or three vari-

ables to deﬁne a sizing chart and cross-tabs to select

the size system covering the highest percentage of the

population. Anyway, anthropometric measures show

a great variability on body proportions, and it is not

possible to cover all the different body morphotypes

with this kind of models. That is why, multivariate

approaches have been proposed to develop sizing sys-

tems. Principal components analysis are often used

to reduce the dimension of our anthropometric data

set, and the two ﬁrst principal components are used

to generate bivariate distributions (Chen et al., 2009;

Hsu, 2009; Luximon et al., 2011; Gupta and Gangad-

har, 2004; Hsu, 2009; Salusso-Deonier et al., 1986).

As an alternative to bivariate distributions, the cluster

techniques using partitioning methods like k-means

algorithms, group the population into morphologies

using the complete set of anthropometric variables as

input (Chunga et al., 2007; Zheng et al., 2007; Ng,

R. and Ashdown, S.P. and Chan, A., 2007). A large

scale implantation of this statistical approach using

data mining and decision trees, has been proposed in

Hsu and Bagherzadeh et al. (Hsu and Wang, 2005;

Bagherzadeh et al., 2010). Different alternative ap-

proaches based on optimization algorithms were ﬁrst

proposed by Tryfos (Tryfos, 1986), who used integer

programming to partition the body dimension space

into a discrete set of sizes by choosing the size sys-

tem to optimize the sales of garment. Later on, Mc-

Culloch et al (McCulloch et al., 1998) modiﬁed this

approach by focusing the problem on the quality of ﬁt

instead of on the sales.

Since ﬁtting cloth is a problem for both the cus-

tomer and the apparel industry (Fan et al., 2004), na-

370

Ibañez M., Simó A., Domingo J., Durá E., Ayala G., Alemany S., Vinué G. and Solves C..

A STATISTICAL APPROACH TO BUILD 3D PROTOTYPES FROM A 3D ANTHROPOMETRIC SURVEY OF THE SPANISH FEMALE POPULATION.

DOI: 10.5220/0003876803700374

In Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods (SADM-2012), pages 370-374

ISBN: 978-989-8425-98-0

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

tional anthropometric surveys have been carried out

in the latest years in different countries (USA, UK,

France, Australia and Germany among others). These

studies show that a high percentage of population has

ﬁtting problems with the cloth. Studies developed in

the UK (Smith, 2007) and Germany (Chunga et al.,

2007) show that 60% and 50% respectively of cus-

tomers manifest to have difﬁculty in ﬁnding clothes

that ﬁt them properly. In the same way, an anthropo-

metric study done in USA (Faust and Carrier, 2010)

to update the sizing ASTM standards also concluded

that 54% of the population was not satisﬁed with the

ﬁtting of the ready to wear (RTW) cloth (Bye et al.,

2008). Additionally, from the technological point of

view, new 3D body scanning techniques constitute a

step forward in the way of conducting and analyzing

anthropometric data and can contribute to promote

new anthropometric surveys to obtain more accurate

measurements (Simmons and C.Istook, 2003).

In this paper we propose a statistical methodol-

ogy to deﬁne prototypes based on the 3D cloud of

points obtained from 3D scans of the body of a sufﬁ-

cient number of women and then we apply it to the 3D

anthropometric survey of the Spanish female popula-

tion. Another work who have been working following

this idea can be found in (Haslera et al., 2009).

From the 3D cloud of points of each woman, a 3D

image of a 3D shape can be built. After registration

of these 3D images, a ﬁxed number of 2D cross sec-

tions can be obtained for each woman. Each of these

sections coincides with an anatomically relevantpoint

detected in each shape. Each set of corresponding

sections for all women can be considered as a sample

of a Random compact closed set whose mean set can

be computed. A random closed set is a popular prob-

abilistic model for shapes with a growing interest in

the Computer Science and in particular in the Com-

puter Vision literature. Its formal deﬁnition jointly

with many examples of this concept can be found in

(Stoyan et al., 1995; Matheron, 1975; Cressie, 1993).

