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One-Dimensional and Multi-Dimensional Studies of the Exocentric Distance Estimates in Frontoparallel Plane, Virtual Space, and Outdoor Open Field

  • J. Antonio Aznar-Casanova (a1), Elton H. Matsushima (a2), Nilton P. Ribeiro-Filho (a3) and José A. Da Silva (a4)


The aim of this study is twofold: on the one hand, to determine how visual space, as assessed by exocentric distance estimates, is related to physical space. On the other hand, to determine the structure of visual space as assessed by exocentric distance estimates. Visual space was measured in three environments: (a) points located in a 2-D frontoparallel plane, covering a range of distances of 20 cm; (b) stakes placed in a 3-D virtual space (range ≈ 330 mm); and (c) stakes in a 3-D outdoors open field (range = 45 m). Observers made matching judgments of distances between all possible pairs of stimuli, obtained from 16 stimuli (in a regular squared 4 × 4 matrix). Two parameters from Stevens' power law informed us about the distortion of visual space: its exponent and its coefficient of determination (R2). The results showed a ranking of the magnitude of the distortions found in each experimental environment, and also provided information about the efficacy of available visual cues of spatial layout. Furthermore, our data are in agreement with previous findings showing systematic perceptual errors, such as the further the stimuli, the larger the distortion of the area subtended by perceived distances between stimuli. Additionally, we measured the magnitude of distortion of visual space relative to physical space by a parameter of multidimensional scaling analyses, the RMSE. From these results, the magnitude of such distortions can be ranked, and the utility or efficacy of the available visual cues informing about the space layout can also be inferred.

En este estudio se pretendía cubrir un doble objetivo. Por un lado, determinar cómo el espacio visual, evaluado en términos de estimaciones de distancias exocéntricas, se corresponde con el espacio físico. Y, por otro lado, determinar la estructura del espacio visual a partir de las mismas estimaciones de distancias. Para ello, registramos la respuesta (métrica) de los observadores en tres entornos espaciales: (a) puntos localizados en un plano 2-D (frontoparalelo) en un rango de distancias de 20 cm; (b) estacas vistas esteroscopicamente y situadas en un espacio virtual 3-D (rango de 33 cm); y (c) estacas físicas dispuestas en un espacio abierto exterior (rango de 45 m). Los observadores hicieron juicios de emparejamiento de distancias entre todos los posibles pares que se podían formar con 16 estacas (dispuestas en una matriz cuadrada regular de 4 filas × 4 columnas). Utilizamos dos parámetros de la ley potencial de Stevens, que nos informaron de la distorsión percibida del espacio visual: el exponente y el coeficiente de determinación (R2). Los resultados permitieron ordenar la magnitud de la distorsión encontrada en cada entorno experimental, proporcionando información sobre la utilidad y eficacia de las claves de profundidad disponibles. Nuestros datos concuerdan con los obtenidos en estudios previos en mostrar una cierta anisotropía espacial que difiere en cada entorno. Adicionalmente, aplicamos el escalamiento multidimensional y medimos la distorsión a través del RECM, lo que también nos permitió ordenar la magnitud de las distorsiones en cada contexto, así como la eficacia de las claves visuales de distancia.


Corresponding author

Correspondence concerning this article should be addressed to J. Antonio Aznar-Casanova, Department of Basic Psychology, Faculty of Psychology, University of Barcelona, Passeig Vall d'Hebron, 171, 08035-Barcelona (SPAIN). Tel: +34 93 312 51 45. Fax: +34 93 402 13 63. e-mail:


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One-Dimensional and Multi-Dimensional Studies of the Exocentric Distance Estimates in Frontoparallel Plane, Virtual Space, and Outdoor Open Field

  • J. Antonio Aznar-Casanova (a1), Elton H. Matsushima (a2), Nilton P. Ribeiro-Filho (a3) and José A. Da Silva (a4)


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