Computer-Aided Design 44 (2012) 56–67

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Computer-Aided Design

journal homepage: www.elsevier.com/locate/cad

Parametric human body shape modeling framework for human-centeredproduct designSeung-Yeob Baek ∗, Kunwoo LeeHuman Centered CAD Laboratory, Seoul National University, 599, Gwanak-ro, Gwanak-gu, Seoul, 151-742, Republic of Korea

a r t i c l e i n f o

Keywords:Digital human modelHuman body modelingHuman-centered product designParametric modelingBody shape parameters

a b s t r a c t

The objective of this study is the development of a novel parametric human body shape modelingframework for integration into various product design applications. Our modeling framework iscomprised of three phases of database construction, statistical analysis, and model generation. Duringthe database construction phase, a 3D whole body scan data of 250 subjects are obtained, and theirdata structures are processed so as to be suitable for statistical analysis. Using those preprocessed scandata, the characteristics of the human body shape variation and their correlations with several items ofbody sizes are investigated in the statistical analysis phase. The correlations obtained from such analysisallow us to develop an interactive modeling interface, which takes the body sizes as inputs and returnsa corresponding body shape model as an output. Using this interface, we develop a parametric humanbody shape modeling system and generate body shape models based on the input body sizes. In ourexperiment, ourmodeler produced reasonable results having not only a high level of accuracy but also finevisual fidelity. Compared to other parametric humanmodeling approaches, ourmethod contributes to therelated field by introducing a novel method for correlating body shape and body sizes and by establishingan improved parameter optimization technique for the model generation process.

© 2010 Elsevier Ltd. All rights reserved.

1. Introduction

In the last few years, concepts such as human-centered designor customer-tailored design have increasingly received attention,making any consideration of the human factors in the productdesign process both significant and compelling. Anticipating suchdemands, there have been a lot of efforts to generate an accurateand reliable digital human model for the purpose of analyzing theeffects between the human user and the product. Modeling theoutside human body shape is one of the key techniques necessaryfor the realization of such objectives.

Most of the time, however, a lot of the research related tohuman body shapemodeling has been accomplishedmainly in thecomputer graphics area, where the focus is highly concentrated onreality and visual fidelity. Although these studies have contributeda great deal to todays development of the digital human model,suitable human modeling methodology for the CAD systems stilldoes not exist regarding the aspects of dimensional accuracy andthe reliability of the results. Despite the large number of studiesin the literature (mainly in the areas of garment CAD [1,2] andergonomics [3–5]) that attempt to integrate the humanmodel intoCAD systems, these are quite restricted to certain applications, and

∗ Corresponding author. Tel.: +82 2 880 7447.E-mail addresses: bsy86@snu.ac.kr (S.-Y. Baek), kunwoo@snu.ac.kr (K. Lee).

0010-4485/$ – see front matter© 2010 Elsevier Ltd. All rights reserved.doi:10.1016/j.cad.2010.12.006

a general methodology for the modeling of the human body shapeneeds to be developed.

For this reason, we propose a novel methodology for modelingthe human body shape based on user-specified body size inputs.We construct a homogeneous body shape database by generatinga consistent mesh structure of a number of 3D whole body scans.The body sizes are then measured from these consistent meshmodels, and, based on this body size information, the database isclustered and statistically analyzed to capture the tendency of bodyshape variation. From this tendency, we finally extract the bodyshape parameters, which become our basic modeling parameters.Furthermore, to provide an interface between these parametersand the body size inputs, we discuss a method for finding theoptimal combination of body shape parameters that produces afinal model capable of satisfying the input body sizes. An overviewof our modeling methodology is illustrated in Fig. 1.

2. Related works

Along with the evolution of computer graphics and human-centered product design methods, there have been a lot of bodyshape modeling methods in the literature. These methods can becategorized into the following four different categories: (1) Directmodel acquisition/creation, (2) Template model-based scaling,(3) Image-based reconstruction, and (4) Statistics-based modelsynthesis.

S.-Y. Baek, K. Lee / Computer-Aided Design 44 (2012) 56–67 57

Fig. 1. An overview of the proposed method.

The direct model creation methods include the 3D whole bodyscanning methods [6–9] and the anatomy-based model construc-tion methods [10–12]. There is no doubt that 3D whole body scan-ning methods are the most accurate way of obtaining the humanbody shape. Those methods provide a 3D model of the humanbody shapewith high accuracy.With the recent development of 3Dimage-capturing technology, the use of 3D scanners for modelingof the human body has become much more popular in the prod-uct design process. However, the 3D scanning methods have failedto overcome two critical problems: the extremely expensive costof the equipment and the necessity of post-processing. Althoughthere have been efforts to overcome these problems by developinglow-cost stereo camera systems [13], they are still not satisfactoryfrom this point of view.

On the other hand, anatomy-based modeling methods con-struct the underlying body structures, such as muscles, bones, andsoft tissues, and derive the outer skin surface from these structures.As these methods take delicate internal structures into considera-tion, the resultant body shapes are highly realistic and plausible.These methods, however, are not quite suitable for application toCAD systems because they require great amounts of knowledge onhuman body structures and expertise in computer graphics. Fur-thermore, as an extra amount of time must be spent modeling theinner structures, which are not of interest, these methods are tooexpensive for general use in the CAD systems.

In contrast to the direct modeling methods, template model-based scaling methods [14,15] produce a newmodel by deforminga single template model. In these methods, a complete modelis prepared by other modeling methods, and then the model isdeformed and scaled per its segments to create different bodyshapes. Due to their simplicity, a lot of commercialized systemsadopt these methods, especially for the online human modelingsystems. However, such methods do not guarantee the reality orthe accuracy of the resultant model because they do not considerthe correlation between the body parts.

