Geometrical-optical illusion

Geometrical-optical illusions are visual illusions, also optical illusions, in which the geometrical properties of what is seen differ from those of the corresponding objects in the visual field.

In studying geometry one concentrates on the position of points and on the length, orientation and curvature of lines. Geometrical-optical illusions then relate in the first instance to object characteristics as defined by geometry. Though vision is three-dimensional, in many situations depth can be factored out and attention concentrated on a simple view of a two-dimensional tablet with its x and y co-ordinates. '

Whereas their counterparts in the observer's object space are public and have measurable properties, the illusions themselves are private to the observer's (human or animal) experience. Nevertheless, they are accessible to portrayal by verbal and other communication and even to measurement by psychophysics. A nulling technique is particularly useful in which a target is deliberately given an opposing deformation in an effort to cancel the illusion.

Visual or Optical Illusions can be categorized according to the nature of the difference between objects and percepts. For example, these can be in brightness or color, called intensive properties of targets, e.g. Mach bands. Or they can be in their location, size, orientation or depth, called extensive. When an illusion involves properties that fall within the purview of geometry it is geometrical-optical, a term given to it in the first scientific paper devoted to the topic by J.J. Oppel, a German high-school teacher, in 1854. It was taken up by W. Wundt, widely regarded as the founder of experimental psychology, and is now universally used, see the several comprehensive treatises devoted to the subject. That by 1972 the first edition of Robinson's book devotes 100 closely printed pages and over 180 figures to these illusions attests to their popularity.

The easiest to explore are the geometrical-optical illusions that show up in ordinary black and white line drawings. A few examples are drawn from the list of optical illusions. They illustrate illusions of position (Poggendorff illusion), of length (Müller-Lyer illusion), of orientation (Zöllner illusion, Münsterberg illusion or shifted-chess-board illusion and its café wall illusion variant), of rectilinearity or straightness of lines (Hering illusion), of size (Delboeuf illusion) and of vertical/horizontal anisotropy (Vertical-horizontal illusion), in which the vertical extension appears exaggerated.

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