Keywords

1 Introduction

Over the past few years, “digital style design” for various kinds of products has been widely applied due to the spread of a variety of CAD systems. On the other hand, those designs with high ergonomic assessment such as easy shape and comfortable user-interface for human grasp and operation, so called “human centered design”, have been receiving much more attention as this could enhance the market competitiveness of products. Current ergonomic evaluation processes require experiments based on a large number of various human subjects and a variety of physical mockups. These create bottlenecks in the product development cycle, are time consuming, have a high cost, and result in fewer implementations of ergonomic assessment. Thus, human models, digital models of various kinds of human, have been proposed to conduct the ergonomic assessment in a virtual environment. This virtual ergonomic assessment, integrating human models with product models, has a high possibility to produce ergonomic design quickly with less cost and its implementation has been highly anticipated.

Reconstruction of functional human models with arbitrary body shapes is the first step to conducting “virtual ergonomic assessment” in the process of human-centered product design. Thus far, we have proposed a reconstruction method of the human model and its postures for arbitrary individuals, conducted by inputting the trajectories of landmark points on the skin surface obtained from a motion capture system [1]. Though the human models obtained are accurate enough for our purpose, experiments with a motion capture system are too time-consuming and too expensive to be conducted for a plurality of real subjects.

In this paper, we describe a novel approach for reconstructing arbitrary whole-body human models from an arbitrary sparse set of anthropometric dimensions. Though this method adopts an approximate approach by referring to the large database for whole-body anthropometric dimensions, it can be conducted much faster than the previously-proposed method.

2 Definitions and Methods

2.1 Human Model Definition

Thus far, we have developed the human models, called “Dhaiba”, achieving the ergonomic assessment of products based on the precise simulation of various types of human size, shape and function in a virtual environment. The Dhaiba models include the “DhaibaBody”, whole body models, and the “DhaibaHand”, hand models (Fig. 1(a)(b)) [2].

Fig. 1.
figure 1

The Dhaiba models. (a) The male template model, (b) the female template model and (c) the model which changed its posture.

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Each Dhaiba model fundamentally contains the following three model elements:

  1. 1.

    A skin surface model consisting of as a triangular mesh which represents the skin surface in a reference posture.

  2. 2.

    A link model which includes a set of the local coordinate system of each joint and their connectivity as the links.

  3. 3.

    Each anthropometric dimension for the Dhaiba model is defined as the distance between two landmark vertices on the skin surface model. In some cases, the distances along the x/y/z-axis in the world coordinate system are used as the definition.

The posture of the Dhaiba model is controlled by rotating the joint angles of the link model. The “Skeletal Subspace Deformation (SSD)” algorithm is used for the deformation of the skin surface model by following the joint rotation [3], so as to represent the whole-body geometry for arbitrary postures (Fig. 1(c)).

2.2 Overview of the Method

Figure 2 shows an overview of the proposed method. Firstly, the user specifies an arbitrary set of whole-body dimensions for a target, which is a subset of a comprehensive set of the dimensions. Then, the comprehensive set of the dimensions for the target is estimated from the input and a large database for the set. Finally, the human model for the target including the skin surface model and the link model is constructed by an optimization method based on the control of the “link scales”.

Fig. 2.
figure 2

Overview of the proposed method.

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The details are described in the following sections.

2.3 Estimation of the Comprehensive Set of Anthropometric Dimensions

The system performs the following steps to estimate a comprehensive set of anthropometric dimensions for the target from the arbitrary subset of the dimensions for the target.

2.3.1 Preparation

A large database for the comprehensive set of the whole-body anthropometric dimensions is prepared. A large dense matrix D is defined, where D i,j , the (i, j)th entry of the D, represents the value of j-th dimension item for an i-th subject included in the database. Then a matrix X is calculated as the standardized matrix for the D:

$$ X_{i,j} = \frac{{D_{i,j} - \dot{a}_{j} }}{{\tilde{a}_{j} }} , $$
(1)

where \( \dot{a}_{j} \) and \( \tilde{a}_{j} \) is the mean and the standard deviation for the j-th column of the D respectively. Hereafter we denote i-th row vector of the D the dimension vector x i . The correlation matrix C is calculated as follows:

$$ C = \frac{1}{n - 1}X^{T} X , $$
(2)

where n is the number of the columns of the X. Then the coefficient matrix W is calculated as the set of the eigenvectors for the C:

$$ W = \left[ {{\mathbf{e}}_{1} \quad {\mathbf{e}}_{2} \; \ldots \;{\mathbf{e}}_{n} } \right] , $$
(3)

where \( {\mathbf{e}}_{1} , \ldots ,{\mathbf{e}}_{n} \) are the (column) eigenvectors related to the C. These vectors are sorted in descending order by their related eigenvalues.

