The concavity effect is a compound of local and global effects

Investigating shape representation using sensitivity to part- and axis-based transformations

Part- and axis-based approaches organize shape representations in terms of simple parts and their spatial relationships. Shape transformations that alter qualitative part structure have been shown to be more detectable than those that preserve it. We compared sensitivity to various transformations that change quantitative properties of parts and their spatial relationships, while preserving qualitative part structure. Shape transformations involving changes in length, width, curvature, orientation and location were applied to a small part attached to a larger base of a two-part shape. Increment thresholds were estimated for each transformation using a 2IFC procedure. Thresholds were converted into common units of shape difference to enable comparisons across transformations. Higher sensitivity was consistently found for transformations involving a parameter of a single part (length, width, curvature) than those involving spatial relations between two parts (relative orientation and location), suggesting a single-part superiority effect. Moreover, sensitivity to shifts in part location - a biomechanically implausible shape transformation - was consistently poorest. The influence of region-based geometry was investigated via stereoscopic manipulation of figure and ground. Sensitivity was compared across positive parts (protrusions) and negative parts (indentations) for transformations involving a change in orientation or location. For changes in part orientation (biomechanically plausible), sensitivity was better for positive than negative parts; whereas for changes in part location (biomechanically implausible), no systematic difference was observed.

Extending JAGS: a tutorial on adding custom distributions to JAGS (with a diffusion model example)

We demonstrate how to add a custom distribution into the general-purpose, open-source, cross-platform graphical modeling package JAGS ("Just Another Gibbs Sampler"). JAGS is intended to be modular and extensible, and modules written in the way laid out here can be loaded at runtime as needed and do not interfere with regular JAGS functionality when not loaded. Writing custom extensions requires knowledge of C++, but installing a new module can be highly automatic, depending on the operating system. As a basic example, we implement a Bernoulli distribution in JAGS. We further present our implementation of the Wiener diffusion first-passage time distribution, which is freely available at https://sourceforge.net/projects/jags-wiener/ .

Processing convexity and concavity along a 2-D contour: figure-ground, structural shape, and attention

Interest in convexity has a long history in vision science. For smooth contours in an image, it is possible to code regions of positive (convex) and negative (concave) curvature, and this provides useful information about solid shape. We review a large body of evidence on the role of this information in perception of shape and in attention. This includes evidence from behavioral, neurophysiological, imaging, and developmental studies. A review is necessary to analyze the evidence on how convexity affects (1) separation between figure and ground, (2) part structure, and (3) attention allocation. Despite some broad agreement on the importance of convexity in these areas, there is a lack of consensus on the interpretation of specific claims--for example, on the contribution of convexity to metric depth and on the automatic directing of attention to convexities or to concavities. The focus is on convexity and concavity along a 2-D contour, not convexity and concavity in 3-D, but the important link between the two is discussed. We conclude that there is good evidence for the role of convexity information in figure-ground organization and in parsing, but other, more specific claims are not (yet) well supported.

The role of convexity in perception of symmetry and in visual short-term memory

Visual perception of shape is affected by coding of local convexities and concavities. For instance, a recent study reported that deviations from symmetry carried by convexities were easier to detect than deviations carried by concavities. We removed some confounds and extended this work from a detection of reflection of a contour (i.e., bilateral symmetry), to a detection of repetition of a contour (i.e., translational symmetry). We tested whether any convexity advantage is specific to bilateral symmetry in a two-interval (Experiment 1) and a single-interval (Experiment 2) detection task. In both, we found a convexity advantage only for repetition. When we removed the need to choose which region of the contour to monitor (Experiment 3) the effect disappeared. In a second series of studies, we again used shapes with multiple convex or concave features. Participants performed a change detection task in which only one of the features could change. We did not find any evidence that convexities are special in visual short-term memory, when the to-be-remembered features only changed shape (Experiment 4), when they changed shape and changed from concave to convex and vice versa (Experiment 5), or when these conditions were mixed (Experiment 6). We did find a small advantage for coding convexity as well as concavity over an isolated (and thus ambiguous) contour. The latter is consistent with the known effect of closure on processing of shape. We conclude that convexity plays a role in many perceptual tasks but that it does not have a basic encoding advantage over concavity.

