Geometrical-optical illusions are
visual illusions
Within visual perception, an optical illusion (also called a visual illusion) is an illusion caused by the visual system and characterized by a visual percept that arguably appears to differ from reality. Illusions come in a wide variety; thei ...
, also
optical illusions
Within visual perception, an optical illusion (also called a visual illusion) is an illusion caused by the visual system and characterized by a visual percept that arguably appears to differ from reality. Illusions come in a wide variety; thei ...
, in which the geometrical properties of what is seen differ from those of the corresponding objects in the visual field.
Geometrical properties
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.'
Illusions are in visual space
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
Psychophysics quantitatively investigates the relationship between physical stimuli and the sensations and perceptions they produce. Psychophysics has been described as "the scientific study of the relation between stimulus and sensation" or, m ...
. A nulling technique is particularly useful in which a target is deliberately given an opposing deformation in an effort to cancel the illusion.
Categories of visual illusions
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
Mach bands is an optical illusion named after the physicist Ernst Mach. It exaggerates the contrast between edges of the slightly differing shades of gray, as soon as they contact one another, by triggering edge-detection in the human visual s ...
. 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
Wilhelm Wundt
Wilhelm Maximilian Wundt (; ; 16 August 1832 – 31 August 1920) was a German physiologist, philosopher, and professor, known today as one of the fathers of modern psychology. Wundt, who distinguished psychology as a science from philosophy and ...
, widely regarded as the founder of experimental psychology, and is now universally used. 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.
Examples of geometrical-optical Illusions
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
The Müller-Lyer illusion is an optical illusion consisting of three stylized arrows. When viewers are asked to place a mark on the figure at the midpoint, they tend to place it more towards the "tail" end. The illusion was devised by Franz Carl ...
), of orientation (
Zöllner illusion
The Zöllner illusion is an optical illusion named after its discoverer, German astrophysicist Johann Karl Friedrich Zöllner. In 1860, Zöllner sent his discovery in a letter to physicist and scholar Johann Christian Poggendorff, editor of ''Anna ...
,
Münsterberg illusion or shifted-chess-board illusion and its
café wall illusion
The café wall illusion is a geometrical-optical illusion in which the parallel straight dividing lines between staggered rows with alternating dark and light "bricks" appear to be sloped, not parallel as they really are.
It was first described u ...
variant), of rectilinearity or straightness of lines (
Hering illusion
The Hering illusion is one of the geometrical-optical illusions and was discovered by the German physiologist Ewald Hering in 1861. When two straight and parallel lines are presented in front of radial background (like the spokes of a bicycle), t ...
), of size (
Delboeuf illusion
The Delboeuf illusion is an optical illusion of relative size perception: In the best-known version of the illusion, two discs of identical size have been placed near to each other and one is surrounded by a ring; the surrounded disc then appears ...
) and of vertical/horizontal anisotropy (
Vertical-horizontal illusion), in which the vertical extension appears exaggerated.
Related phenomena
Visual illusions proper should be distinguished from some related phenomena. Some simple targets such as the
Necker Cube
The Necker cube is an optical illusion that was first published as a Rhomboid in 1832 by Swiss crystallographer Louis Albert Necker. It is a simple wire-frame, two dimensional drawing of a cube with no visual cues as to its orientation, so it c ...
are capable of more than one interpretation, which are usually seen in alternation, one at a time. They may be called ambiguous configurations rather than illusion, because what is seen at any time is not actually illusory. The configurations of the
Penrose or
Escher type are illusory in the sense that only on a detailed logical analysis it becomes apparent that they are not physically realizable. If one thinks of an ''illusion'' as something out there that is misinterpreted, and of a ''delusion'' when a demonstrable substrate is lacking, the distinction breaks down for such effects as the
Kanizsa triangle
Illusory contours or subjective contours are visual illusions that evoke the perception of an edge without a luminance or color change across that edge. Illusory brightness and depth ordering often accompany illusory contours. Friedrich Schumann i ...
and ''
illusory contours
Illusory contours or subjective contours are visual illusions that evoke the perception of an edge without a luminance or color change across that edge. Illusory brightness and depth ordering often accompany illusory contours. Friedrich Schumann i ...
.''
