A new method for determining the personal constants in the Luneburg theory of binocular visual space

Hagino, Genichi; Yoshioka, Ichiro

doi:10.3758/bf03211218

Cited by 4 publications

(4 citation statements)

References 24 publications

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“…Clearly, σ is an increasing function of e 1 and | K | is larger for Q 1 at about 16 m (in a gymnasium) than for Q 1 of less than 5 m in the laboratory. Dependency of K upon { Q i } has also been reported by others (Ehrenstein, 1977; Hagino & Yoshioka, 1976; Higashiyama, 1981, 1984).…”

Section: Luneburg's Mapping Functionssupporting

confidence: 82%

“…It is an open question, however, whether the same gap would occur if Q4 and Q5 were set at a more natural position closer to the base and hence the interval between Q4 and Q5 were larger. Hagino and Yoshioka (1976) presented small light points QI at various positions on the x-axis and asked the 5 subjects to set Qs around each Q1 to form a perceptual circle on HZ(E). They analyzed the result according to Luneburg's model.…”

Section: W2o°smentioning

confidence: 99%

“…Hagino and Yoshioka (1976) presented small light points Q 1 at various positions on the x -axis and asked the 5 subjects to set Q s around each Q 1 to form a perceptual circle on HZ(E). They analyzed the result according to Luneburg's model.…”

Section: On Conditions That Lead To Rccmentioning

confidence: 99%

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A critical review of Luneburg's model with regard to global structure of visual space.

Indow¹

1991

Psychological Review

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Visual space (VS) is a coherent self-organized dynamic complex that is structured into objects, backgrounds, and the self. As a concrete example of geometrical properties in VS, experimental results on parallel and (equi) distance alleys in a frameless VS were reviewed, and Luneburg's interpretation on the discrepancy between these 2 alleys was sketched with emphasis on the 2 hypotheses involved: VS is a Riemannian space of constant curvature (RCC) and the a priori assumed correspondence between VS and the physical space in which stimulus points are presented. Dissociating these 2 assumptions, the author tried to see to what extent the global structure of VS under natural conditions is in accordance with the hypothesis of RCC and to make explicit the logic underlying RCC. Several open questions about the geometry of VS per se have been enumerated.

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Section: Luneburg's Mapping Functionssupporting

confidence: 82%

Section: W2o°smentioning

confidence: 99%

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A critical review of Luneburg's model with regard to global structure of visual space.

Indow¹

1991

Psychological Review

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“…Table 1 shows the values of parameters of δ = ad b and root mean squares (RMS) by applying the least square method to the perceived distance (δ) and the corresponding physical distance (d) for each angle condition (4, 8, 12, 16, and 20°). The anisotropic property in visual space was found in other studies (Foley, 1966;Hagino & Yoshioka, 1976;Higashiyama, 1992), but the important thing in the present finding is that the amount of anisotropy is larger in photographic space than in visual space. Figure 6 and Table 1 suggest that the amount of anisotropy in photographic space is larger than in visual space.…”

Section: Resultssupporting

confidence: 61%

Geometrical Structures of Photographic and Stereoscopic Spaces

Watanabe

2006

Span. J. Psychol.

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Two experiments were conducted to investigate the geometrical structures of photographic and stereoscopic spaces. In Experiment 1, it was investigated how accurately photographic space reproduces real physical space, and the geometrical structure of photographic space was compared with that of visual space. As a result, the mapping function of distance between photographic and physical spaces (δ = ad b ) shows that a and b range from 0.96-1.1 and 0.69-0.78. The mapping function of angle between photographic and physical spaces (Φ = gφ h ) shows that g and h range from 2.37-5.29 and 0.74-0.97. Further, photographic space has larger anisotropic property than visual space and photographic space may be hyperbolic. In Experiment 2, the geometrical structure of stereoscopic space was compared with that of visual space. It was found that stereoscopic space was almost the same as visual space. Keywords: depth perception, photograph, stereoscopic visionSe realizaron dos experimentos para investigar las estructuras geométricas de los espacios fotográficos y estereoscópicos. En el Experimento 1 se investigó la precisión con que el espacio fotográfico reproduce el espacio físico real, y se comparó la estructura geométrica del espacio fotográfico con la del espacio visual. Como resultado la función de correspondencia para la distancia entre los espacios fotográficos y los físicos (δ = ad b ) muestra que a y b varían entre 0.96-1.1 y 0.69-0.78. La función de correspondencia angular del ángulo entre los espacios fotográficos y los físicos (Φ = gφ h ) muestra que g y h varían entre 2.37-5.29 y 0.74-0.97. Además, el espacio fotográfico tiene una propiedad anisotrópica mayor que el espacio visual, y el espacio fotográfico podría ser hiperbólica. En el Experimento 2, se comparó la estructura geométrica del espacio estereoscópico con la del espacio visual. Se encontró que el espacio estereoscópico era casi igual que el espacio visual. Palabras clave: percepción de la profundidad, fotografía, visión estereoscópica

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Non-Riemannian approach to geometry of visual space: An application of affinely connected geometry to visual alleys and horopter

Yamazaki

1987

Journal of Mathematical Psychology

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A new method for determining the personal constants in the Luneburg theory of binocular visual space

Cited by 4 publications

References 24 publications

A critical review of Luneburg's model with regard to global structure of visual space.

A critical review of Luneburg's model with regard to global structure of visual space.

Geometrical Structures of Photographic and Stereoscopic Spaces

Non-Riemannian approach to geometry of visual space: An application of affinely connected geometry to visual alleys and horopter

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