Perception & Psychophysics 1984.36 (f). 50·64 Shape constancy: The effects of changing shape orientation and the effects of changing the position of focal features GLYN W. HUMPHREYS Birkbeck College, University ojLondon, London, England Five experiments examined the time taken to judge that two consecutive elongated geometrical shapes had the same structure, irrespective of their orientation. Shape transformations either changed the orientation of the principal axis while maintaining the relative locations of focal features or maintained the orientation of the principal axis while changing the relative locations of focal features, or they changed both. Experiment 1 demonstrated that changes in the orien­ tation of the principal axis were more detrimental to matching than were changes in the loca­ tions of the shape's focal features. Indeed, the time taken to match same-orientation shapes was the same as that taken to match shapes that maintained the same position in the visual field. Further experiments showed that this result was not due to differential apparent motion in the transformation conditions, that it was not due to response bias, and that it generalized across shapes. However, the result was different when subjects could predict the location of the to-be-matched stimulus. In this case, performance was principally affected by the position of the focal feature of the shape and not by the shape's orientation. It is suggested that the results reflect the efficiency with which subjects can construct matching representations for the stim­ uli. When subjects cannot predict stimulus locations, they generate representations by describ­ ing shape structure relative to the shape's principal axis. When the axis of the to-be-matched shapes is constant, subjects can use the same procedure in generating this representation for both shapes, facilitating matching relative to the case in which the orientation of the axis changes. When subjects can predict the stimulus location, they selectively attend to the focal features of shapes, minimizing the effects of shape orientation. People can recognize familiar shapes when they are & Shepard, 1973, 1975; Metzler & Shepard, 1974; seen from novel viewpoints. This ability to achieve Shepard, 1975; Shepard & Metzler, 1971). In some shape constancy even when the retinal projection tasks, subjects discriminate between transformed changes is a primary characteristic required of any shapes and their reflections, knowing the structural visual processing system, and should be accounted identity ofthe shapes and the type of transformation for by any theory of shape recognition (Marr, 1980). by which they will differ. For instance, Shepard and The present paper explores some of the processes Metzler (1971) presented subjects with perspective that enable shape constancy to be achieved. line drawings of three-dimensional shapes at differ­ Studies of the efficiency with which subjects achieve ent orientations and asked them to decide whether shape constancy across a range of stimulus transfor­ the shapes were physically the same or whether one mations can inform us about the nature of the pro­ was a reflection of the other. A common finding is cesses involved. A common task in such studies is that reaction time (RT) to match forms is a linear simultaneous or successive form matching, in which function of the size of the transformation, suggesting subjects decide whether two forms have the same that shape constancy is achieved by the transforma­ identity. A number of studies have investigated the tion of an internal representation of a shape in a effects, on matching, of transformations in size (e.g., manner isomorphic with the external transformation. Bundesen & Larsen, 1975; Larsen & Bundesen, 1978; However, this is not the only, or perhaps even the Sekuler & Nash, 1972) or orientation (e.g., Cooper usual, means of achieving shape constancy. There are cases in which subjects cannot predict the trans­ formation or the internal representation appropriate This work was supported by a grant from the Social Science Research Council. I would like to thank Penny Wilcox for her to a shape. Shape constancy in this circumstance re­ help in producing the presentation programs, Philip Quinlan and quires the generation of a representation that is Jane Riddoch for their discussion of earlier drafts of this paper, viewpoint-independent from one that is viewpoint­ and an anonymous referee for helpful comments during its pro­ dependent. For instance, Rock, DiVita, and Barbeito cessing. My mailing address is: Department of Psychology, Birkbeck College, University of London, Malet Street, London, WCIE (1981) showed subjects novel two- or three-dimensional 7HX, England. wire figures, and then tested for the recognition of Copyright 1984 Psychonomic Society, Inc. 50 SHAPE CONSTANCY 51 the figures following an orientation transformation. controlled. Nevertheless, many of the transforma­ They found that altering the relative positions of the tions producing changes of the top and bottom posi­ top and