Explanations
Explanations of geometrical-optical illusion are based on one of two modes of attack:
* the ''physiological'' or ''bottom-up,'' seeking the cause of the deformation in the eye's optical imaging or in signal misrouting during neural processing in the retina or the first stages of the brain, the primary visual cortex, or
* the ''cognitive'' or ''perceptual'', which regards the deviation from true size, shape or position as caused by the assignment of a percept to a meaningful but false or inappropriate object class.
The first stage in the operations that transfer information from a visual target in front of an observer into its neural representation in the brain and then allow a percept to emerge, is the imaging by the eye and the processing by the neural circuits in the retina. Some components of geometrical-optical illusions can be ascribed to aberrations at that level. Even if this does not fully account for an illusion, the step is helpful because it puts elaborate mental theories in a more secure place. The
moon illusion is a good example. Before invoking concepts of apparent distance and
size constancy Subjective constancy or perceptual constancy is the perception of an object or quality as constant even though our sensation of the object changes. While the physical characteristics of an object may not change, in an attempt to deal with the extern ...
, it helps to be sure that the retinal image hasn't changed much when the moon looks larger as it descends to the horizon.
Once the signals from the retina enter the visual cortex, a host of local interactions are known to take place. In particular, neurons are tuned to target orientation and their response are known to depend on context. The widely accepted interpretation of, e.g. the Poggendorff and Hering illusions as manifestation of expansion of acute angles at line intersections, is an example of successful implementation of a "bottom-up," physiological explanation of a geometrical-optical illusion.
However, almost all geometrical optical illusions have components that are at present not amenable to physiological explanations. The subject, therefore, is a fertile field for propositions based in the disciplines of perception and cognition. To illustrate: Instead of interpreting them as just a pair the sloping lines within which one feature is seen smaller than an identical one nearer to the point of convergence, the Ponzo pattern may be taken for a railroad track rendered as a
perspective drawing. A barrel lying within the rails would have to be physically wider to cover the increased portion of the width of the track if it were farther away. The consequence is the judgment that the barrels differ in diameter, whereas their physical size in the drawing is equal.
A scientific study will include the recognition that a representation of the visual word is embodied in the state of the organism's nervous system at the time the illusion is experienced. In the discipline of experimental neuroscience, a top-down influence has the meaning that signals originating in higher neural centers, repository of memory traces, innate patterns and decision operations, travel down to lower neuronal circuits where they cause a shift of the excitation balance in the deviated direction. Such a concept is to be distinguished from the bottom-up approach which would look for aberrations that are imposed on the input in its path through the sensory apparatus. Top-down neural signaling would be a fitting implementation of the
gestalt
Gestalt may refer to:
Psychology
* Gestalt psychology, a school of psychology
* Gestalt therapy, a form of psychotherapy
* Bender Visual-Motor Gestalt Test, an assessment of development disorders
* Gestalt Practice, a practice of self-exploration ...
concept enunciated by
Max Wertheimer
Max Wertheimer (April 15, 1880 – October 12, 1943) was an Austro-Hungarian psychologist who was one of the three founders of Gestalt psychology, along with Kurt Koffka and Wolfgang Köhler. He is known for his book, ''Productive Thinking'', and f ...
that the "properties of any of the parts are determined by the intrinsic structural laws of the whole."
Mathematical transformation
When objects and associated percepts, in their respective spaces, correspond to each other albeit with deformations describable in terms of geometry, the mathematically inclined are tempted to search for transformations, perhaps non-Euclidean, that map them on each other. Application of differential geometry has so far not been notably successfu
; the variety and complexity of the phenomena, significant differences between individuals and dependence on context, previous experience and instruction set a high bar for satisfying formulations.
[Westheimer, G. (2008) "Geometrical-optical illusions and the neural representation of space". ''Vision Res'', 48, 2128-2142]
See also
*
Visual illusions
Within visual perception, an optical illusion (also called a visual illusion) is an illusion caused by the visual system and characterized by a visual percept that arguably appears to differ from reality. Illusions come in a wide variety; thei ...
*
List of optical illusions
*
Richard Gregory
Richard Langton Gregory (24 July 1923 – 17 May 2010) was a British psychologist and Professor of Neuropsychology at the University of Bristol.
Life and career
Richard Gregory was born in London. He was the son of Christopher Clive Langton ...
References
External links
Remapping object space to visual space
{{Optical illusions
Vision
Eye
Perception
Optical illusions