Different deﬁnitions of the mean set of a randomcom-

pact set can also be found in the literature (Stoyan and

Stoyan, 1994; Baddeley and Molchanov, 1998; Sim´o

et al., 2004). In this paper the Baddeley-Molchanov

deﬁnition of mean set will be used. Finally, each pro-

totype will be obtained as the 3D-reconstruction of a

complete body using these cross section means.

The description of our data set and is given in

section 2.1. The computational details to obtain and

process the images and the deﬁnition of Baddeley-

Molchanov mean are explained in section 2.2. Sec-

tion 3 illustrates the results of the application of

our methodologies to the anthropometric database of

Spanish women. Some conclusions and possible fur-

ther developments conclude the paper in section 4.

2 MATERIALS AND METHODS

2.1 Data Set

A sample of 10415 Spanish females from 18 to 70

years old were randomly selected. They were scanned

by using the Vitus Smart 3D body scanner from Hu-

man Solutions, a non-intrusive laser system formed

by four columns allocating the optic system, which

moves from the head to the feet in about ten seconds

performing a sweep of the body. Several cameras cap-

ture images and associated software provided by the

scanner manufacturers, makes a triangulation that al-

lows the knowledge of the 3D spatial location of a

great amount of points on the body surface. These

points are grouped in triangles forming a mesh which

is stored as a ﬁle in Stereo-Lithography format (.stl).

Standard white garments were used to harmo-

nize the measurements, and seven small wooden half-

spheres were attached to the body surface on anatom-

ically relevant points. One of them was ﬁxed on the

third neck vertebra, two more over the left and right

clavicles, a couple of them on the low waist and high

waist in the right side, and the corresponding pair on

the left side. These marks were automatically de-

tected by the software from the mesh of points, and

their coordinates are stored in a separated ﬁle in .xml

format.

2.2 Methodology

As a ﬁrst step, a 3D binary image is produced from

the collection of points located on the surface of each

woman scanned. Running through the vertical axis of

the body (z-axis), the image is divided into thin slices.

The points that belong to each slice are enclosed by

their convex hull (Rosenfeld and Kak, 1982) which is

then ﬁlled.

Some special cases must be taken into account:

when a horizontal plane cuts not only the trunk but

also the arms we would wish not a convexhull enclos-

ing the three shapes but one for each of them. This

is tackled by imposing limits to the point coordinates

which are considered: only those into a parallelepiped

(box) limited by certain proportions of body height

and width are considered. Using proportions assures

us that this limitation is valid for all individuals, since

the box does not need to be too tight to separate ap-

propriately the arms from the main body.

This method does not provides a global 3D con-

vex hull, neither a prefect ﬁt because human body

A STATISTICAL APPROACH TO BUILD 3D PROTOTYPES FROM A 3D ANTHROPOMETRIC SURVEY OF THE

SPANISH FEMALE POPULATION

371

sections are not always convex. Nevertheless, more

accurate methods to reconstruct the shape would have

need many ad-hoc adjustments and would have been

too prone to error with a so wide spectrum of cases.

We think that approximationby height-section convex

hull is enough for the purpose of this work.

Once the 3D matrix of voxels is available, each

shape is rotated to place the origin of coordinates at

the center of mass of each shape and to make its prin-

cipal inertia axis coincide with the canonical axis of

coordinates. Volumes are supposed to be homoge-

neous and the inertia matrix is calculated and diag-

onalized. The diagonalizing change of basis is taken

as the 3D rotation to be applied to each voxel of the

shape. Also, the minimal enclosing parallelepiped

whose faces are parallel to the coordinate planes (en-

closing box) is calculated after the rotation. This will

be used to know the minimal box that encloses all the

shapes which in turn will be used to dimension the

matrix to hold the result of the mean shape.

The last step in our data ”preprocessing” is to

obtain the 2D cross sections of each 3D aligned

shape. Six anatomical ﬁxed points are identiﬁed on

the women’s body surface and a pre-stated number of

2D cross sections are extracted between each pair of

them for all women.

