Visual representation of malleable and rigid objects that deform as they rotate

Most studies and theories of object recognition have addressed the perception of rigid objects. Yet, physical objects may also move in a nonrigid manner. A series of priming studies examined the conditions under which observers can recognize novel views of objects moving nonrigidly. Observers were primed with 2 views of a rotating object that were linked by apparent motion or presented statically. The apparent malleability of the rotating prime object varied such that the object appeared to be either malleable or rigid. Novel deformed views of malleable objects were primed when falling within the object's motion path. Priming patterns were significantly more restricted for deformed views of rigid objects. These results suggest that moving malleable objects may be represented as continuous events, whereas rigid objects may not. That is, object representations may be "dynamically remapped" during the analysis of the object's motion.     

Property Designators,Predicates, and Rigidity

The article discusses an idea of how to extend the notion of rigidity to predicates, namely the idea that predicates stand in a certain systematic semantic relation to properties, such that this relation may hold rigidly or nonrigidly. The relation (which I call signification) can be characterised by recourse to canonical property designators which are derived from predicates (or general terms) by means of nominalization: a predicate signifies that property which the derived property designator designates. Whether signification divides into rigid and non-rigid cases will then depend uponwhether canonical property designators divide into rigid and non-rigid ones. But, I shall argue, they do not, and so the only notion of rigidity gained this way is trivial. To show this, I first focus on the kind of canonical property designators which could be thought to be nonrigid, canonical designators such as having the colour of ripe tomatoes which themselves contain non-rigid property designators. An argument to the effect that such complex canonical designators are non-rigid is rebutted, five arguments to the effect that they are rigid are formulated, and finally an explanation of their rigidity based on the general nature of canonical property designators is presented.     

Visual information about rigid and nonrigid motion: a geometric analysis

A mathematical analysis is presented that attempts to describe the available visual information about rigid and nonrigid motion and the three-dimensional structure of rigidly moving objects. Unlike other approaches, the analysis is based on the geometric relations among a set of trajectories defined over an extended region of space-time. Two experiments are reported in which observers viewed computer simulations of moving objects and were required to judge whether the observed motion appeared to be rigid or nonrigid. The results suggest that the mathematical limitations of a trajectory-based analysis of visual information are consistent with the perceptual limitations of actual human observers.     

Rigidity in cinema seen from the front row, side aisle

Pictures and cinema seen at a slant present the optics of virtual objects that are distorted and inconsistent with their real counterparts. In particular, it should not be possible for moving objects on slanted film and television screens to be seen as rigid, at least according to rules of linear perspective. Previous approaches to this problem have suggested that some process (perhaps cognitive) rectifies the optics of objects in slanted pictures to derive true shape and preserve shape constancy. The means for this rectification is usually thought to be based on recovery of true screen slant. In three experiments I show that this account is unnecessary and insufficient to explain the perception of rotating, rectangular objects in slanted cinema. I present data in favor of an alternate view, one in which the information is sufficient for perceivers to determine rigidity in an object on slanted screens, at least for parallel projections. In the human visual system, local measurements of objects are apparently made according to projective geometry; in those measurements, small amounts of certain distortions in projection are tolerated. Stimuli that appear nonrigid are ones that violate certain local principles, known as Perkins's laws, of projections of rectangular solids.     

Rigid and non-rigid kinetic depth effect with rotating discrete helices

Summary To examine the conditions in which human observers fail to recover the rigid structure of a three-dimensional object in motion we used simulations of discrete helices with various pitches undergoing either pure rotation in depth (rigid stimuli) or rotation plus stretching (non-rigid stimuli). Subjects had either to rate stimuli on a rigidity scale (Experiments 1 and 2) or to judge the amount of rotation of the helices (Experiments 3 and 4). We found that perceived rigidity depended on the pitch of the helix rather than on objective non-rigidity. Furthermore, we found that helices with a large pitch/radius ratio were perceived as highly non-rigid and that their rotation was underestimated. Experiment 5 showed that the detection of a pair of dots rigidly related (located on. the helix) against a background of randomly moving dots is easier at small phases in which the change of orientation across frames is also small. We suggest that this is because at small phases the grouping of dots in virtual lines does occur and that this may be an important factor in the perceived nonrigidity of the helices.This research was supported by MPI 60% (1987, 1988) and CNR (1986), 1987, 1988) grants to Clara Casco and Sergio Roncato and Grant CNR 90.01603.PS93 to Giorgio Ganis.     