In contrast to the above-described constructive methods,image-based reconstruction methods [16–19] reconstruct the 3Dhuman body shape from a set of images obtained from prescribedangles of view. Adopting the image processing techniques,they extract shape information such as the body silhouette oranthropometric measurements, which then become the basis ofthe 3D reconstruction of the body shape. The use of these methodsreduces the costs and labor because these methods only require

a set of 2D images; however, the noise and the dependency onthe background environment are inherent weaknesses of thisapproach and still have not been solved.

Statistics-basedmodel synthesis methods create a human bodymodel based on the study of the body shape distribution. A numberof body shapemodelingmethods of this category are inspired fromthe work of Blanz et al. [20]. They gather 3D human face scan dataand capture the shape variation by analyzing them with principalcomponent analysis (PCA). The foundation of this work is based onthe consistentmesh generation technique, which ensures identicaltopologies and mesh connectivities of the example models. Bygenerating a consistent mesh structure for every example facescan data, one can successfully construct a homogeneous facemodel database from those examples. Using this database, one cananalyze and extract the dominant variables determining the facialshape. Based on these variables, a 3D morphable face model isgenerated.

Motivated from such a method, Allen et al. [21] applied thisto a set of 3D human body scan data. Even if their work wassignificantly influenced by and originated from Ref. [20], theycontributed to the field by establishing a technique for fittingtemplate meshes to the target scan data to ensure a consistentmesh topology. Rather than depending on the conventional meshparameterization techniques, they developed a novel methodof generating a consistent mesh structure by introducing thetemplate fitting method. They defined three different energyfunctions for the fitting and minimized the sum of those functionsusing the numerical optimization. In this simple but effectivemanner, they could ensure the consistency of the mesh structure.

Although they prepared a foundation for the other statistics-based methods such as [22,23], these methods still do not satis-factorily achieve the goal of developing a human modeling systembecause they do not include a technique for generating a newmodel that satisfies the input constraints, which is an indispens-able technique for an interactive body shape modeler.

To overcome such a limitation, Seo et al. [24,25] introduced aconcept of parametric modeling into their modeler. After measur-ing the body sizes of the examples in the 3D body scan database,they correlated the body sizes with the body shapes through a ra-dial basis function (RBF) network. Performing a random-search-based learning procedure, they figured out a relationship betweenthe body shape and the body sizes. Based on this relationship, theycould synthesize a new model with user-specified body sizes by

58 S.-Y. Baek, K. Lee / Computer-Aided Design 44 (2012) 56–67

Fig. 2. Example models in the database and the 68 landmarks located on those models (green dots). (For interpretation of the references to colour in this figure legend, thereader is referred to the web version of this article.)

combining the example shapes in their database. Through such anapproach, they could develop an interactive parametric body shapemodeler.

In a similarmanner,Wang [26] proposed amethod for paramet-rically designing mannequins. As opposed to the previous meth-ods, however, they first defined the feature points to construct afeature wireframe. By parameterizing the 3D body scan models bythe feature wireframe, they described the entire body shapes ofevery human model in their database with the patches interpo-lating the feature wireframe. In this way, they ensured the topo-logical consistency of their database. Furthermore, in the modelgeneration process, they adopted an optimizationmethod tomini-mize the gap between the input body sizes and the actual body sizeof the resultant model. By iteratively calculating the body sizes ofthe mannequin of the current iteration, they searched for an op-timum model that satisfies the input body sizes. Through such anapproach, they could establish a new framework for generating afeature-based mannequin model.

On the foundation of [26], Chu et al. [27] extended the para-metric modeling method. By finding the regression function thatrelates the body sizes and the body shape models, they developedmore advanced methodology for modeling the human body.

Based on such concepts of the statistics-based modeling meth-ods, we proposed a parametric human body modeling method inour previous work [28]. To develop a simple and concise model-ing pipeline, we employed a feature point-based shape analysistechnique and successfully captured a statistics of the human bodyshape. Furthermore, using an RBF network-based surface approxi-mation method, we could generate a body shape surface in a rapidmanner. However, although themodeling accuracy of the resultantmodel was satisfactory, the reality and visual fidelity were rela-tively poor.

The new method proposed throughout this study is also basedon such a concept of statistics-based modeling methods. In ourstudy, we adopt or extend the previous methods related to theconsistent mesh generation procedure. Our way of deriving therelation between the body sizes and the body shapes is noveland has not been attempted before, and it yields a number ofbenefits compared to previous methods. In such a derivation,even a consideration of the effect of age becomes possible, whichwas not the case in previous methods. In addition, the way offormulating the optimization problem is also useful in that noiterative search is needed and an analytic solution can be obtained.Thismakes ourmodelingmethodmuch faster than othermethods,while the quality of the resultantmodel is improved. Therefore, ourmain contribution is summarized into the above two aspects, andthese will be discussed throughout the rest of the article.

3. Homogeneous body shape database

3.1. Preprocessing

As a first step of our modeling method, it is necessary toconstruct a database that is not just reliable but also coversa wide range of the statistical population. For this reason, weused a SizeKorea whole body scan database [29] as our sourceof the statistical analysis. The SizeKorea database is composedof anthropometric body size measurements and 3D whole bodyscan models measured and collected by the Korean Agencyfor Technology and Standards (KATS). The measurement ofanthropometric body sizes was performed directly on subjectsusing aMartin ruler under ISO7250 and KSA7004 related to humanbody measurement, and the scanning of 3D body shapes wasdone using a laser-range whole body scanner. While scanning,each individual wore tight short pants and a swimming cap, inaddition to a bra-top for the females. Each of the scan data wascomposed of a point cloud containing 120,000–130,000 points anda per-point color in RGB (for privacy issues, their facial colorswere eliminated). For our study, we randomly selected the 3Dscans of 250 individuals (125 males, 125 females) from among theSizeKorea database.

