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Hershenson (1992) Size-Distance Invariance. Kinetic Invariance Is Perception & Psychophysics 1992, 51 (6), 541-548 Size-distance invariance: Kinetic invariance is different from static invariance MAURICE HERSHENSON Brandeis University, Waltham, Massachusetts The static form of the size-distance invariance hypothesisasserts that a given proximal stimu- lus size (visual angle) determines a unique and constant ratio of perceived-object size to perceived object distance. A proposed kinetic invariance hypothesis asserts that a changing proximal stim- ulus size (an expanding or contracting solid visual angle) produces a constant perceived size and a changing perceived distance such that the instantaneous ratio of perceived size to perceived distance is determined by the instantaneous value of visual angle. The kinetic invariance hy- pothesis requires a new concept, an operating constraint, to mediate between the proximal ex- pansion or contraction pattern and the perception of rigid object motion in depth. As a conse- quence of the operating constraint, expansion and contraction patterns are automatically represented in consciousness as rigid objects. In certain static situations, the operation of this constraint produces the anomalous perceived-size-perceived-distance relations called the size- distance paradox. The size-distance invariance hypothesis (SDIH) asserts STATIC INVARIANCE RELATIONSHIP that a given proximal stimulus size (visual angle) deter- mines a unique constant ratio of perceived object size to Traditional Formulation perceived object distance (Epstein, 1977; Epstein, Park, The traditional form of the SDIH is derived from the & Casey, 1961; Kilpatrick & Ittelson, 1953). Is it possible analysis of stationary objects (Epstein, 1977; Gilinsky, to explain the moon illusion and retain this form of the 1951; Ittelson, 1951a; Johansson, 1977; Kilpatrick & It- SDIH? To do so, Kaufman and Rock (1962, 1989; Rock telson, 1953; Weintraub & Gardner, 1970). This static & Kaufman, 1962) found it necessary to assume that re- invariance hypothesis (Sill) describes a relationship be- ports about the perceived distance of the moon were not tween perception and the proximal stimulus. These rela- reports of perception at all. They asserted that verbal state- tionships, simplified for purposes of discussion, are II- ments describing the relative distance of the moon were lustrated in Figure 1. The physical (distal-proximal) based on the knowledge that things that look largeare near. relationship that produces the proximal stimulus is illus- But what if reports about the perceived distance of the trated in (a), and the psychological (proximal-perceptual) moon are reasonabledescriptions of perceptual experience relationship is illustrated in (b). The figure shows a rigid rather than cognitive deductions? Is it necessary toaban- object of size S at a distance D from an observer at P. don the SDIH, as a number of authors suggest (Coren, The object subtends a visual angle 4> at the eye of the 1989; Day & Parks, 1989; Haber & Levin, 1989), or is viewer, where visual angle is defined as the envelope en- it possibleto retain an invariant relationship between per- closing the sheaf of light rays reflected from the object ceived size and perceived distance? The answer proposed to the viewer at P. Visual angle is used to represent the here is that it is possible to retain the relationship only linear extent of stimulation on the receptor surface be- by assuming that static invariance is a special case of a cause the size of the eye is assumed to be constant. Con- more general kinetic invariance relationship that acts sequently, the distal-proximal relationship illustrated is within a rigidity constraint (Hershenson, 1982, 1989b; tan 4> = S/D, which, for small angles, can be written Johansson, 1964, 1977; Noguchi & Taya, 1981). While the purpose of this paper is to discuss the kinetic invari- 4> = SID. (1) ance relationship, it is necessary first to examine the static The traditional SIH describes the perceptions that are formulation. possible given a constant proximal stimulus. It asserts that perception is constrained by the proximal stimulus (the visual angle 4>) such that the ratio of perceived size s to This paper is an expanded version of a talk presented ata symposium entitled “Moon illusion and size-distance invariance” at the meeting perceived distance d is constant (Kilpatrick & Irtelson, of the Eastern Psychological Association in Philadelphia, March 1990. 