Emmert's law

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

Emil Emmert (1844-1911) discovered it in 1881. He experimented with afterimages and realized that their perceived size proportional to the distance of the considered background changed despite unchanged size on the retina. This knowledge can be generally applied to the perception of size. The relationship is:

Wherein G is the perceived size, k is a proportionality factor, w is the angle at which the viewed object is displayed, and e being the object distance. The proportionality factor k is an indeterminate value, which can also be omitted for this analysis; human perception of size is indeed not absolute but relative. Thus:

In words, the perceived size of an object is proportional to the product of distance e and angle variable w, also called apparent or visual size. Here, the angle can be w of the object is replaced by the size of its retinal image. When changing the distance and w is changed; in doubling of E w decreases by half. Your product remains constant. This causes the perception of a (within limits) independent of distance constant object size; the effect is known as size constancy. In this case, the object appears in relevant relations to other objects, in a relative size - an important requirement of a sound size estimate.

Without dwelling on the possibilities of the eyes for distance determination, we can see that the perception of size constancy of a single object would require a largely accurate distance determination. For equidistant objects, the Czech Emmer formula reduces to:

This value is similar to the real size ratio of the two objects. The finding of equidistance - without knowing the distances - is a service of low visual acuity based on different depth criteria; it ranges in human eye up to a maximum in the single digits kilometer area.

The application of Emmert 's law is not rooted in the perception rules. The orientation of the visual perception of the reality is not accidental, but necessary and the Emmer Czech law describes this reality mathematically. Both true striking good agreement which, although allowed on a certain realism, but not to the inner methodology conclusions, the way in which perception is constructed. This requires the fulfillment of a whole series of sometimes not completely known conditions. One of these conditions is about the existence of a minimum number of other objects, which emphasizes the relativity of visual perception.

A clear violation of the Emmer Czech law is clear in some contradictions between the determined distance and some image content. These provide qualitative evidence to different distances, for example active / passive cover, color changes by atmospheric haze, perspective, Fußpunktlagen and with the distance becomes finer texture of the landscape, which differs in certain circumstances the perceived relative size from that of Emmert or their construction completely suppressed. The result is reduced to the apparent size perception of objects, which depending on the situation considerable size illusions triggered - or can be also avoided.