舌の側面輪郭の2次曲線による近似

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The representation of tongue shape with a quadratic curve model was studied. The side profile of tongue is given by the coordinate system in Fig. 1. The procedures of fitting a quadratic curve to the data points by the use of the singular decomposition technique are expressed in Eqs. (1), (2), (3), (4), and (5). This is the quadratic curve model of adaptive version, and the most data can be approximated with this model with considerable accuracy. However, with this model, the accuracy declines in case of such consonants as /t/, /d/, /n/, /s/, or /z/. The features can be represented as the distortion of tongue shape from a shape-fixed quadratic curve. Fig. 2 shows the distributions of parameters of an adaptive quadratic curve. The shape-fixed quadratic curve is given as the curve with the average value of the parameters in Fig. 2. The shape-fixed curve is fitted to the data of these consonants by means of variable metric method illustrated in Fig. 4. Fig. 5 shows an example of conversion. Each residual can be calculated as the deformation from the curve. Fig. 6 shows two typical examples of the residuals successively calculated in the respective frames of /t/ and /d/. Fig. 7 shows the eigenvectors and the loci of components in a_1-a_2 space obtained from the principle component analysis of tongue blade residuals. Similar results are obtained from the analysis of tongue root residuals and the synthetic analysis of blade and tongue root residuals, as are shown in Figs. 8 and 9, respectively. From the results, it is seen that the main part of the synthetic residuals of tongue blade and tongue root is taken by the blade residuals. The cross-correlation coefficients of seven representative points of tongue blade to all other points of tongue surface are plotted in Fig. 10, and the canonical correlation coefficients between blade and root are shown in Fig. 11. It is interpreted that these two figures show the deep interrelation between the blade and root of tongue. Next, main component analysis was applied to the tongue surface vector of 14 demensions defined by the coordinate system in Fig. 1, and their eigenvectors are shown in Fig. 12. Fig. 13 shows the loci of the principal components of tongue vector in contrast to the loci of curvature center of the shape-fixed curve. By comparing these two, the underlying relationship between them is obvious. Finally, the accuracy of these tongue models was compared in terms of S/D ratios and contribution rate (%), and the result is shown in Table 1. Fig. 14 shows the typical examples of tongue profiles approximated by various versions. As the of the quadratic curve model. Subject of this research for future from practical point of view the identification of quadratic curves by acoustia analysis remains.
社団法人日本音響学会の論文
1978-03-01

舌の側面輪郭の2次曲線による近似

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