Geometrical illusions: study and modelling

Abstract

The phenomena of geometrical illusions of extent suggest that the metric of a perceived field is different from the metric of a physical stimulus. The present study investigated the Müller-Lyer and Oppel-Kundt illusions as functions of spatial parameters of the figures, and constructed a neurophysiological model. The main idea of the modelling is based on the uncertainty principle, according to which distortions of size relations of certain parts of the stimulus, so-called geometrical illusions, are determined by processes of spatial filtering in the visual system. Qualitative and quantitative agreement was obtained between psychophysical measurement of the strength value of the illusions and the predictions of our model.

An effect of continuous contextual filling in the filled‑space illusion

“…In our previous seeking of underlying principles behind the misperception of extent (Bulatov et al 1997, Bulatov and Bertulis 1999, the main attention was drawn to the cortical processes of spatial-frequency filtering. Since the computational procedures of the current model represent some calculations of convolution and spatial integration, it can be considered as a further development of the "filtering" hypothesis.…”

“…It has been demonstrated that a stimulus with a certain number of evenly allocated identical fillers induces a considerably stronger illusion than that with an irregular distribution (Lewis 1912, Noguchi 2003 or with many fillers fused into one continuous unit (Bailes 1995, Bertulis andBulatov 2001). At the same time, the region of the illusion maximum was relatively flat and varied between studies: the greatest effect was found for the number of fillers from 11 to 23 (Spiegel 1937), 9 to 14 (Piaget and Osterrieth 1953), 4 to 13 (Bulatov et al 1997), 11 to 13 (Wackermann and Kastner 2010), and 8 to 12 (Mikellidou and Thompson 2014). If the stimulus elements differed in shape or size then the effect of the illusion was substantially diminished (Obonai 1954, Wackermann and Kastner 2009, Wackermann 2012a.…”

“…During this period, various modifications of stimuli have been used in a great number of investigations aimed to identify the principal parameters governing the effect of the illusion. The studies resulted in a more or less broad consensus that the most relevant factors determining the illusion magnitude are the uniformity of the contextual filling elements (fillers) and the density of their distribution (Obonai 1933, Coren et al 1976, Noguchi et al 1990, Bulatov et al 1997, Deregowski and McGeorge 2006, Wackermann and Kastner 2010, Giora and Gori 2010. It has been demonstrated that a stimulus with a certain number of evenly allocated identical fillers induces a considerably stronger illusion than that with an irregular distribution (Lewis 1912, Noguchi 2003 or with many fillers fused into one continuous unit (Bailes 1995, Bertulis andBulatov 2001).…”

“…According to the "contour density" hypothesis (Craven andWatt 1989, Watt 1990), the number of zero-crossings of the spatial profile of neural excitation caused by the filled part of the Oppel-Kundt figure can be one of the most important factors determining the illusion magnitude. A rather adequate description of illusory effects was obtained from the computational model seeking to explain the misperception of extent in terms of physiological (i.e., based on the spatial properties of the receptive fields of neurons in the primary visual cortex) spatial-frequency filtering (Bulatov et al 1997, Bulatov and Bertulis 1999, as well as from the quantitative approach that explains the illusion occurrence by internal noises in the neural networks (Fermüller and Malm 2004).…”

Contrasting Three Popular Explanations for the Muller-Lyer Illusion

“…So, the inward-pointing arrowheads have large inter-tip distances that "stretch" the perceived line length and the outward-pointing arrowheads have small inter-tip distances, compressing the perceived line length. This is not the only such explanation put forth for Muller-Lyer that implies a perceptual 'stretching' of the fins-in and 'compression' of the fins-out (for example, Bulatov et al (1997) spatial filter model, or Findlay (1982 'center of gravity' for alternatives). The work presented here is not intended to specifically test between these various alternatives, since for the most part, they will make similar predictions for the stimulus configurations employed.…”