The different cross sections will be considered as

realizations of random compact sets (Stoyan et al.,

1995; Matheron, 1975; Cressie, 1993). So we will

have a random compact set corresponding to each

level, and the sample mean of these cross sections

will give us a natural way to deﬁne each prototype.

The 3D reconstruction of these 2D means would lead

us to obtain the desired prototype.

Different deﬁnitions of the mean set of a ran-

dom compact set can be found in the literature, the

most important ones being the Aumann mean (Stoyan

and Stoyan, 1994), the Vorob’ev mean (Stoyan and

Stoyan, 1994) and the Baddeley-Molchanov mean

(Baddeley and Molchanov, 1998), with the Baddeley-

Molchanov mean being the most ﬂexible one. A brief

review of the Baddeley-Molchanovdeﬁnition of mean

set is given below.

Let Φ be a random compact set on ℜ

. Let F

′

be the space of non-empty closed sets with hit-miss

topology (see (Matheron, 1975)) and let d : ℜ

′

→ ℜ be a generalized distance function i.e. a

lower semi-continuous function with respect to the

ﬁrst argument and measurable with respect to the sec-

ond argument in such a way that the two following re-

quirements are fulﬁlled: (i) If F

⊂ F

then d(x, F

) ≥

d(x, F

) for all x in ℜ

, and (ii) F = {x : d(x, F) ≤ 0}.

Let m be a metric (or pseudo-metric) on the fam-

ily of distance functions and let m

be the restric-

tion of m to W (a certain compact set, here a win-

dow). Suppose that d(x, Φ) is integrable for all x

and we deﬁne the mean distance function d

∗

(x) =

Ed(x, Φ). Let Φ(ε) = {x ∈ W : d

∗

(x) ≤ ε} with ε ∈ ℜ

and let ε

∗

= argmin

(Φ(ε),d

∗

). The Baddeley-

Molchanov mean of Φ, E

Φ, is the set Φ(ε

∗

Let Φ

with i = 1, . . ., n be a random sample of the

random set Φ, i.e. a collection of independent and

identically distributed (as Φ) random sets. The esti-

mation of E

Φ results from the empirical distance

average deﬁned as

∗

(x) =

∑

i=1

d(x, Φ

). (1)

In our case we have m samples of m random sets

j = 1, . . . , m, corresponding to each cross section

of the body of the woman, and the procedure to com-

pute the m sample mean sets E

, j = 1, . . . , m

would be very complex and would require a lot of

computation.

Alternatively, Lewis et al. in (Lewis et al., 1999)

propose a different empirical approximation to the

Baddeley-Molchanov mean set. They suggest to use

another ”discrepancy criteria” when choosing the op-

timal threshold, namely the ε

∗

that minimizes

∑

i=1

kA(Φ

) − A(

Φ(ε))k,

where A(Φ) denotes the area of Φ. The optimal

threshold ε

∗

is then the value that makes more sim-

ilar the area of

Φ(ε

∗

) to the average of the areas. This

value can be easily determined from the histogram of

d. They call this procedure area-matching. This is the

one we use for our application.

As mentioned previously, one of the main advan-

tages of the Baddeley-Molchanov mean is that it de-

pends on the chosen distance function, d. Thus we

can get different kinds of mean sets using the most ap-

propriate distance function for each application. Bad-

deley and Molchanov give a list of examples with dif-

ferent distance functions. In our application we use

the Euclidean distance function deﬁned as:

d(x, Φ) = inf{ρ(x, y), y ∈ Φ},

where ρ denotes the Euclidean distance in ℜ

. It is

used because it is the simplest and most natural in our

context.

3 RESULTS

Our main aim is to show a methodology to get proto-

types for the different sizes, so, as an illustration, we

ICPRAM 2012 - International Conference on Pattern Recognition Applications and Methods

372

have segmented our data set in different groups, get-

ting a prototype for each of them. Pregnant women,

those who are breast feeding at the time, who have

undergone any type of cosmetic surgery (breast aug-

mentation, liposuction, breast reduction, etc), who are

younger of 20 or older than 65 , are deleted from the

data set for this study. According with the European

regulation, the European sizing system is built by tak-

ing into account girth and height measurement ranges.