In addition to those scanned models, we placed landmarks onthe locations of 68 feature points (as shown in Fig. 2) for everysubject. These feature points were based on the H-Anim markerset and ISB marker set [30], as listed in Table 4, and the detectionof the feature points was manually done with the support of afeature detection algorithm; based on the fuzzy rules determiningthe locations of the feature points, the computer algorithm firstdetermined several candidate locations on the subject, and thenthe exact locations were manually selected from those candidates.By applying such a feature point detection process to every subject,we collected point indices of the feature points and stored themwith the corresponding 3D models.

The position and orientation of the example models werethen aligned by performing rigid-body registration based on thefeature points. One model in the database was set to be a basisof registration, and the other models were registered to the basis.Such alignment aimed to eliminate the effects of the differentpositions and the orientation during the statistical analysis, as willbe discussed in Section 4.

3.2. Consistent mesh fitting

One of the inherent problems of 3D scanning technology is thefact that an incidental but great deal of effort is needed to refine the

S.-Y. Baek, K. Lee / Computer-Aided Design 44 (2012) 56–67 59

Fig. 3. Result of approximately mapping the template surface (a) to the target surface (b). The resultant surface is shown in (c), and its overlapping to the target is in (d). Tosee the reliability of this approximate fitting technique, the surface disparity between the resultant surface and the target surface is inspected using RapidForm2006 [32], asin (e). A graph shows a disparity histogram, and its vertical axis is in millimeters (mm).

noisy and incomplete surfaces. Performing this effort for every 3Dscan model in the database is a tedious and time-consuming task.Furthermore, keeping the refinement problem aside, the statisticaltendency cannot be characterized from raw 3D scanned modelsdirectly. This is due to the discordance in their mesh topologies.Therefore, to perform a statistical analysis of those data and tocharacterize their statistical properties, a technique for ensuringthe identical mesh topology is required.

For this reason, we borrow the energy minimization frame-work-based surface-fitting technique proposed by B. Allen et al.[21]. Under this framework, three different error terms are definedas components of the objective energy function to fit the templatesurface to the target scan models. In our study, we improve such aframework with an additional error term of distortion error. Thispromotes a relaxation of the distorted facets that occurred duringthe surface-fitting process. Furthermore, to prevent the result frombeing stuck at the local minimum and to improve the convergencespeed of the energy minimization operation, we roughly fit thetemplate surface to the target surface at the initial stage by em-ploying the RBF network-based surface deformation techniquethat was discussed in our previous work [28].The following is anoverview of our modified version of the surface-fitting process:

a. Align the template surface with the target model by using therigid-body registration technique based on the feature pointlandmarks.

b. Using the RBF network-based surface deformation technique,roughly deform the template surface to approximate the targetsurface.

c. Considering the approximated surface as an initial setup of thetemplate, perform the energy minimization process using anumerical optimization solver.

As an initial step of the surface-fitting process, we first prepareda template human model that was composed of 66,536 facetsbounded by 33,270 vertices. The same feature points listed inTable 4 were then located on the template model. Based on thesefeature points, the template model was then registered to thetarget scan model through the rigid-body registration technique.

After such an initial setup was done, the RBF network-basedsurface deformation technique was applied. To do so, we defineda mapping f : ℜ

3→ ℜ

3 from the template surface as a weightedsum of the RBF functions:

f (x) = x +

m−j=1

wjψ(‖x − cj‖), (1)

where ψ(‖x − cj‖) is an RBF function centered at a point cj, andwj ∈ ℜ

3 is a vector containing the corresponding weight values

of each direction. In our problem, the RBF centers, cj, are selectedto be the feature points on the template surface. Therefore, to mapthe feature points on the template surface to those of the targetsurface, the following constraints must be satisfied:

f (ci) = ci +m−j=1

wjψ(‖ci − cj‖) = mi, ∀i, (2)

and, consequently,m−j=1

wjψ(‖ci − cj‖) = mi − ci, ∀i, (3)

where mi is a feature point on the target surface correspondingto ci. From such constraints, the weight values are then obtainedby solving the system of equations in Eq. (3). It can be shown thatthe linear system appearing in Eq. (3) is symmetric and positivesemi-definite [31]. Thus, there always exists a unique solution tothe system. Then, by substituting those weight values back in toEq. (1), a mapping from the template surface to the target surfaceis obtained. In this manner, we can approximately fit the templatesurface to the target surface while ensuring the feature points tobe mapped to their corresponding locations.

Among the various types of RBF functions, we determined theuse of the Gaussian basis function ψ(r) = exp(−r2/σ 2) with acoefficient of σ = 15. Such a determination was derived after thetedious trial of examining the different basis function conditions.Fig. 3 shows the result of mapping the template surface using theRBF network.

After finishing the rough fitting process, a final accurate fittingprocess based on the energy minimization technique was appliedto the template surface. To do so, we defined four different typesof error functions as a composition of the objective function.

The first error function is a disparity error Ed, which regulatesthe disparity between the template surface and the target surface:

Ed =

N−i=1

‖ti − Tipi‖2 (4)

where pi ∈ ℜ4 is an ith point of the template model in the

homogeneous coordinate system, Ti ∈ ℜ4×4 is the corresponding

affine transformation, and ti is a corresponding matching pair inthe target surface. Here, the matching pair ti is selected fromamong the points of the target surface to have the closest distancefrom pi. To prevent pi from being matched to a wrong pair point,the selection of thematching pair is restrictedwith two thresholds;the location should no more than dthres apart, and the surfacenormal should no more than θthres apart. In our experiment, it wasfound that the appropriate distance threshold was about dthres =

10 cm, and the appropriate angle threshold was about θthres = 45

60 S.-Y. Baek, K. Lee / Computer-Aided Design 44 (2012) 56–67

Fig. 4. Result of performing the surface-fitting process and the verification.

degrees. Furthermore, due to the noise of the scan data in the handregion, disparity error was not calculated in this region and theerror was forced to have a zero value.

