Geometrical illusions are not always where you think they are: a review of some classical and less classical illusions, and ways to describe them

Abstract

Geometrical illusions are known through a small core of classical illusions that were discovered in the second half of the nineteenth century. Most experimental studies and most theoretical discussions revolve around this core of illusions, as though all other illusions were obvious variants of these. Yet, many illusions, mostly described by German authors at the same time or at the beginning of the twentieth century have been forgotten and are awaiting their rehabilitation. Recently, several new illusions were discovered, mainly by Italian authors, and they do not seem to take place into any current classification. Among the principles that are invoked to explain the illusions, there are principles relating to the metric aspects (contrast, assimilation, shrinkage, expansion, attraction of parallels) principles relating to orientations (regression to right angles, orthogonal expansion) or, more recently, to gestalt effects. Here, metric effects are discussed within a measurement framework, in which the geometric illusions are the outcome of a measurement process. There would be a main “convexity” bias in the measures: the measured value m(x) of an extant x would grow more than proportionally with x. This convexity principle, completed by a principle of compromise for conflicting measures can replace, for a large number of patterns, both the assimilation and the contrast effects. We know from evolutionary theory that the most pertinent classification criteria may not be the most salient ones (e.g., a dolphin is not a fish). In order to obtain an objective classification of illusions, I initiated with Kevin O'Regan systematic work on “orientation profiles” (describing how the strength of an illusion varies with its orientation in the plane). We showed first that the Zöllner illusion already exists at the level of single stacks, and that it does not amount to a rotation of the stacks. Later work suggested that it is best described by an “orthogonal expansion”—an expansion of the stacks applied orthogonally to the oblique segments of the stacks, generating an apparent rotation effect. We showed that the Poggendorff illusion was mainly a misangulation effect. We explained the hierarchy of the illusion magnitudes found among variants of the Poggendorff illusion by the existence of control devices that counteract the loss of parallelism or the loss of collinearity produced by the biased measurements. I then studied the trapezium illusion. The oblique sides, but not the bases, were essential to the trapezium illusion, suggesting the existence of a common component between the trapezium and the Zöllner illusion. Unexpectedly, the trapeziums sometimes appeared as twisted surfaces in 3d. It also appeared impossible, using a nulling procedure, to make all corresponding sides of two trapeziums simultaneously equal. The square-diamond illusion is usually presented with one apex of the diamond pointing toward the square. I found that when the figures were displayed more symmetrically, the illusion was significantly reduced. Fur...

Geometrical features underlying the perception of collinearity

“…It is not understood how the visual system makes elementary geometrical constructions, such as measuring the collinearity of separated line segments (Morgan, 1999, Ninio, 2014 We should not be surprised, then, that we also fail to understand the causes of biases in perceived collinearity, such as the bias shown in the famous Poggendorff figure (Fig. 1).…”

Analiza podatności na złudzenia wzrokowe ze względu na zależność od pola i płeć

“…Efekt ten jest wyjaśniany procesami kontrastowania wielkości przedmiotów (relative size comparisons, Künnapas, 1955;Aglioti, DeSouza, Goodale, 1995). Ninio (2014) zalicza to złudzenie do typowo metrycznych, bowiem wymaga oszacowania wielkości okręgów.…”

“…Z przeglądu literatury (Gregory, 2005;Ninio, 2014) wynika, że dotychczas nie udało się opracować jednej, spójnej kategorii złudzeń, nie ma także jednej teorii wyjaśniającej złudzenia wzrokowe. Badacze często odwołują się do teorii filtru Ginsburga (1984) oraz teorii stałości przechylenia The Tilt-Constancy Theory (Prinzmetal, Beck, 2001;Prinzmetal, Shimamura, Mikolinski, 2001).…”

“…W ostatniej dekadzie pojawiło się wiele prac analizujących złudzenia wzrokowe zarówno od strony poznawczej (Gregory, 2005;Króliczak, 1999Króliczak, , 2002Ninio, 2014;Prinzmetal, Beck, 2001;Bednarek, 2011 -dla przeglądu), jak i neuropsychologicznej (Karmiloff-Smith, 2007;Milner, Goodale, 2008;Walter, Dassonville, 2008).…”

“…Niektórzy badacze (Ninio, 2014) wyróżniają złudzenia, u podstaw których leżą zasady metryczne (np. ocena rozmiaru czy wagi obiektów) i orientacyjne.…”