Geometrical illusions are not always where you think they are: a review of some classical and less classical illusions, and ways to describe them - Ninio, Jacques (Frontiers in Human Neuroscience, 2014)
Geometrical illusions are known through a small core of classical illusions that were discovered in the second half of the 19th 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 20th 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. It is possible to oppose, to many a classical stimulus, an illusion that apparently contradicts the lesson derived from this stimulus. Furthermore, some well-known illusory patterns may not be illusions at all, they capture legitimate paradoxes of shape perception. 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 mammal). 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