Vol.1 No.1 2008

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Research paper : Technologies for the design and retail service of well-fitting eyeglass frames (M. Mochimaru, et al.)−41−Synthesiology - English edition Vol.1 No.1 (2008) and cameras were carefully located in order to reduce the occlusion of regions such as under the chin, under the nose and back of the ear. Using this system, the head shapes of 52 Japanese males (18-35 yr) were measured. The obtained data consists of millions surface data points, RGB color information of the data points, and around 80 anatomical landmarks (Figure 3(a)). A homologous head model without the external ears consisting of 485 vertices and 838 polygons was then generated (Figure 3(b)).3.2 Size variation design[4]Conventional eyeglass frames vary in size. The sizing method is very simple; lens width and temple length are changed in proportion. The sizing method does not represent variations in the human face. Thus, we designed a new sizing system that could effectively cover the variations in the human face using a mid-facial homologous shape model consisting of 211 vertices (Figure 4). As mentioned in Section 3.1, PCA can compress information on shape variation. However, PCA is not efficient enough for grouping subjects because it is based on linear transformation. Therefore, we used the multi-dimensional scaling method (MDS). The inter-individual shape distance was defined by the following formula:Dij = | Ti - Tj |where, Ti indicates the vertices vector of i-th subject and Tj indicates that of j-th subject. The inter-individual distance Dij is calculated from the summation of the Euclidean distances between the corresponding vertices. When the number of subject is m, the distance matrix (m × m) of inter-individual shape distances is calculated. By analyzing the distance matrix using MDS, the location of each subject is assigned in a low-dimensional space. The fit of the model is evaluated using RSQ, the squared correlation coefficient between elements of original distance matrix and elements of the distance matrix calculated from the obtained low-dimensional solution.Analyzing the variation in mid-facial shapes by MDS, the coefficient of determination (RSQ) was 0.95 for the 5-dimensional solution, whereas at least 15 principal components are needed to explain 95 % of the total variance. Figure 5 shows the distribution map of the subjects based on the scores for the 1st and the 2nd scales of the MDS. The obtained MDS scales were interpreted using correlation coefficients between the MDS scores and facial dimensions. The 1st scale was related to the face size, particularly the depth, and the 2nd scale to the face width and the inclination of the face. These two scales account for 83 % of the variation in the Japanese face. The 3rd scale was related to shape of the nose, and the 4th scale to the proportion between the face width and the interpupillary distance. The 3rd and the 4th scales are not strongly related to fitting of the eyeglass frames.We decided to develop 4 eyeglass frame sizes considering profitability of manufacturing and distribution. Four size groups were defined as shown in Figure 5; namely subjects were divided into 3 groups based on the scores for the 1st scale representing the size, and the mid-size group was divided into two groups based on scores for the 2nd scale. The average face shape to represent the size group was calculated for each group. Well-fitting eyeglass frames were designed and manufactured based on the average face by the collaborating company (Figure 6).In order to validate the fitting of new eyeglass frames, 38 male subjects were recruited (average age, 24.5 yr). For each subject, the location in the MDS distribution map (Figure 5) was estimated by multiple regression based on 15 facial dimensions, and the size group was determined. New frames for the 4 size groups and a conventional frame of the same style design were used for the validation study. The tightening force and the slip range after the subject shook the head were measured. Sensory evaluation of fitting was also conducted using a 5-point scale rating. New frames of the Fig. 4 Homologous model for the middle faceFig. 5 Distribution of middle face shapes in 52 young adult male JapaneseFig. 6 Preproduction sample of eyeglass frame using the new sizing system

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