Rigid objects that appear to bend

Simple rigid objects are presented that appear to bend when viewed from certain angles. These illusions illustrate that perspective information is used by the stereo system, that projective distortions can override rigidity constraints in motion perception, and that touch only corrects the illusion for a local region.     

The perceptual analysis of structure from motion for rotating objects undergoing affine stretching transformations

In two experiments, we evaluated the ability of human observers to make use of second-order temporal relations across three or more views of an apparent motion sequence for the perceptual analysis of three-dimensional form. Ratings of perceived rigidity were obtained in Experiment 1 for objects rotating in depth that were simultaneously subjected to sinusoidal affine stretching transformations along the line of sight or in a direction parallel to the image plane. Such transformations are theoretically interesting because they cannot be detected by analyses that are restricted to first-order temporal relations (i.e., two views), but they can be detected by more conventional analyses of structure from motion in which second-order temporal relations over three or more views are used. The current results show that human observers can perceive stretching transformations of a rotating 3-D object in a direction parallel to the image plane but that they fail to perceive stretching transformations along the line of sight. This result suggests that human observers can make use of some limited second-order temporal information. This finding was confirmed in Experiment 2, in which we investigated the effects of several specific optical consequences of sinusoidal stretching transformations applied in different directions. The results indicate that observers may be sensitive to the sign of acceleration, but that. they cannot make use of the precise magnitude of second-order relations necessary to recover euclidean metric structure.     

Development of three-dimensional form perception

In three experiments with infants and one with adults we explored the generality, limitations, and informational bases of early form perception. In the infant studies we used a habituation-of-looking-time procedure and the method of Kellman (1984), in which responses to three-dimensional (3-D) form were isolated by habituating 16-week-old subjects to a single object in two different axes of rotation in depth, and testing afterward for dishabituation to the same object and to a different object in a novel axis of rotation. In Experiment 1, continuous optical transformations given by moving 16-week-old observers around a stationary 3-D object specified 3-D form to infants. In Experiment 2 we found no evidence of 3-D form perception from multiple, stationary, binocular views of objects by 16- and 24-week-olds. Experiment 3A indicated that perspective transformations of the bounding contours of an object, apart from surface information, can specify form at 16 weeks. Experiment 3B provided a methodological check, showing that adult subjects could neither perceive 3-D forms from the static views of the objects in Experiment 3A nor match views of either object across different rotations by proximal stimulus similarities. The results identify continuous perspective transformations, given by object or observer movement, as the informational bases of early 3-D form perception. Detecting form in stationary views appears to be a later developmental acquisition.     

Apparent reversals of a rotating mask: A new demonstration of cognition in perception

A mask of a face rotated about its vertical axis of symmetry can appear to oscillate rather than rotate. Do stimulus features (e.g., shape) or cognitive factors (e.g., differential familiarity with convex and concave views of faces) explain this new illusion? In Experiment 1, differential familiarity was varied across stimuli by using familiar and unfamiliar objects rotating at 4 rpm and within stimuli by showing the objects upright and inverted. True motion was seen more with unfamiliar objects than with familiar objects and more with an inverted mask than with an upright mask. The results of Experiment 2, which was done with static views, suggest that the upright and inverted masks present similar structure to the visual system. In Experiment 3, the objects were shown rotating at 8 rpm; the results are similar to those of Experiment 1. These experiments favor a differential familiarity account of this illusory motion. Cognitive constraints on perceived motion and perceived rigidity are discussed.     

Apparent reversals of a rotating mask: a new demonstration of cognition in perception.