The second error function is a smoothness error Es, whichregulates the template point pi from being mapped far from itsneighboring points:

Es =

N−i=1

−j∈Ni

‖Ti − Tj‖2F (5)

where ‖·‖F is the Frobenius norm, andNi is a set of vertex indices ofthe neighboring vertices of pi. Through the smoothness error, thedifference between the transformations of neighboring points ispenalized and thus prevents adjacent parts of the template surfacefrom being mapped to disparate parts of the target surface.

The third error term is a landmark error Em to guide everytemplate feature point to be mapped to the corresponding targetfeature point:

Em =

m−i=1

‖mi − TKipKi‖2 (6)

wheremi is a target feature point, and Ki is the vertex index of thecorresponding feature point on the template surface.

The last error term is a distortion error Et to prevent the facetsfrombecoming the abnormal facets such as spikes and turned-overfacets:

Et =

N−i=1

Tipi −1ni

−j∈Ni

Tjpj

2

(7)

where ni is the number of neighboring vertices. By minimizing thedistance from the geometric center of the neighboring vertices,the distortion error prevents the vertices from being biasedto the boundary of the neighborhoods or from being outsidethe boundary of the neighborhoods, and this thus relieves thedistortions of the facets.

Composed of the above four error functions, the final objectivefunction E is defined as follows:E = aEd + bEs + cEm + dEt (8)where the weight values a, b, c , and d lead the template surface tobe fitted to the target surface. For better performance, optimizationis not done at once, but the weight values are tuned in three steps,as described in the following:a. Assign a = 1, b = 10, c = 10, and d = 20 and perform the

optimization so that the overall shape can be deformed roughlyto the target surface.

b. Modify the values to a = 10, b = 5, c = 5, and d = 10 andperform the optimization again so that the disparity betweenthe surfaces now becomes much more important.

c. Set a = 10, b = 1, c = 1, and d = 5 and perform the finaloptimization so that the template surface can finally fit to thetarget surface.

As a tool of the optimization, we used a quasi-Newtonian solvernamed L-BFGS-B, the limited-memory BFGS solver for bound-constrained optimization [33].

Fig. 4 shows the result of performing the above-describedsurface-fitting operation and the verification of the result. As onecan notice from the figure, the template surface and the targetsurface have a disparity less than 5 mm except for the finger tips,where the disparity error is not calculated during the optimization.

3.3. Hierarchical clustering of the database

To implement an interactive modeling interface, it is necessaryto define the relationship between the body sizes and the bodyshapes. For this reason, the body sizes of the examplemodels wereconsidered additionally. For the major body sizes, a total of 25items were selected as listed in Table 1.

Although the SizeKorea database provides 119 items of bodysizemeasurements for each subject,we decided to take only four ofthem, including sex, age, height, and weight, which are impossibleto measure from 3D surface models (as the standing postureshave their legs wide apart, measuring the height directly fromthe 3D models may result in inaccuracy); the other body sizeitems were obtained by directly measuring the 3D models. Thisis due to the slight disparity between the surface-fitted modeland the actual human body. Such a disparity may be consideredas a negligible factor because the amount is relatively small, butfor better accuracy, we decided to use values that were directlymeasured from the 3D models.

For the measurement of the body sizes of the 3D models,we categorized the items into two categories of lengths andcircumferences. Items in the length category were measured bycalculating the distances between the joints, whose locations wereestimated from the feature points. For example, Upper-Leg Lengthwas evaluated from the distance between the hip joint and theknee joint. The locations of the hip joint and the knee joint wereestimated as mid-points of the FTC and GRO and the FME andFLE, separately (for acronyms, readers are directed to Table 4). Bydetermining such measurement protocols for every other item,length sizes could be calculated without any difficulties.

S.-Y. Baek, K. Lee / Computer-Aided Design 44 (2012) 56–67 61

Table 1The body size items to be measured.

Categories Items

Sex and age 1. Sex2. Age

Height and weight 3. Height4. Weight

Lengths 5. Biacromial breadth6. Biiliac breadth7. Upper-arm length (L/R)8. Lower (fore)-arm length (L/R)9. Upper-leg (thigh) length (L/R)10. Lower-leg (calf) length (L/R)

Circumferences 11. Chest circumference12. Abdominal (waist) circumference13. Buttock (hip) circumference14. Upper-arm circumference (L/R)15. Lower (fore)-arm circumference (L/R)16. Upper-leg (thigh) circumference (L/R)17. Lower-leg (calf) circumference (L/R)

Measurements of items in the circumference category areslightlymore complicated. Tomeasure the circumferences,we firstcomputed the cross-sectionbetween themodel and aplane locatedand oriented at a certain position. For example, a cross-sectionbetween the model and a plane at the navel level whose normalis in the height direction will lead to an abdominal circumference.Then, from the cross-sectional curve, which is actually a polygonbecause the model surface is comprised of triangular facets, aconvex hull of the curve is derived. Finally, the outer girth of theconvex hull becomes the circumference of our interest.

The reason behind measuring the girth of the convex hullinstead of the cross-sectional curve is derived from intuition on theactual measuring process using the measuring tape. For instance,when we measure the abdominal circumference, which is definedas a circumference of the torso at the navel, we do not stick themeasuring tape to all of the concave parts of our body. Rather, westretch the tape tightly and surround the torso with the support ofthe convex parts. Therefore, directlymeasuring the cross-sectionalcurve may add some unnecessary lengths of the concave parts,and thus the measurement of the convex hull is much moreappropriate.

The convex hull of the cross-sectional curve is obtained byapplying the Jarvis march algorithm [34], which is also known as agift-wrapping algorithm. This algorithm begins with the leftmostpoint p0 and selects the next point pi+1 such that all points are tothe right of the line pipi+1. Repeating such a selection until onereaches pi+1 = p0 yields the convex hull.