1953): The author’s mailing address is: Department of Psychology, Brandeis University, Waltham, MA 02254-9110. s/d = 4>. (2) 541 Copyright 1992 Psychonomic Society, Inc. 542 HERSHENSON predicting perceived size from perceived distance appears simple. Typically, the invariance equation is rewritten s = d4>, a form that is frequently called Emmert’s law (Weintraub & Gardner, 1970). What is unusual about this use of the invariance relationship is that perceived distance now plays the role of an input variable. In the traditional view, (a) Distal—proximal relations this term represents input information about distance that affectsboth the perceived size and the perceiveddistance of the target object in accordance with the SIH. This in- putinformation could take many forms: proximal stimu- lus input from context such as a texture gradient, cogni- tive input about the object’s relative position in image space, and so forth. When predicting perceived distance from perceived size, the static invariance relationship is typically written I~ ~~d d 2 1 d = s/4>. ~J3 ~1 (b) Proximal-perceptual relations Now perceived size plays the role of an input variable. In the traditional view, this term represents input infor- mation about size that affects boththe perceived size and the perceived distance of the target object in accordance with the SIH. This input information could take many forms: proximal stimulus input from a texture gradient (relative size or size scaling), cognitive input about the absolute size of an object (familiar size), and so forth. p d Sifi and Constancy (c) Perceived visual angle In experiments, static size constancy is usually mea- Figure 1. The traditional form of the Sm. (a) The distal—proximal sured by (defined as) a linear size comparison; that is, relations for a distal object of size S at a distance D from a viewer a proximal extent of size 4>~appears tobe the same linear at P. (b) The SIR for a given proximal stimulus 4~.Three possible size as a proximal extent 4>2. The two visual-angleinputs perceptions are illustrated: an object of size s, at d , ~2 at d , and may be compared simultaneously or successively. How- s , at d . (c) McCready’s (1985) reformulation of the1 SIR. An2 ob- 3 3 ever, the SIH does not describe comparisons—it relates jectof perceived linear sizesappears to be at a distanced. Simulta- neously, the edges of the object subtend an apparent visual angle the perceived size and perceived distance of a target ob- ~‘, the direction difference between PA and PB. ject to a specific proximal stimulusof constant size. Con- sequently, the SIH is typically used in conjunction with additional concepts in explanations of perceptual con- Part b of Figure 1 illustrates three possible perceptions stancy. For example, given a proximal stimulus containing two that satisfy the Sill: s11d1 = s21d2 = s31d3 = 4>. Note that the SIll does not constrain the absolute values of perceived retinal extents, constancy results if the two objects are size or perceived distance—it asserts that their ratio must assumed to be the same size. This can occur if the two be equal to the proximal extent. When the Sill is stated proximal extents are produced by similarobjects, for ex- in this form, the visual angle is understood as a stimulus ample, two ping pong balls or two basketballs. The se- input variable, and perceived size and perceived distance quence just described represents an input of size infor- are understood as output variables of a perceptual black mation for two independent applications of the SIll. In box. (Ofcourse, the observation and measurementof these this case, the relative perceived distances would be in- output variables involves understanding other blackboxes versely proportional to the visual angles, but that would whose output ultimately is behavior, an important distinc- be a fortuitous consequence of equating the input size tion that is beyond the scope of the present discussion.) values. The link is not a part of the SIll but a result of The static invariance relationship has frequently been other factors (e.g., familiar size) that produced the size used to predict perceived size from perceived distance, values. This example invokes familiar size to determine and vice versa. However, this apparently simple mathe- both perceived size and perceived distance according to matical transposition of terms masks some important in- the Sill, but the constancy is more directly a consequence terpretations of the nature of perceptual processing that of the familiarity of the object than the application of this are not always acknowledged. For example, the task of input to the SIH. KINETIC INVARIANCE 543 The assignment of same-size values could also have terrain, and clouds). Therefore, the moon appears larger been produced by context, scaling, learning, knowledge, at the horizon than in elevation. Knowledge accounts for or simply an assumption (explicit or implicit) that the ob- verbal reports that the horizon moon looks closer. jects producing the two visual angles were the same. The Partitioning size information: Perceived visual an- point is that these inputs are not features of the SIH but gle. McCready (1965, 1985, 1986) introduced a new form are outside processes that provide information used to de- of the SIH that distinguished two types of perceived size: termine one of the terms. Constancy is not determined perceived linear size (s) and perceived visual-angle size by the SIH but is produced only when additional infor- (4>’), defined as the perceived direction difference between mation is available to determine one of the terms that enter the edges of an object. According to McCready (1985), the SIH.
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