A mask of a face rotated about its vertical axis of symmetry can appear to oscillate rather than rotate. Do stimulus features (e.g., shape) or cognitive factors (e.g., differential familiarity with convex and concave views of faces) explain this new illusion? In Experiment 1, differential familiarity was varied across stimuli by using familiar and unfamiliar objects rotating at 4 rpm and within stimuli by showing the objects upright and inverted. True motion was seen more with unfamiliar objects than with familiar objects and more with an inverted mask than with an upright mask. The results of Experiment 2, which was done with static views, suggest that the upright and inverted masks present similar structure to the visual system. In Experiment 3, the objects were shown rotating at 8 rpm; the results are similar to those of Experiment 1. These experiments favor a differential familiarity account of this illusory motion. Cognitive constraints on perceived motion and perceived rigidity are discussed.     

THIS ARTICLE HAS BEEN RETRACTED: Enumeration of objects and substances in non‐human primates: experiments with brown lemurs (Eulemur fulvus)

Both human infants and adult non‐human primates share the capacity to track small numbers of objects across time and occlusion. The question now facing developmental and comparative psychologists is whether similar mechanisms give rise to this capacity across the two populations. Here, we explore whether non‐human primates’ object tracking abilities are subject to the same constraints as those of human infants. In particular, we examine whether one primate species, the brown lemur (Eulemur fulvus), also fails to represent and enumerate objects when they behave non‐rigidly or non‐cohesively. We presented lemurs with a series of expectancy violation studies involving simple 1 + 1 addition events in which we varied the entities to be enumerated. Like infants, lemurs successfully enumerated the two objects when those objects were rigid, cohesive individuals, but failed to enumerate similar‐looking non‐rigid piles of sand. In contrast to human infants, however, lemurs successfully enumerated non‐cohesive objects that broke into multiple pieces. These results are discussed in light of recent theories about object processing in human infants and adults.     

Discriminating rigid from nonrigid motion: minimum points and views

Theoretical investigations of structure from motion have demonstrated that an ideal observer can discriminate rigid from nonrigid motion from two views of as few as four points. We report three experiments that demonstrate similar abilities in human observers: In one experiment, 4 of 6 subjects made this discrimination from two views of four points; the remaining subjects required five points. Accuracy in discriminating rigid from nonrigid motion depended on the amount of nonrigidity (variance of the interpoint distances over views) in the nonrigid structure. The ability to detect a rigid group dropped sharply as noise points (points not part of the rigid group) were added to the display. We conclude that human observers do extremely well in discriminating between nonrigid and fully rigid motion, but that they do quite poorly at segregating points in a display on the basis of rigidity.     

Perception of biomechanical motions by infants: implementation of various processing constraints

Geometry informs us that there exist a large number of possible connectivity patterns consistent with a point-light display of a person walking. Yet there is only one pattern consistent with a "stick figure" representation of the human form, and that pattern is uniquely specified by those pairwise connections that remain locally rigid. In this study, sensitivity to local rigidity in biomechanical displays was investigated in 3- and 5-month-old infants. The results of Experiment 1 revealed that by 5 months of age, infants discriminate a locally rigid point-light walker display from one in which local rigidity is perturbed. In Experiment 2 we tested infants' sensitivity to the same stimuli when those stimuli were inverted. Contrary to the preceding experiment, the results revealed no evidence of discrimination. Taken together, these findings suggest that infants are sensitive to local rigidity in biomechanical displays but that this sensitivity is orientation specific. Possible mechanisms for this specificity are discussed in the context of additional constraints on the processing of biomechanical displays.     

The role of dynamic information in the recognition of unfamiliar faces

The effects of movement on unfamiliar face recognition were investigated. In an incidental learning task, faces were studied either as computer-animated (moving) displays or as a series of static images, with identical numbers of frames shown for each. The movements were either nonrigid transformations (changes in expression) or rigid rotations in depth (nodding or shaking). At test, participants saw either single, static images or moving sequences. Only one experiment showed a significant effect of study type, in favor of static instances. There was no additional advantage from studying faces in motion in these experiments, in which both study types showed the same amounts of information. Recognition memory was relatively unaffected by changes in expression between study and test. Effects of viewpoint change were large when expressive transformations had been studied but much smaller when rigid rotations in depth had been studied. The series of experiments did reveal a slight advantage for testing memory with moving compared with static faces, consistent with recent findings using familiar faces. Future work will need to examine whether such effects may also be due to the additional information provided by an animated sequence.     