By applying these length and circumference measuring pro-tocols, we measured all body size items of all individuals in thedatabase. Based on those body sizes, we clustered the database toobtain a better analysis result and a better modeling result. Forclustering, we employed a hierarchical clustering technique [35].

The hierarchical clustering is a method for building a hierarchyof clusters. Based on the similarity between the sets of datasamples, the method decides which clusters should be combined.By repeating this accumulatively, a hierarchical structure of thesets of samples is determined based on their similarity, and usingsuch a structure, one can divide the data into several clustersaccording to certain similarity levels they want. Moreover, theresult of hierarchical clustering can be displayed in diagramcalled a dendrogram as shown in Fig. 5. The dendrogram consistsof many upside-down U shaped lines connecting each set ofsamples in a hierarchical tree. The height of each connecting linerepresents dissimilarity between the two objects being connected.The similarity (or dissimilarity) between the objects is determined

by the linkage criterion. The linkage criterion includes a distancecalculation between the objects and the distance can be calculatedthrough diverse distance metrics.

Before to perform a cluster analysis, we first divide the exam-ples into two categories according to their sex. Then we calculatethe distances between every two elements to decide which ele-ments should be combined or split. As the units of each body sizeitem are different and their variations are also not identical, thestandardized Euclidean distance,

‖x1, x2‖s = (x1 − x2)TV−1(x1 − x2) (9)

is used as a metric of the distance between the elements, where Vis a diagonal matrix whose diagonal elements are the variances ofeach element of the examples.

Further, to create an agglomerative cluster tree,we calculate thelinkage between the clusters with the Wards linkage scheme,

d2(r, s) = nrns‖xr − xs‖nr + ns

(10)

where xr and xs are the centroids of clusters r and s, respectively,and nr and ns are the numbers of elements in the correspondingclusters.

By calculating such distances and linkages to the body sizesof the example models, we could obtain the dendrograms of thehierarchical clusters, as shown in Fig. 5. Based on these clusteringresults, we subdivided the database into four to five groupsaccording to their cluster. The red-colored rectangles in Fig. 5denote such groups. To examine the statistics of each group, theaverages and standard deviations of the several body size itemswere calculated and are listed in Table 2.

4. Statistical analysis and parameter extraction

To characterize the distributional tendencies of the body shapesand their relationships with the body sizes, we first defined boththe body size vector xs ∈ ℜ

k and the body shape vector xp ∈ ℜ3n

as follows:

xs =s1 s2 · · · sk

T, xs =

pT1 pT

2 · · · pTn

T (11)

where si are the body size items listed in Table 1, and pi are thevertices of the body shape surface.By assigning such vectors toevery model in the database and applying a principal componentanalysis (PCA) to those vectors, we obtained approximatedstatistical models in each vector space:

xs = xs + Psbs, xp = xp + Ppbp, (12)

where xs and xp are the average body size and average body shape,respectively, Ps and Pp are the matrices whose column vectors arethe principal components, and bs and bp are the weight values ofthe corresponding principal components.

However, such a statistical model as in Eq. (12) is not quitesatisfactory because it does not imply a correlation between thebody sizes and body shapes as two different statistics are charac-terized in two different vector spaces. Therefore, it is necessary tosomehow combine these two statisticalmodels to correlate to eachother.

For this reason, we concatenated the two vectors and appliedPCA to obtain a combined model as follows:

xs = xs + 8sw, xp = xp + 8pw, (13)

or, consequently,[xsxp

]=

[xsxp

]+

[8s8p

]w, (14)

where 8s and 8p are the principal component matrices of theconcatenated model, and w is a vector whose elements are the

62 S.-Y. Baek, K. Lee / Computer-Aided Design 44 (2012) 56–67

Fig. 5. Dendrograms of the hierarchical clusters of male models (left) and female models (right). Red-colored rectangles denote the groups divided on the basis of theclustering results. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Table 2Body size statistics of each group.

Age (yrs) Height (mm) Weight (mm) Chest (mm) Waist (mm) Hip (mm)

Male Group 1 Avg. 37.4 1666.1 74.0 982 907.4 971.2Std. Dev. 15.5 46.8 6.9 44.9 51.8 34.7

Group 2 Avg. 23.9 1753.2 72.1 935.5 833.1 947.3Std. Dev. 8.5 36.1 5.3 46.0 56.9 36.2

Group 3 Avg. 13.9 1538.1 51.0 837.9 768.6 838.7Std. Dev. 3.7 96.7 10.2 100.6 102.9 83.6

Group 4 Avg. 26.4 1702.4 58.1 852.6 746.2 875.6Std. Dev. 11.4 50.9 5.8 56.0 58.7 37.9

Female Group 1 Avg. 26.1 1565.6 58.4 882.9 809.9 919.8Std. Dev. 11.8 45.0 5.3 47.7 55.5 37.4

Group 2 Avg. 50.0 1520.3 58.6 949.3 864.9 928.4Std. Dev. 5.7 38.0 5.8 65.0 68.6 39.5

Group 3 Avg. 18.6 1534.7 44.8 770.0 684.8 811Std. Dev. 6.4 52.7 4.8 40.1 48.0 43.3

Group 4 Avg. 21.7 1630.1 55.3 835.6 759.0 886.2Std. Dev. 6.5 31.6 4.2 37.7 45.4 30.5

Group 5 Avg. 25.1 1612.5 48.1 791.5 703.0 832.8Std. Dev. 12.6 30.4 2.7 40.5 35.8 19.0

weight values. It should be noted that 8s and 8p include thecorrelated variation of two different models, and one weight valuew affects the two vectors xs and xp at the same time. Therefore,the tuning the weight value w will result in the various humanmodels, and thus the elements of the vector w are considered asthe modeling parameters, which are defined as the body shapeparameters in our study.

