The effect of rotation and tilt on the magnitude of the Poggendorf illusion

We describe the Drifting Edge Illusion (DEI), in which a stationary edge appears to move when it abuts a drifting grating. Although a single edge is sufficient to perceive DEI, a particularly compelling version of DEI occurs when a drifting grating is viewed through an oriented and stationary aperture. The magnitude of the illusion depends crucially on the orientations of the grating and aperture. Using psychophysics, we describe the relationship between the magnitude of DEI and the relative angle between the grating and aperture. Results are discussed in the context of the roles of occlusion, component-motion, and contour relationships in the interpretation of motion information. In particular, we suggest that the visual system is posed with solving an ambiguity other than the traditionally acknowledged aperture problem of determining the direction of motion of the drifting grating. In this ‘second aperture problem’ or ‘edge problem’, a motion signal may belong to either the occluded or occluding contour. That is, the motion along the contour can arise either because the grating is drifting or because the edge is drifting over a stationary grating. DEI appears to result from a misattribution of motion information generated by the drifting grating to the stationary contours of the aperture, as if the edges are interpreted to travel over the grating, although they are in fact stationary.

It is proposed in this paper that many geometrical optical illusions, as well as illusory patterns due to motion signals in line drawings, are due to the statistics of visual computations. The interpretation of image patterns is preceded by a step where image features such as lines, intersections of lines, or local image movement must be derived. However, there are many sources of noise or uncertainty in the formation and processing of images, and they cause problems in the estimation of these features; in particular, they cause bias. As a result, the locations of features are perceived erroneously and the appearance of the patterns is altered. The bias occurs with any visual processing of line features; under average conditions it is not large enough to be noticeable, but illusory patterns are such that the bias is highly pronounced. Thus, the broader message of this paper is that there is a general uncertainty principle which governs the workings of vision systems, and optical illusions are an artifact of this principle.

Measurements are reported on the perceived orientation of a line segment in a frontal plane (test line). For an isolated test line, perceived orientation is biased towards the horizontal H or vertical V, whichever is nearer, H and V are named preference orientations. The presence of a second line (induction line) brings about an extra bias towards the perpendicular of the induction line: induced preference orientation. The phenomenon is well known from many visual illusions. H or V induction lines exert greater influences than do oblique induction lines, H or V test lines are less susceptible to induction effects than are oblique test lines.

If a short test line is replaced by two dots at its ends, the induction effect remains unchanged. If the test line is presented to one eye and the induction line to the other, the induction effect remains almost unchanged, which is indicative of extensive cooperation between the two eyes.

In a qualitative model, in which preference orientations are represented by a maximum sensitivity of orientation sensors along the slant axis, the induction effect can be incorporated by an additional assumption. Physiological evidence as to the origin of the induction effect is scanty.

On décrit des mesures de l'orientation perçue d'un segment de droite dans un plan frontal (ligne test). Pour une ligne test isolée, l'orientation perçue est influencée vers l'horizontale H ou la verticale V selon celle qui est le plus voisine, H et V sont nommées les orientations préférées. La présence d'une seconde ligne (ligne inductrice) provoque une déviation supplémentaire vers la perpendiculaireàla ligne inductrice: c'est l'orientation préférée d'induction. Ce phénomène est bien connu dans beaucoup d'illusions visuelles. Des lignes inductrices H ou V ont plus d'action que des lignes obliques. Des lignes tests H ou V sont moins sensibles aux effets d'induction que des lignes tests obliques.

Si on remplace une courte ligne test par deux pointsàses extrémités, l'effet d'induction reste intact. Si la ligne test est présentéeàun oeil et la ligne inductriceàl'autre, l'effet d'induction reste presque identique, ce qui indique une coopération extensive entre les deux yeux.

Dans un modèle qualitatif oùles orientations préférées sont représentées par un maximum de sensibilitéd'éléments sensoriels d'orientation le long de l'axe incliné, l'effet d'induction peuteˆtre inclus grâceàune hypothèse supplémentaire. On a peu de données physiologiques sur l'origine possible de l'effet d'induction.

Es wirdüber Messungen der beobachteten Orientierung eines Liniensegmentes (der Testlinie) in der Stirnenfläche berichtet. Die beobachtete Orientierung einer isolierten Testlinie neigt sich zur Waagrechten H oder zur Senkrechten V je nach dem, welche näher ist. Man nennt H und V die Vorzugsneigungen. Die Gegenwart einer zweiten (Induktions-) Linie ruft eine extra Neigung gegen die Senkrechte der Induktionslinie hervor: dies wird als eine induzierte Vorzugsneigung bezeichnet. Das Phänomen ist von vielen optischen Täuschungen bekannt. H und V Induktionslinienüben einen stärkeren Einfluss als schräge Induktionslinien aus. H und V Testlinien sind auf Induktionseinflüsse weniger als schräge Testlinien empfindlich.

Wenn eine kurze Testlinie durch zwei Punkte an ihren beiden Enden ersetzt wird, so bleibt der Induktionseffekt unverändert. Wenn die Testlinie dem einen und die Induktionslinie dem anderen Auge dargeboten wird, so bleibt der Induktionseffekt beinahe unverändert, dies weist auf eine weitgehende Zusammenarbeit der beiden Augen hin.

Es ist möglich, den Induktionseffekt mit einer weiteren Annahme in ein qualitatives Modell, in welchem Vorzugsneigungen durch Maximalempfindlichkeiten des Neigungssensors längs einer Neigungsachse gegeben sind, einzuordnen. Es gibt nur wenige Beweise für den Ursprung des Induktionseffekts.

Cooбщaeтcя oб измepeниях вocпpинимaeмoй opиeнтaции oтpeзкa линии вo фpoнтaльнoй плocкocти (тecтoвaя линия). Для изoлиpoвaннoй тecтoвoй линии вocпpинимaeмaя opиeнтaция cмeщaeтcя пo нaпpaвлeнию к гopизoнтaли (H) или вepтикaли (V), в зaвиcимocти oт тoгo, кaкaя из них близe, пoэтoмu Hи V нaзвaны пpeдпoхитaeмыми opиeнтaциями. Пpиcuтcтвиe втopoй линии (индuциpuющeй линии) вызывaeт, cвepх тoгo, cмeщeниe пo нaпpaвлeнию к пepпeндикuляpu индuциpuющeй линии: индuциpoвaннaя пpeдпoхитaeмaя opиeнтaция. Этoт фeнoмeн хopoшo извecтeн из мнoгих зpитeльных иллюзий. H и V-индuциpuющиe линии oбнapuзивaют бoльшee влияниe, хeм кocыe тecтoвыe линии. B тoм cлuхae, ecли тecтoвaя линия нa ee кoнцaх зaмeняeтcя двuмя тoхкaми, дeйcтвиe индuкции ocтaeтcя нeизмeнeнным. Ecли тecтoвaя линия пpeдлaгaeтcя oднoмu глaзu, a индuциpuющaя линия дpuгoмu глaзu, тo эффeкт индuкции ocтaeтcя пoхти нeизмeнeнным, хтo uкaзывaeт нa шиpoкuю кooпepaцию двuх глaз.

B кaхecтвeннoй мoдeли, гдe пpeдпoхитaeмaя opиeнтaция пpeдcтaвлeнa мaкcимuмoм хuвcтвитeльнocти opгaнoв ceнcopнoй opиeнтaции вдoль нaклoннoй ocи, эффeкт индuкции мoзeт быть вклюхeн, пpи дoпoлнитeльных дoпuщeниях. Физиoлoгихecки eмeхaнизмы пpoиcхoздeния эффeктa индuкции мaлo извecтны.