Principles of contour information: Reply to Lim and Leek (2012)

Lim and Leek (2012) presented a formalization of information along object contours, which they argued was an alternative to the approach taken in our article (Feldman & Singh, 2005). Here, we summarize the 2 approaches, showing that--notwithstanding Lim and Leek's (2012) critical rhetoric--their approach is substantially identical to ours, except for the technical details of the formalism. Following the logic of our article point by point, Lim and Leek (a) defined probabilistic expectations about the geometry of smooth contours (which they based on differential contour geometry, while we used a discrete approximation--the only essential difference in their approach), (b) assumed that information along the contour was proportional to the negative logarithm of probability, following standard information theory, and then (c) extended this formulation to closed contours. We analyze what they described as errors in our approach, all of which rest on mathematical misunderstandings or bizarre misreadings of our article. We also show that their extension to 3-dimensional surfaces and their "modified minima rule" contain fatal deficiencies.

Delayed shape matching benefits from simplicity and symmetry

The aim of this study was to evaluate the influence of complexity and symmetry on shape recognition, by measuring the recognition of unfamiliar shapes (created using Fourier Boundary Descriptors, FBDs) through a delayed matching task. Between complexity levels the shapes differed in the frequency of the FBDs and within complexity levels in their phase. Shapes were calibrated to be physically equally similar for the different complexity levels. Matching two sequentially presented shapes was slower and less accurate when complexity increased and for asymmetrical compared to symmetrical versions of the shapes. Thus, we show that simplicity in general and symmetry in particular enhance the short-term recognition of unfamiliar shapes.

Identification of everyday objects on the basis of fragmented outline versions

Although Attneave (1954 Psychological Review 61 183 193) and Biederman (1987 Psychological Review 94 115-147) have argued that curved contour segments are most important in shape perception, Kennedy and Domander (1985 Perception 14 367-370) showed that fragmented object contours are better identifiable when straight segments are shown. We used the set of line drawings published by Snodgrass and Vanderwart (1980 Journal of Experimental Psychology: Human Learning and Memory 6 174-215), to make outline versions that could be used to investigate this issue with a larger and more heterogeneous stimulus set. Fragments were placed either around the 'salient' points or around the midpoints (points midway between two salient points), creating curved versus relatively straight fragments when the original outline was fragmented (experiment 1), or angular and straight fragments when straight-line versions were fragmented (experiment 2). We manipulated fragment length in each experiment except the last one, in which we presented only selected points (experiment 3). While fragmented versions were on average more identifiable when straight fragments were shown, certain objects were more identifiable when the curved segments or the angles were shown. A tentative explanation of these results is presented in terms of an advantage for straight segments during grouping processes for outlines with high part salience, and an advantage for curved segments during matching processes for outlines with low part salience.

The Awakening of Attneave's Sleeping cat: Identification of Everyday Objects on the Basis of Straight-Line Versions of Outlines

Attneave (1954 Psychological Review61 183–193) demonstrated that a line drawing of a sleeping cat can still be identified when the smoothly curved contours are replaced by straight-line segments connecting the positive maxima and negative minima of contour curvature. Using the set of line drawings by Snodgrass and Vanderwart (1980 Journal of Experimental Psychology: Human Learning and Memory6 174–215) we made outline versions (with known curvature values along the contour) that can still be identified and that can be used to test Attneave's demonstration more systematically and more thoroughly. In five experiments (with 444 subjects in total), we tested identifiability of straight-line versions of 184 stimuli with different selections of points to be connected (using 24 to 28 subjects per stimulus per condition). Straight-line versions connecting curvature extrema were easier to identify than those based on inflections (where curvature changes sign), and those connecting salient points (determined by 161 independent subjects) were easier than those connecting midpoints. However, identification varied considerably between objects: some were almost always identifiable and others almost never, regardless of the selection criterion, whereas identifiability depended on the specific shape attributes preserved in the straight-line version of the outline in other objects. Results are discussed in relation to Attneave's original hypotheses as well as in the light of more recent theories on shape perception and object identification.