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An Empirical Test of Formal Equivalence between Emmert's Law and the Size-Distance Invariance Hypothesis

Published online by Cambridge University Press:  10 April 2014

Mariko Imamura  and
Sachio Nakamizo
Mariko Imamura
Affiliation:
Kyushu University, Japan
Sachio Nakamizo*
Affiliation:
Kyushu University, Japan
*
Correspondence concerning this article should be sent to Sachio Nakamizo. Department of psychology, Faculty of Human-Environment Studies, Kyushu University, 9-19-1, Hakozaki, Higashik, Fukuoka, Japan. Tel & Fax: +81-92-642-2416. E-mail: [email protected]
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Abstract

Emmert's law and the size-distance invariance hypothesis have been said to be formally equivalent, provided that Emmert's law means that the perceived size of an afterimage is proportional to the perceived distance of the projected surface of the afterimage. However, there have been very few studies that have attempted to verify this formal equivalence empirically. We measured both the perceived size and distance of afterimages and real objects with the same proximal size. Nineteen participants projected afterimages of 1 deg in visual angle on the wall located at distances of 1 to 23 meters from the participants. They also observed real objects, disc-shaped and made from a sheet of Styrofoam board, with the same proximal size as that of the afterimages, which were located at the same physical distances as those of the wall on which the afterimages were projected. Each participant reproduced the apparent sizes of the afterimages and real objects using the reproduction method and estimated the apparent distances using the magnitude estimation method. When the mean apparent sizes of the afterimages and real objects, represented as a function of apparent distance, were fitted to a linear function, the slopes for the afterimages and real objects did not differ significantly. These results are interpreted as evidence for the formal equivalence of Emmert's law and the size-distance invariance hypothesis.

Es común considerar a la ley de Emmert y la hipótesis de la invarianza del tamaño-distancia como equivalentes formalmente. Para llegar a esta conclusión se parte de considerar que, al aplicar la ley de Emmert, el tamaño percibido de la postimagen es proporcional a la distancia percibida de la superficie en la que se proyecta. A pesar de lo anterior, muy pocos estudios han intentado verificar empíricamente esta equivalencia formal. En este trabajo se midió tanto el tamaño percibido como la distancia de postimágenes y de objetos reales con el mismo tamaño proximal. 19 participantes proyectaron postimágenes con un ángulo visual de 1 grado sobre una pared de 1 a 23 metros respecto a los participantes. Estos también observaron objetos reales, en forma de discos, hechos de una plancha de espuma Styrofoam, con el mismo tamaño proximal que el de las postimágenes, que se colocaron a las mismas distancias físicas que las de la pared sobre la que se proyectaron las postimágenes. Cada participante reprodujo los tamaños aparentes de las postimágenes y de los objetos reales usando el método de reproducción y estimó las distancias aparentes empleando el método de estimación de magnitudes. Cuando los tamaños medios aparentes de las postimágenes y de los objetos reales, representados en función de la distancia aparente, se ajustaron a una función lineal, las pendientes de las postimágenes y de los objetos reales no diferían significativamente. Estos resultados se interpretan como evidencia para la equivalencia formal de la ley de Emmert y la hipótesis de la invarianza del tamaño-distancia.

Keywords

Emmert's lawsize-distance invariance hypothesisafterimagesize perceptiondistance perceptionLey de Emmerthipótesis de la invarianza tamaño-distanciapostimagenpercepción del tamañopercepción de la distancia
Type
Monographic Section: Spatial Vision and Visual Space
Information
The Spanish Journal of Psychology , Volume 9 , Issue 2 , November 2006 , pp. 295 - 299
Copyright
Copyright © Cambridge University Press 2006

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