2.3.2 Principal Component Analysis

By using the obtained matrix W, the dimension vector x = [x 1 x 2 … x n ]T can be mutually transformed into the n-dimensional column vector of the principal component scores z = [z 1 z 2 … z n ]T (the principal component vector) as follows:

$$ {\mathbf{z}} = W{\kern 1pt} {\dot{\mathbf{x}}} , $$
(4)
$$ {\dot{\mathbf{x}}} = W^{T} {\mathbf{z}} , $$
(5)

where \( {\mathbf{\dot{x} = }}\left[ {\dot{x}_{1} \,\dot{x}_{2} \, \ldots \,\dot{x}_{n} } \right]^{T} \) and \( \dot{x}_{j} = (x_{j} - \dot{a}_{j} )/\tilde{a}_{j} \).

2.3.3 Estimation of the Dimension Vector

Here, the user chooses several dimension items from the complete dimension set and specifies values for them. By using these arbitrary n s values in x, the first n s principal component scores can be estimated. For instance, in the case where n s  = 2 and the dimension item a and b are chosen as the subset, the approximate values of z 1 and z 2 are calculated as follows:

$$ \left[ {\begin{array}{*{20}c} {\dot{x}_{a} } \\ {\dot{x}_{b} } \\ \end{array} } \right] \cong \hat{W}\,\left[ {\begin{array}{*{20}c} {z_{1} } \\ {z_{2} } \\ \end{array} } \right] , $$
(6)

where

$$ \hat{W} = \left[ {\begin{array}{*{20}c} {(W^{T} )_{a,1} } & {(W^{T} )_{a,2} } \\ {(W^{T} )_{b,1} } & {(W^{T} )_{b,2} } \\ \end{array} } \right] . $$
(7)

Thus, the following equation is obtained:

$$ \left[ {\begin{array}{*{20}c} {z_{1} } \\ {z_{2} } \\ \end{array} } \right] \cong \hat{W}^{ - 1} \left[ {\begin{array}{*{20}c} {\dot{x}_{a} } \\ {\dot{x}_{b} } \\ \end{array} } \right] . $$
(8)

So, in this case, the approximate value of complete dimension vector x is calculated by Eqs. (5) and (8), where the other principal component scores z 3,…, z n are set to zero.

2.4 Construction of the Human Model

In this section, the Dhaiba model for the target is constructed from the Dhaiba model template, based on the dimension vector x obtained in the previous section.

2.4.1 The Dhaiba Model Template

Construction of the Dhaiba model template is the first step to carrying out the optimization process for constructing the Dhaiba model for the target described in the following sections.

Figure 1 (a) (b) shows the Dhaiba model templates reconstructed from a dense polygon soup obtained by a laser scanner. The Dhaiba model for the target is obtained by deforming one of the template model, so the skin surface model and the link model for the target are “homologous” with the ones for the template. That is, the following are common among all Dhaiba models respectively:

  1. 1.

    The number of vertices, faces and the topological structure of the skin surface models

  2. 2.

    The vertex index of each landmark on the skin surface models

  3. 3.

    The structure of the link models

2.4.2 Skin Surface Deformation Based on Link Scales

Once the Dhaiba model template is prepared, the shape of the template model can be dynamically changed by controlling the “link scales”.

The link scale \( s_{j,k} \) is defined as a variable for an axis k (\( k \in \{ + x, - x, + y, - y, + z, \) \( - z\} \)) of each joint j of the link model. Based on the link scales, the origin of the local coordinate system \( \varSigma_{j} \) for each joint j is updated as follows:

$$ {\mathbf{o^{\prime}}}_{j} = {}^{W}T^{\prime}_{j - 1} \,S(j,{\mathbf{o}}_{j} )\,\left( {{}^{W}T_{j - 1} } \right)^{ - 1} {\mathbf{o}}_{j} , $$
(9)

where o j  = [o jx o jy o jz 1]T is the position vector of the origin of the \( \varSigma_{j} \) and \( {\mathbf{o^{\prime}}}_{j} \) is the updated one. \( {}^{W}T_{j - 1} \) is the 4 × 4 matrix which transforms the world coordinate system into the local coordinate system \( \varSigma_{j - 1} \) (j−1 indicates the index of the parent joint of the j) and \( {}^{W}T^{\prime}_{j - 1} \) is the updated one. The 4th column vector of \( {}^{W}T_{j} \) is updated from \( {\mathbf{o}}_{j} \) to \( {\mathbf{o^{\prime}}}_{j} \) and \( {}^{W}T^{\prime}_{j} \) is obtained as the result. S(j, v) is the 4 × 4 scaling matrix defined as follows:

$$ S(j,{\mathbf{v}}) = \left[ {\begin{array}{*{20}c} {s_{{j,x^{\prime}}} } & {} & {} & O \\ {} & {s_{{j,y^{\prime}}} } & {} & {} \\ {} & {} & {s_{{j,z^{\prime}}} } & {} \\ O & {} & {} & 1 \\ \end{array} } \right],\;\;\left( {{\mathbf{v}} = [v_{x} \;v_{y} \;v_{z} \;1]^{T} } \right) , $$
(10)

where

$$ x^{\prime} = \left\{ {\begin{array}{*{20}c} x & {(v_{x} \ge 0)} \\ { - x} & {(v_{x} < 0)} \\ \end{array} } \right.,\quad y^{\prime} = \left\{ {\begin{array}{*{20}c} y & {(v_{y} \ge 0)} \\ { - y} & {(v_{y} < 0)} \\ \end{array} } \right.,\quad z^{\prime} = \left\{ {\begin{array}{*{20}c} z & {(v_{z} \ge 0)} \\ { - z} & {(v_{z} < 0)} \\ \end{array} } \right.. $$
(11)