One may wonder how the concatenation of the two vectors canyield such a combinedmodel. This is due to the following propertyof the covariance matrix. In the PCA calculation, the covariancematrix is used, as its eigenvectors are the principal components ofthe statistics. From the statistical data xs and xp, the correspondingcovariance matrices Cs and Cp are calculated as follows:

Cs =1

ns − 1(xs − xs)(xs − xs)T ,

Cp =1

np − 1(xp − xp)(xp − xp)T ,

(15)

where np and np are the numbers of examples in each of thedatasets.

Now, let us assume that the numbers of the examples in eachdatabase are the same, that is, that ns = np = n; then, thecovariance matrix of the concatenated vector of xs and xp iscalculated as follows:

C =1

n − 1(x − x)(x − x)T

=1

n − 1

[xs − xsxp − xp

] xTs − xTs xTp − xTp

=

1n − 1

[(xs − xs)(xs − xs)T (xs − xs)(xp − xp)T

(xp − xp)(xs − xs)T (xp − xp)(xp − xp)T

]=

[Cs Csp

CTsp Cp

]. (16)

Therefore, from the result of Eq. (16), it can be said that thecovariance matrix of the concatenated vectors is a combinationof the separate covariance matrices via matrix Csp, and thusthe eigenvectors in the concatenated space include a correlationbetween the eigenvectors in each separate vector space.

Further, to eliminate the noise and to reduce the data dimen-sion, we selected the first t dominant components among the en-tire eigenvectors using the following criterion:

t−i=1

σi ≥ ζ

n−i=1

σi, (17)

where σi is a square-root of an eigenvalue of the ith eigenvector(that is, the ith principal component), and ζ is a selection rate.Because the eigenvalue of the covariance matrix implies variancealong with the direction of the ith eigenvector, the above criterionin Eq. (17) would lead us to find the first t dominant componentscovering the portion ζ of the entire population. In our experiment,

S.-Y. Baek, K. Lee / Computer-Aided Design 44 (2012) 56–67 63

the most appropriate selection rate ζ was determined to be ap-proximately 0.8; values greater than 0.8 resulted in noisy data, andvalues less than 0.8 resulted in flattened data.

5. Modeling parameter optimization

Only with these body shape parameters can we generate bodyshape models without any difficulties. However, such a mannerof modeling the human body shape is not very intuitive, as thereare no exact physical and geometrical meanings of the givenbody shape parameters. Therefore, to realize the interactive bodyshape modeler, it is necessary to create a modeling interfacethat takes the body sizes as inputs and generates the humanmodel accordingly. To do so, we formulate the problem of creatinga human model satisfying the constraints on body sizes in anoptimization framework. The input body sizes are classified intothe groups appearing in Table 2, and the modeling parametersof that group are taken into account for the optimization.Furthermore, to provide a more flexible modeling interface to theusers, we add a supplementary algorithm that takes user-definedbody sizes as additional constraints andmodifies the humanmodelaccordingly.

5.1. Initial modeling from major body sizes

Using the major body sizes listed in Table 1 as the inputs,we now implement a modeling algorithm based on the bodyshape parameter optimization framework. Our problem here isdetermining the optimal combination of body shape parametersthat produces a human model satisfying the input body sizes. Todo so, the following should be satisfied:

3Tyc = 3T (xs + 8sw), (18)

where yc is a vector consisting of body size constraints, and 3 isa diagonal matrix whose diagonal elements are composed of theBoolean values of 0 or 1 indicating whether or not the constraintis active. In Eq. (18), the number of unknowns w ∈ ℜ

t is generallymuch greater than the number of constraints yc ∈ ℜ

k, that is, t isalways greater than k in general. Therefore, the systemof equationsappearing in Eq. (18) is indefinite, and thus there are an infinitenumber of solutions. For this reason, a criterion for selecting themost appropriate solution fromwithin the solution space (a vectorspace of w satisfying Eq. (18)) is needed. In this study, we decidedto choose a solution in the solution space that was as close to theaverage model as possible:

minw

12wT6w

subject to 3T (yc − xs − 8sw) = 0,(19)

where 6 is a diagonal matrix whose diagonal elements are theeigenvalues of the corresponding body shape parameters (i.e.,variance along the eigenvector direction). The reason behindadding the eigenvalue matrix is the consideration of the differentdominances of each eigenvector, as in the same context with thestandardized Euclidean distance in Eq. (9).

To solve the optimization problem defined in Eq. (19), weintroduce a Lagrange multiplier µ and differentiate the objectivefunction and the optimization constraint:

L(w,µ) =12wT6w + µT3T (yc − xs − 8sw); (20)

∂L∂w

(w,µ) = wT6 − µT3T8s,

∂L∂µ(w,µ) = 3T (yc − xs − 8sw).

(21)

From the first-order necessary condition of optimization, we get

∂L∂w

(w∗,µ∗) ≡ 0 : w∗T6 − µ∗T3T8s = 0,

∂L∂µ(w∗,µ∗) ≡ 0 : 3T (yc − xs − 8sw∗) = 0.

(22)

By solving Eq. (22) for w∗ and µ∗, we finally get the optimalsolution

w∗= K(yc − xs), (23)

where K = 6−18Ts 3(8s6

−18Ts 3)

−1. Here, it should be notedthat the calculation of the matrix K can be done without anycomputational load. This is because the only inverse operationrequired for calculatingK is (8s6

−18Ts 3)

−1, which is a k×kmatrix(note that the calculation of the inverse of 6−1 is done directly byinversing the elements, as the matrix 6 is a diagonal matrix). Asthe value of k is very low (in our application, k = 24 because weuse 24 body size items.), the inverse of K can be calculated in anextremely short time.