So nine sizes are usually deﬁned for the bust measure-

ment and another nine sizes for the height (Table 1).

Table 1: Standard size coding according with the bust and

height dimensions (in cm).

Code 1 2 3

Bust [74-82) [82-90) [90-98)

Height [154-158) [158 - 162) [162 - 166)

Code 4 5 6

Bust [98-106) [106-118) [118-131)

Height [166 - 170) [170 - 174) [174 - 178)

Code 7 8 9

Bust [131-143) [143-155) [155-167)

Height [178 - 182) [182 - 186) [186-190)

Instead of segmenting the population according

with the 81 possible combinations of these bust and

height codes, we segment the population in a lower

quantity of groups, maintaining the nine groups for

the bust measurement, by deﬁning just three height

groups (Table2)

Table 2: Height groups (in cm).

Code 1 2 3

Height <162 [162 - 174) ≥ 174

As bust and height are the corporal dimensions

used to segment the population, in order to get ac-

curate prototypes, instead of working with the whole

body, a region of interest comprising the trunk of the

women, is isolated for our study, and prototypes will

be built to ﬁt this region. Fig 1 shows, as an exam-

ple the prototype built for those women whose bust

ranges between 74 and 82 cm, and whose height is

under 162 cm. In ﬁg 2 different views of the same

prototype are also shown.

4 CONCLUSIONS

A new statistical methodology has been developed to

build prototypes from 3D anthropometric data. From

a 3D cloud of points, a 3D image of a 3D shape has

been built and registered to get homogeneous vol-

umes. Once a group of women sharing similar anthro-

Figure 1: Prototype for the segment of women with a bust

measurement ranging between 74 and 82 cm, and whose

height is under 162 cm.

Figure 2: Different views of a prototype.

pometric measurements is selected, their 3D ”mean

shape” is a valuable information for apparel industry.

Our contribution in this work has been to build this 3D

”mean shape”. From 2D cross sections of these 3D

aligned shapes, we have computed the sample (Bad-

deley - Molchanov) mean of each homological sec-

tion. The 3D reconstruction of these 2D means allows

us to obtain the desired prototype. In our opinion, to

average the 2D homologous sections has allowed us

to build prototypes that reproduce in a quite accurate

way the shape (and proportions)of the woman’s body.

Our aim for future works is to work directly with the

3D volumes to obtain 3D ”mean shapes”.

A STATISTICAL APPROACH TO BUILD 3D PROTOTYPES FROM A 3D ANTHROPOMETRIC SURVEY OF THE

SPANISH FEMALE POPULATION

373

ACKNOWLEDGEMENTS

This paper has been partially supported by grants GV/

2011/004, DPI2008-06691, TIN2009-14392-C02-01

and TIN2009-14392-C02-02. We would like also

to thank the Biomechanics Institute of Valencia for

providing us the data set, and to the ”Ministerio de

Sanidad y Consumo” for having promoted and co-

ordinated the ”Anthropometric Study of the Female

Population in Spain”.

REFERENCES

Baddeley, A. and Molchanov, I. (1998). Averaging of ran-

dom sets based on their distance functions. Journal of

Mathematical Imaging and Vision, 8:79–92.

Bagherzadeh, R., Latiﬁ, M., and Faramarzi, A. (2010). Em-

ploying a three-stage data mining procedure to de-

velop sizing system. World Applied Sciences Journal,

8(8):923–929.

Bye, E., LaBat, K., McKinney, E., and Kim, D.-E. (2008).

Optimized pattern grading. International Journal of

Clothing Science and Technology, 20(2):79–92.

Chen, Y., Zeng, X., Happiette, M., Bruniaux, P., Ngb, R.,

and Yu, W. (2009). Optimisation of garment de-

sign using fuzzy logic and sensory evaluation tech-

niques. Engineering Applications of Artiﬁcial Intel-

ligence, 22:272–282.