On the other hand, the position of each vertex v on the skin surface model of the template is updated as follows:

$$ {\mathbf{v^{\prime}}} = \sum\limits_{j} {w_{v}^{j} \;{}^{W}T^{\prime}_{j} \;S(j,{}^{j}{\mathbf{v}})\left( {{}^{W}T_{j} } \right)^{ - 1} {\mathbf{v}}} , $$
(12)

where v is the position vector of the v and \( {\mathbf{v^{\prime}}} \) is the updated one. \( w_{v}^{j} \) is a vertex weight of v for the link bound to the joint j, which represents the degree of the relation between each vertex on the skin surface model and each link. This weight set is also used as the parameter of the skeletal subspace deformation method (a.k.a. the linear blend skinning) [3]. For calculation of the weight set, we use the skin attachment method based on heat equilibrium [3].

Figure 3 shows an example of the relation between the link scales, the modified link model and the deformed shape of the skin surface affected by the link scales.

Fig. 3.
figure 3

The effect of link scales in the human model deformation. (a) The original shape and (b) the deformed shape. In this case, the link scales for the +x (red) and the +y (green) axis of the root joint are set to 2.0.

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2.4.3 Optimization Method for Constructing the Target Human Model

By using the comprehensive set of anthropometric dimensions for the target obtained in Sect. 2.3, the system optimizes the body shape of the Dhaiba model template by controlling the link scales and obtains the Dhaiba model for the target. This nonlinear optimization problem is represented as follows:

  1. 1.

    The link scales for the link model of the Dhaiba model template are the variables. Based on the change of the link scales, each local coordinate system of the link model and each vertex position of the skin surface model is updated.

  2. 2.

    The comprehensive set of anthropometric dimensions obtained for the target should be satisfied as the constraints. As described in Sect. 2.1, each dimension is calculated as the distance between two landmark points on the skin surface model. Euclidean distance or the distance along x/y/z-axis is used as the definition of these distances. In this study, the following kinds of the dimensions are not used as the constraints: (1) dimensions which were not measured with the standard standing position and (2) ones which can not to be represented as linear distances.

  3. 3.

    The following energy function E is used as the objective function to be minimized:

$$ E = c_{S} E_{S} + c_{I} E_{I} + c_{V} E_{V} , $$
(13)

where c S , c I and c V are user-specified coefficients. E S and E I are the energy functions defined in the correspondence optimization algorithm [4]. E S , deformation smoothness, indicates that the transformations for adjacent triangles should be equal. E I , deformation identity, is minimized when all transformations are equal to the identity matrix. E V is the variance of the link scales.

3 Results and Discussion

An anthropometry database for Japanese adults collected in the national project called “size-JPN” in 2004–2006 [5] was used for the estimation of the comprehensive set of the anatomical dimensions, described in Sect. 2.3. This database includes results of the anthropometric measurements of 217 dimensions for 6,700 Japanese 18–80 year old subjects. Figure 4 shows distribution of the mean errors and the coefficients of variation of the estimated comprehensive set of dimensions. We picked up comprehensive sets of dimensions for 500 randomly chosen subjects from the database, and, by using the body height and the body mass of each set as the input, each comprehensive set of the dimensions was estimated from the method proposed in Sect. 2.3.

Fig. 4.
figure 4

Distribution of the mean errors and the coefficients of variation of the estimated comprehensive set of dimensions.

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Figures 5 and 6 shows the construction result of the Dhaiba models for several targets and their error distribution of the dimensions of the obtained models. The process described in Sects. 2.3–2.4 was done in 6–7 s for each target.

Fig. 5.
figure 5

Constructed Dhaiba models for several targets. Height and weight were specified for each construction as the input. Specified height was (a) 1800 mm, (b) 1700 mm, (c) 1600 mm and (d) 1500 mm. Specified weight was 67.93 kg, mean value of Japanese 30–34 year old males.

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Fig. 6.
figure 6

Mean errors and their standard deviations of the dimensions of the obtained models for the estimated dimensions (the input of the method described in Sect. 2.4).

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The method deforms the target mesh to satisfy the dimension constraints while keeping the details of the mesh shape, so the initial shape of the template model has a major effect on the result. Therefore constructing the appropriate template models is one of the critical issues for obtaining good results. In addition, there is a wide variety of individual whole-body shapes, so, though we currently use single template model for any target, we need to prepare several kinds of the template models and select an appropriate model suitable for the target shape.

4 Conclusions

In this paper, we proposed a novel approach for reconstructing arbitrary whole-body human models from an arbitrary sparse subset of anthropometric dimensions. The comprehensive set of dimensions was estimated from the subset via the principal component space for the dimensions. The skin surface model with the obtained comprehensive set of dimensions is constructed by the optimization of the shape of the whole-body human model template based on the link scales control.