Based on such an optimization framework, we generated sev-eral body shapemodels (appearing in Fig. 6) by assigning the inputbody sizes listed in Table 3. As shown in the figure, the resultantbody shapes appeared to be realistic and feasible considering theinput body sizes (verification of the modeling result accuracy willbe discussed in Section 6).

5.2. Detailed modeling with user-defined constraints

For our previous experience, we know that there could bevarious body shapes even when the body sizes are the same. Tocover such variety, we added an additional modeling procedure tomodify the body shape to amore detailed level. For this reason, weadded an additional modeling interface.

Using the graphical user interface (GUI) of ourmodeler, one candefine their own constraint by selecting the reference points orcurves and defining the constraints on them. Then, the modelerperforms an iterative optimization operation using the geneticalgorithm-based numerical optimizer described in Ref. [36], whilechecking the constraints for every step during the iteration. That is,in every iteration step, a number of body models are generated aschromosomes of the genetic algorithm, and the user-defined bodysizes of these models are measured by calculating the distancebetween the reference points, the length of the curve, or thecircumference along the cross-sectional curve. Such calculationsare done in a similar manner as the body-measuring method wediscussed in Section 3.3.

6. Results and validation

As discussed throughout the previous sections, we could suc-cessfully formulate the problem of modeling human body shapefrom the input body sizes. As we already observed from Figs. 6 and7 and Table 3, the resultant models were highly realistic, and theirbody sizes were also very feasible.

To examine the modeling accuracy of our modeler in a morequantitative way, we validated the body size values by comparingthe input body sizes and the actually measured body sizes fromresultant models. Fig. 8 shows the results of such validation onthe models appearing in Fig. 6. As can be noted from the figure,the error of the result was less than 2.7125% and was 0.7220% onaverage. Such a validation result proves that our modeling methodis accurate and reliable.

Moreover, to verify the computational load, we examined themodeling speed and the maximum memory consumption on thecomputer having an Intel(R) Core(TM) 2 CPU 6300 @ 1.86 GHz

64 S.-Y. Baek, K. Lee / Computer-Aided Design 44 (2012) 56–67

Fig. 6. The body shape models resulting from the parameter optimization method. The input constraints of the models are listed in Table 3.

Table 3Input body sizes of the body shape models appearing in Fig. 6.

Age Height Weight Chestcircum.

Waistcircum.

Hipcircum.

Biacromialbreadth

Biiliacbreadth

Upr.armlength

Lwr.armlength

Upr.armcircum.

Lwr.armcircum.

Upr.leglength

Lwr.armlength

Upr.legcircum.

Lwr. legcircum.

1 30 1750 55 910 730 940 390 310 255 260 250 195 370 380 480 3302 45 1650 70 1050 960 1030 380 360 230 245 310 220 325 360 510 3453 15 1600 40 720 630 780 330 260 230 230 185 150 330 340 400 2804 60 1580 70 1060 980 1020 370 360 210 240 320 210 300 340 470 3205 20 1700 48 850 700 880 360 290 240 250 220 180 350 360 450 3006 16 1500 40 700 620 750 315 250 220 220 185 150 310 320 380 2607 15 1350 35 620 550 670 280 220 195 200 160 135 280 290 340 2308 22 1620 85 1125 1030 1110 370 360 240 240 380 250 330 360 620 4209 35 1600 60 930 850 940 360 320 225 240 270 195 320 340 470 320

10 50 1520 63 965 890 950 350 330 205 220 280 195 300 320 450 30011 40 1700 60 900 820 900 380 300 240 250 260 220 340 380 460 32012 20 1800 85 1050 930 1040 420 350 260 265 330 250 355 395 560 39013 15 1600 50 790 700 815 350 275 235 240 230 185 320 360 420 30014 24 1720 64 910 810 920 390 310 250 260 270 220 340 380 480 33015 25 1750 48 850 750 850 380 290 260 260 230 200 350 400 430 31016 58 1620 75 970 900 940 390 320 230 240 300 240 320 350 480 34017 25 1820 89 1070 960 1060 430 350 260 270 345 260 360 400 580 40018 30 1710 69 940 840 940 390 315 245 250 285 225 340 380 490 34519 63 1650 50 850 800 850 370 290 235 240 220 200 330 365 400 29020 15 1400 35 650 575 675 295 230 210 205 180 150 280 320 340 240

and a 2046 MB RAM platform. The calculation time did not exceed134 ms (ms), and the memory consumption at the peak was about260.56 MB. Furthermore, even when we applied the additionaluser-defined constraints, which required the genetic algorithmcalculation, themodeling timewas 2.372 s on average and the peakmemory consumption was about 282.54 MB. Such results provethat our modeling method shows extremely fast performancewhile maintaining a fine level of memory consumption.

7. Conclusions and future work

In this study, we proposed a method for modeling the humanbody shape from input body sizes. The proposed method includedsteps of database construction, statistical analysis, and parameteroptimization. Throughout those steps, we could obtain various

body shape models, which proved to be reasonable. The maincontributions of this study are summarized as follows.

One of the main contributions of this study is a statistical mod-eling of the body shape variations when deriving the correlationbetween body shape and body size (Section 4). We defined both abody shape vector and a body size vector in two separate vectorspaces and analyzed them using amulti-cluster analysis techniquethat classified each vector element into several clusters and calcu-lated the distributional tendencies of each cluster. In this way, notonly the body shape distribution but also the correlationwith bodysizeswere extracted at the same time from the training body shapeexamples in the database. Although similar work has been doneby Seo et al. [24,25] using a radial basis function (RBF) network tocalculate the correlation between body sizes and body shapes, ourway of formulating such a problem is much simpler and more in-tuitive, and it directly produces modeling parameters as well. In

S.-Y. Baek, K. Lee / Computer-Aided Design 44 (2012) 56–67 65

a

b

c

Fig. 7. Results of varying a particular input body size while other sizes are fixed. (a) Results of varying the age while the height and weight are fixed at 160 cm and 70 kgfor males and at 160 cm and 50 kg for females. (b) Results of varying the height while the age and weight are fixed at 25 yrs and 70 kg for males and at 25 yrs and 50 kg forfemales. (c) Results of varying the weight while the age and height are fixed at 25 yrs and 170 cm for males and at 25 yrs and 165 cm for females. Note that the other bodysizes not mentioned above are set to be inactive constraints.