Chunga, M., Lina, H., and Wang, M. (2007). The develop-

ment of sizing systems for taiwanese elementary- and

high-school students. International Journal of Indus-

trial Ergonomics, 37:707–716.

Cressie, N. (1993). Statistics for spatial data. Wiley Se-

ries in Probability and Mathematical Statistics. (pages

753-775).

Fan, J., Yu, W., and Hunter, L. (2004). Clothing apperance

and ﬁtt. Science and technology. Woodhead Publish-

ing in Textiles.

Faust, M.-E. and Carrier, S. (2010). Women’s wear sizing:

a new labelling system. Journal of Fashion Marketing

and Management, 14(1):88–126.

Gupta, D. and Gangadhar, B. (2004). A statistical model

for developing body size charts for garments. Inter-

national Journal of Clothing Science and Technology,

16(5):458–469.

Haslera, N., Stolla, C., Rosenhahnb, B., Thormhlena, T.,

and Seidela, H. (2009). Estimating body shape of

dressed humans. Computers & Graphics. IEEE In-

ternational Conference on Shape Modelling and Ap-

plications 2009, 33:211–216.

Hsu, C.-H. (2009). Developing accurate industrial stan-

dards to facilitate production in apparel manufactur-

ing based on anthropometric data. Human Factors and

Ergonomics in Manufacturing, 19(3):199–211.

Hsu, C.-H. and Wang, M.-J. J. (2005). Using decision tree-

based data mining to establish a sizing system for the

manufacture of garments. The International Journal

of Advanced Manufacturing Technology, 26:669–674.

Lewis, T., Owens, R., and Baddeley, A. (1999). Averaging

feature maps. Pattern Recognition, 32:1615–1630.

Luximon, A., Zhang, Y., Luximon, Y., and Xiao, M. (2011).

Sizing and grading for wearable products. Computer-

Aided Design.

Matheron, G. (1975). Random Sets and Integral Geometry.

J. Wiley & Sons, New York. (pages 54-155).

McCulloch, C., Paal, B., and Ashdown, S. (1998). An op-

timization approach to apparel sizing. Journal of the

Operational Research Society, 49:492–499.

Ng, R. and Ashdown, S.P. and Chan, A. (2007). Intelligent

size table generation. Proceedings of the Asian Tex-

tile Conference (ATC), 9th Asian Textile Conference,

Taiwan.

Rosenfeld, A. and Kak, A. (1982). Digital Picture Process-

ing. Academic Press, Inc., Second Edition.

Salusso-Deonier, C., DeLong, M., Martin, F., and Krohn,

K. (1985-1986). A multivariate method of classifying

body form variation for women’s apparel. Clothing

and Textiles Research Journal, 4(1):38–45.

Simmons, K. and C.Istook (2003). Body measurement tech-

niques: Comparing 3d body-scanning and anthropo-

metric methods for apparel applications. Journal of

Fashion Marketing and Management, 7.

Sim´o, A., de Ves, E., and Ayala, G. (2004). Resuming

shapes with applications. Journal of Mathematical

Imaging and Vision, 20:209–222.

Smith, D. C. (2007). Process, ﬁt and appearance analysis of

three-dimensional to two-dimensional automatic pat-

tern unwrapping technology. Thesis submitted to the

Graduate Faculty of North Carolina State University.

Stoyan, D., Kendall, W., and Mecke, J. (1995). Stochastic

Geometry and its applications. Chichester John Wiley

& Sons, Second Edition. (pages 65-95).

Stoyan, D. and Stoyan, H. (1994). Fractals, Random Shapes

and Point Fields. Methods of Geometrical Statistics.

Wiley.

Tryfos, P. (1986). An integer programming approach to the

apparel sizing problem. The Journal of the Opera-

tional Research Society, 37(10):1001–1006.

Zheng, R., Yu, W., and Fan, J. (2007). Development of

a new chinese bra sizing system based on breast an-

thropometric measurements. International Journal of

Industrial Ergonomics, 37:697–705.

ICPRAM 2012 - International Conference on Pattern Recognition Applications and Methods

374