bottom of the object was more detrimental tions also appear to have changed the orientation of to recognition than altering only the positions of the the principal axis (see Figures 1 and 2 in Rock et al., sides. This result led Rock et al. to argue that shapes 1981). It seems reasonable to conclude that their were represented by a description of their top and findings are consistent with these proposals. bottom features and the location of the sides between There are also other examples supporting the axis­ the top and bottom. Consequently, the most disrup­ based account. For instance, consider the shapes pre­ tive orientational transformation will alter the rela­ sented in Figure 1. Mach (1897) first noted that, de­ tive positions of the top and bottom features. spite the fact that all the individual shapes were at the A related proposal concerning the processing of same orientation, subjects reported that the isolated simple geometric shapes has been made by Braine shape was seen as a diamond whereas the shapes in (1978; Braine, Relyea, & Davidman, 1981). She, like the oblique line were seen as squares. The different Rock et aI., argues that shapes are recognized by a descriptions for these shapes appear to arise because hierarchical process of feature description; however, the shapes in the oblique line are represented relative she proposes that this process first codes only the to a coordinate system based on the elongated axis top position, and then proceeds in a top-to-bottom of the configuration; in contrast, the isolated shape direction. The top position is characterized by the is represented relative to its salient vertical axis of presence of a focal feature and by the vertical orien­ symmetry (cf. Goldmeier, 1936; Julesz, 1971; Rock tation of the main axis of the shape. Because the & Leaman, 1963).Relative to these axes, descriptions feature-description process is hierarchical, recogni­ appropriate to a square and a diamond arise. Consis­ tion will proceed most efficiently when the focal fea­ tent empirical evidence has been reported by ture is at the top of the shape. Transformations pro­ Humphreys (1983). Subjects had to decide as quickly ducing a change in the relative position of the top of as possible whether successive forms had the same or the shape willmost affect recognition. different numbers of sides. Two types of shape were The proposals of Rock et al. and Braine maintain used, those with an unambiguous, elongated prin­ that shapes are represented internally by a structural cipal axis (isosceles triangles and elongated penta­ description based on important characteristics of the gons) and those with an ambiguous principal axis shape. They differ in the importance assigned to (squares and regular hexagons). Matching shapes bottom-position features and in specifying a means could be orientational transformations of one another, by which the top position can be assigned. However, so the task demanded matches of shape identity in­ both suggest that the top-position feature provides dependent of the transformation. Humphreys found the primary reference coordinates for the representa­ that orientational transformations that changed the tion. Because the coordinate system is then based on axis aligned with the vertical disrupted the matching a feature of the object, the representation so formed of shapes with ambiguous principal axes (e.g., when is viewpoint-independent and so would enable shape a square was transformed 45 deg within-the-plane, constancy to occur. Transformations generating into a diamond). Similar transformations did not changes in viewpoint-dependent codings of the (top) disrupt the matching of shapes with an unambiguous reference feature will giverise to problems in deriving principal axis (e.g., when an isosceles triangle was shape constancy. transformed 45 deg within-the-plane). These data Work in the field of computer vision also suggests suggest that shapes were matched using a coordinate that shape constancy depends on a structural descrip­ system derived from the shape's principal axis. For tion based on an object-centered coordinate system shapes with an ambiguous principal axis, the axis (e.g., Hinton, 1981; Marr, 1979, 1980, 1982; Marr of description will be determined by alignment of the & Nishihara, 1978). However, this approach con­ trasts with the feature-based account in proposing that the coordinate system is derived from a more global property of the shape than the position of focal features. For instance, Marr and his co-workers have argued that a suitable coordinate system may be determined by the orientation of the principal axis of the shape (Marr, 1982; Marr & Nishihara, 1978). According to this account, changes in the orientation of a shape may be more disruptive to shape constancy than changes in the position of focal features. It is difficult to apply this argument directly to Rock et al. experiment becausethe effects of the trans­ o formations on the principal axis were not directly Figure 1. Mach's demonstration. 52 HUMPHREYS axis with the vertical.