THE RELATION BETWEEN BINOCULAR VISUAL SPACE AND PHYSICAL SPACE

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  • 両眼視空間と物理的空間との対応関係
  • リョウ ガンシ クウカン ト ブツリテキ クウカン ト ノ タイオウ カンケイ mapping function ニ ツイテ
  • AN EXPERIMENTAL STUDY OF MAPPING FUNCTIONS
  • mapping functionについて

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The aim of this paper was to test experimentally the mapping functions in the Luneburg's model. In particular, Eq. (1) and (3) were explored in detail.<br>ψ=φ (1)<br>ϑ=θ (2)<br>ρ=2e-σγ (3)<br>where ψ, ϑ and ρ respectively denote an azimuth angle, an angle of elevation, a radial distance in the Euclidean map. φ, θ and γ respectively denote a bipolar azimuth, an angle of elevation, a bipolar parallax in the physical space. Six Ss participated in the experiment. In a dark room, three light points were presented on the plane of given θ; F was fixed on the line φ=0 and I was fixed at the position of a given φ (Fig. 2). The S was asked to adjust Ij so as to match its azimuth angle to that of I. For a given I, Ij was presented with 3-6 different radial distances. If Eq. (1) holds, then the adjusted positions of Ij are to be on the same straight line of the given angle φ. In so far as 1 is fixed, Ij were found to be on the same straight line irrespective of the radial distance and also of θ. However, the straight line was not the one expected in all the case of I having different values in φ. Either a set of straight lines converging to a point on the y axis or a set of straight lines converging to a point on the x axis can be fitted to the data (Fig. 3). The S was also asked to assess the apparent radial distance to Ij in terms of ratio to the apparent radial distance to I or to F. Let dIj be the scaled radial distance. As a function of γ, dIj was found to be not in the form of Eq. (3) (Fig. 7 (A) (B)). Then, the relation between the apparent radial distance dIj and the radial distance ρ on the Euclidean map was made explicit for the various values of K, that is, Gaussian curvature of the visual space (Fig. 6). Through the relationship, dIj was converted to ρ and still it was found that ρ is not related with γ as is assumed in Eq. (3) (Fig. 7 (C) (D)). It became clear, however, the data are fitted irrespective of φ and θ by the equation<br>ρ-ρ0=2e-σγ (4)<br>as is shown in Fig. 8. The value of σ estimated through Eq. (4) was too large compared with the value obtained in previous studies by the 3- and 4-point experiments and the alley experiments.

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