Emmert's law

The Emmer Paget's law describes a quantitative relationship between the image size of an object on the retina , its distance and the perceived size.

Emil Emmert (1844–1911) discovered it in 1881. He experimented with afterimages and realized that, despite the unchanged size on the retina, their perceived size changed proportionally to the distance of the background viewed. This knowledge can be applied to the perception of size in general. The context is:

${\displaystyle G=k\cdot w\cdot e}$

Where G is the perceived quantity, k is a proportionality factor , w is the angle at which the viewed object appears and e is the object distance. The proportionality factor k is an indefinite value which can also be omitted for this consideration; human size perception is not absolute, but relative. The following applies:

${\displaystyle G\sim w\cdot e}$

In words: The perceived size of an object is proportional to the product of distance e and angle size w , also called the apparent or visual size. Here, the angle w of the object can be replaced by the size of its retinal image. When the distance is changed, w is also changed; when e doubles , w decreases by half. Your product remains constant. This causes the perception of a (within limits) distance-independent constant object size; the effect is called constancy of size . The object appears in the correct relation to the other objects, in a relative size - an important prerequisite for a well-founded size estimate.

Without going into more detail about the possibilities of the eyes to determine the distance , one can state that the perception of the constant size of an individual object would require a largely accurate determination of the distance. For equidistant objects, Emmert's formula is reduced to:

${\displaystyle G1/G2=w1/w2}$

This value equals the real size ratio of the two objects. The determination of the equidistance - without knowledge of the distances - is an achievement of the depth of vision on the basis of various depth criteria; In the case of human eyes, it extends into the single-digit kilometer range.

The application of Emmert's law is not anchored in the rules of perception . The alignment of visual perception with reality is not a coincidence, but necessary, and Emmert's law describes this reality mathematically. Both agree remarkably well, which allows for a certain closeness to reality, but not for the internal methodology, as to how perception is constructed. This requires the fulfillment of a number of partly not fully known requirements. One of these prerequisites is the existence of a minimum number of other objects, which underlines the relativity of visual perception.

A clear violation of Emmert's law can be seen in some contradictions between the determined distance and certain image content. These provide qualitative indications of different distances, for example active / passive coverage, color changes due to atmospheric haze, perspective , base point locations and a texture of the landscape that becomes finer with distance , whereby the perceptible relative size may differ from that according to Emmert or its construction completely omitted. The result is a perception of the objects that is reduced to their apparent size, which, depending on the situation, can trigger or even avoid considerable size illusions.

See also

• visual perception
• Constancy of size

literature

• Emil Emmert: The proportions of the afterimages. In: Clinical monthly sheets for ophthalmology. 19, 1881, pp. 443-450.
• J. Dwyer, R. Ashton et al .: Emmert's Law in the Ames Room . In: Perception. 19, 1990, pp. 35-41