Fig. 8. Result of the validation of modeling accuracy.

our formulation, the consideration of intrinsic factors, such as ageand weight, which are not measurable from 3D models, becomespossible.

Another main contribution is a body size based optimal bodyshape parameter calculation technique for generating an optimalhuman body shape model satisfying the body size inputs (Sec-tion 5). We formulated a vector-space optimization problem tosolve for the body shape parameters. Compared to the other para-metric modeling methods such as [24,25], which only allow thedirect manipulation of modeling parameters in an open-loop way,our method could strictly control the resultant model in a closed-loop manner. For instance, in open-loop methods, if the user mod-ifies the modeling parameter directly for the purpose of changinga certain body size of the model, then the other body sizes might

be affected by themodification of themodeling parameter. For thisreason, applying the multiple constraints becomes a difficult taskin an open-loop system. However, using a closed-loop manner ofmodeling, which calculates the optimal combination of all of themodeling parameters at once, one can easily apply the multipleconstraints without any direct modification of the parameters. Forexample, Ref. [26] allowed the user to assign several body sizes andallowed the modeler to calculate optimal parameters from thoseinputs. In this spirit, we also calculated optimal parameters fromthe input body sizes. However, a distinguishing aspect of our workis themanner of formulating the optimization problem. In the pre-viouswork, the body sizes of the resultantmodel were obtained bymeasuring themodel directly. For this reason, the optimal solutionhad to be calculated through a number of iterations and the body

66 S.-Y. Baek, K. Lee / Computer-Aided Design 44 (2012) 56–67

Table 4A list of the feature points used in this study. Note that the feature points of the None category are newly defined by the authors to further improve the surface-fittingprocess.

Index Name Acronym Category

1 Skull external occipital protuberance SOP H-Anim2, 3 Skull infraorbital foramen (R/L) SIF H-Anim4 Skull—Nasion SNA H-Anim5 Skull—Glabella SGL H-Anim6, 7 Jaw Angle (R/L) JAN ISB, H-Anim8 Jaw—Mental protuberance JMP H-Anim9 Sternum—Jugular notch SJN ISB, H-Anim10 Sternum—XiphiSternal joint SXS ISB, H-Anim11, 12 Scapula—Acromial edge (R/L) SAE H-Anim13, 14 Humerus—Medial epicondyle (R/L) HME ISB, H-Anim15, 16 Humerus—Lateral epicondyle (R/L) HLE ISB, H-Anim17, 18 Ulna Olecranon (R/L) UOA H-Anim19, 20 Ulna—Styloid process (R/L) USP ISB, H-Anim21, 22 Radius—Styloid process (R/L) RSP ISB, H-Anim23–32 Hand/phalanges—head (R/L) DC(n) None

(n = 1:thumb, n = 2:forefinger, n = 3:middlefinger,n = 4: annular finger n = 5: auricular finger)

33, 34 Ilium—Anterior superior iliac spine (R/L) IAS ISB, H-Anim35, 36 Ilium—Posterior superior iliac spine (R/L) IPS ISB, H-Anim37 Ilium—Pubic joint, anterior angle IPJ H-Anim38, 39 Ilium—Crest tubercle (R/L) ICT H-Anim40, 41 Femur—Greater trochanter (R/L) FTC H-Anim42, 43 Femur—Medial epicondyle (R/L) FME ISB, H-Anim44, 45 Femur—Lateral epicondyle (R/L) FLE ISB, H-Anim46, 47 Tibia—Apex of the medial malleolus (R/L) TAM ISB, H-Anim48, 49 Fibula—Apex of the lateral malleolus (R/L) FAL ISB, H-Anim50, 51 Foot/calcaneus—posterior surface (R/L) FCC H-Anim52, 53 Nipples (R/L) NIP None54 Navel NAV None55 Groin GRO None56, 57 Armpit (R/L) API None58, 59 Foot/phaleange head (R/L) FPH None60, 61 Upper root of ears (R/L) URE None62, 63 Lower root of ears (R/L) LRE None64, 65 Tip of the ear wings (R/L) TEW None66, 67 End of the lips (R/L) ELI None68 Crown of the head CRH None

sizes also had to be calculated for every iteration step. However,in our formulation, the body sizes of the model could be directlyobtained through the body size vector, which allowed the optimalsolution to be obtained in an analytic manner. Therefore, none ofthe iteration methods were needed to find the optimal solution,and the solution was obtained through a single matrix operation.Furthermore, in our formulation, the number and the types of con-straints could be modified without any restriction, and this thuscould implement a much more flexible modeling interface.

Despite such distinguishing aspects, there are still some futureworks that are necessary. The first thingmight be the developmentand implementation of a skin-deformation technique. The bodyshapemodel itself has some difficulties for application in the prod-uct design process, as the posture cannot bemodified. Therefore, toovercome such a limitation, the development and implementationof skin deformation is necessary.

As an extension of this study, we are currently working onthe implementation of such a modeling method through the CADapplication programming interface (API). Based on the SolidWorksplatform, we are developing a parametric modeling system and away of interacting with the product models. It is expected that alot of product design processes, especially for wearable products,will benefit from such an implementation.

Acknowledgement

This work was supported by the Korea Science and EngineeringFoundation (KOSEF) grant funded by the Korea government(MOST) (No. R11-2007-028-02001-0).

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