Adventures with gelatinous ellipses--constraints on models of human motion analysis

An ellipse rotating rigidly about its center may appear to rotate rigidly or to deform nonrigidly so that it appears gelatinous. We use this ambiguous stimulus to study how motion information is propagated across space. We find that features that are quite far from the contour of the ellipse may have a strong influence on the percept of the ellipse, provided they move in a way consistent with the motion of the ellipse. We show that the percept cannot be accounted for by computational models that pool constraints over a local area only, or by models that propagate information along contours, or by models that indiscriminately propagate information across space. However, the percept can be accounted for by a class of models that assume smoothness in a layered representation.     

Mental representation of three-dimensional objects in visual problem solving and recognition

Subjects inspected sets of flat, separated orthographic projections of surfaces of potential three-dimensional objects. After solving problems based on these orthographic views, subjects discriminated between isometric views of the same objects and drawings of distractor structures. Recognition of the isometrics, which had never been shown during the problem solving phase of the experiment, was excellent. In addition, recognition of isometrics corresponding to problems that had been solved correctly when presented in orthographic form was significantly superior to recognition of isometrics based on problems solved incorrectly. In Experiment 2, conditions were included in which either orthographic or isometric views functioned as problem solving or recognition displays. Only in the case of orthographic problem solving followed by isometric recognition (Experiment 1) was the superiority of recognition for correctly-solved problems over incorrectly-solved problems obtained. The pattern of results suggests that viewers construct mental representations embodying structural information about integrated, three-dimensional objects when asked to reason about flat, disconnected projections.     

On the limits of perceptual complementarity in the kinetic depth effect

In a series of experiments, we have investigated the abilities of human observers to perceive geometric properties of moving three-dimensional objects as a function of their perspective and rotational complexities. The results indicate a decreasing ability of observers to extract metric, angular, and rigid motion as the perspectives and rotations depart from parallel projections and one-parameter central rotations. In this way, quantitative limits are suggested for the principle of perceptual complementarity suggested by Shepard (1981).     

Perception of structure from two-, four-, or eight-dot oscillatory motion: restoration of rigidity with the aid of structural information

The motion of two dots corresponding to the two endpoints of an oscillating rigid pendulum produces the perception of an elastic rod, not a rigid one. The possibility that structural information about a rigid object whose motion is simulated plays an important role in the perceptual restoration of the rigidity is examined. Two experiments are reported in which the motion of the endpoints of rigid objects (two endpoints for a rod, four for a sheet, and eight for a board) was displayed. Rigid structure was restored whenever structural information could be used to activate a knowledge data-base on the properties of the objects.     

Attentive tracking of objects versus substances

Recent research in vision science, infant cognition, and word learning suggests a special role for the processing of discrete objects. But what counts as an object? Answers to this question often depend on contrasting object-based processing with the processing of spatial areas or unbound visual features. In infant cognition and word learning, though, another salient contrast has been between rigid cohesive objects and nonsolid substances. Whereas objects may move from one location to another, a nonsolid substance must pour from one location to another. In the study reported here, we explored whether attentive tracking processes are sensitive to dynamic information of this type. Using a multiple-object tracking task, we found that subjects could easily track four items in a display of eight identical unpredictably moving entities that moved as discrete objects from one location to another, but could not track similar entities that noncohesively "poured" from one location to another-even when the items in both conditions followed the same trajectories at the same speeds. Other conditions revealed that this inability to track multiple "substances" stemmed not from violations of rigidity or cohesiveness per se, because subjects were able to track multiple noncohesive collections and multiple nonrigid deforming objects. Rather, the impairment was due to the dynamic extension and contraction during the substancelike motion, which rendered the location of the entity ambiguous. These results demonstrate a convergence between processes of midlevel adult vision and infant cognition, and in general help to clarify what can count as a persisting dynamic object of attention.