Constant curvature segments as building blocks of 2D shape representation

Measures of angularity in digital images

In light of the growing interest in studying the affective and aesthetic attributes of curvature, the present paper describes four digital image processing techniques that can be used to objectively discriminate between angular and curvilinear stimuli. MATLAB scripts for each of the techniques accompany the paper. Three studies are then reported that evaluate the efficacy of five metrics, derived from the four techniques, at quantifying the degree of angularity depicted in an image. Images of simple polygons (Study 1), artistic drawings of everyday objects (Study 2), and real-world objects, typefaces, and abstract patterns (Study 3) were analyzed. Logistic regression models were used to determine the relative importance of the metrics at distinguishing between angular and curvilinear items. With one exception, all of the metrics were capable of distinguishing between angular and curvilinear items at a level above chance, but some metrics were better at doing so than others, and their discriminative capacity was influenced by the characteristics of the image. The strengths and limitations of the metrics are discussed, as well as some practical recommendations.

Caricaturing Shapes in Visual Memory

When representing high-level stimuli, such as faces and animals, we tend to emphasize salient features-such as a face's prominent cheekbones or a bird's pointed beak. Such mental caricaturing leaves traces in memory, which exaggerates these distinctive qualities. How broadly does this phenomenon extend? Here, in six experiments (N = 700 adults), we explored how memory automatically caricatures basic units of visual processing-simple geometric shapes-even without task-related demands to do so. Participants saw a novel shape and then immediately adjusted a copy of that shape to match what they had seen. Surprisingly, participants reconstructed shapes in exaggerated form, amplifying curvature, enlarging salient parts, and so on. Follow-up experiments generalized this bias to new parameters, ruled out strategic responding, and amplified the effects in serial transmission. Thus, even the most basic stimuli we encounter are remembered as caricatures of themselves.

Compositionality in perception: A framework

Perception involves the processing of content or information about the world. In what form is this content represented? I argue that perception is widely compositional. The perceptual system represents many stimulus features (including shape, orientation, and motion) in terms of combinations of other features (such as shape parts, slant and tilt, common and residual motion vectors). But compositionality can take a variety of forms. The ways in which perceptual representations compose are markedly different from the ways in which sentences or thoughts are thought to be composed. I suggest that the thesis that perception is compositional is not itself a concrete hypothesis with specific predictions; rather it affords a productive framework for developing and evaluating specific empirical hypotheses about the form and content of perceptual representations. The question is not just whether perception is compositional, but how. Answering this latter question can provide fundamental insights into perception. This article is categorized under: Philosophy > Representation Philosophy > Foundations of Cognitive Science Psychology > Perception and Psychophysics.

Combining and segmenting geometric shapes into parts depending on symmetry type: Evidence from children and adults

Symmetry is an important geometric feature that affects object segmentation into parts, though De Winter and Wagemans note that partly occluded objects can still be identified by the remaining visible parts. In two sets of experiments with children (n = 31, age 7-11, M = 8.8, SD = 1.4) and adults (n = 19, age 17-57, M = 30.4, SD = 12.6), we used 13 basic geometric figures distinguished by symmetry types to test how they are naturally segmented or combined and what the developmental impacts are on the segmentation and combination. In the first experiment, participants were asked to cut figures into two along a straight line; in the second experiment, participants had to create five sets of connected two-figure combinations where overlapping figures were allowed. The results confirmed the importance of the symmetry axis in both tasks. Other relevant criteria were dividing into half, maximal/minimal curvature, and use of edges or corners for reference. This study allows comparisons of the impact of symmetry type on the segmentation and combining of geometric figures and indicates developmental differences between children and adults.

Clarifying status of DNNs as models of human vision

On several key issues we agree with the commentators. Perhaps most importantly, everyone seems to agree that psychology has an important role to play in building better models of human vision, and (most) everyone agrees (including us) that deep neural networks (DNNs) will play an important role in modelling human vision going forward. But there are also disagreements about what models are for, how DNN-human correspondences should be evaluated, the value of alternative modelling approaches, and impact of marketing hype in the literature. In our view, these latter issues are contributing to many unjustified claims regarding DNN-human correspondences in vision and other domains of cognition. We explore all these issues in this response.

Configural relations in humans and deep convolutional neural networks

Deep convolutional neural networks (DCNNs) have attracted considerable interest as useful devices and as possible windows into understanding perception and cognition in biological systems. In earlier work, we showed that DCNNs differ dramatically from human perceivers in that they have no sensitivity to global object shape. Here, we investigated whether those findings are symptomatic of broader limitations of DCNNs regarding the use of relations. We tested learning and generalization of DCNNs (AlexNet and ResNet-50) for several relations involving objects. One involved classifying two shapes in an otherwise empty field as same or different. Another involved enclosure. Every display contained a closed figure among contour noise fragments and one dot; correct responding depended on whether the dot was inside or outside the figure. The third relation we tested involved a classification that depended on which of two polygons had more sides. One polygon always contained a dot, and correct classification of each display depended on whether the polygon with the dot had a greater number of sides. We used DCNNs that had been trained on the ImageNet database, and we used both restricted and unrestricted transfer learning (connection weights at all layers could change with training). For the same-different experiment, there was little restricted transfer learning (82.2%). Generalization tests showed near chance performance for new shapes. Results for enclosure were at chance for restricted transfer learning and somewhat better for unrestricted (74%). Generalization with two new kinds of shapes showed reduced but above-chance performance (≈66%). Follow-up studies indicated that the networks did not access the enclosure relation in their responses. For the relation of more or fewer sides of polygons, DCNNs showed successful learning with polygons having 3-5 sides under unrestricted transfer learning, but showed chance performance in generalization tests with polygons having 6-10 sides. Experiments with human observers showed learning from relatively few examples of all of the relations tested and complete generalization of relational learning to new stimuli. These results using several different relations suggest that DCNNs have crucial limitations that derive from their lack of computations involving abstraction and relational processing of the sort that are fundamental in human perception.

One-shot generalization in humans revealed through a drawing task

Humans have the amazing ability to learn new visual concepts from just a single exemplar. How we achieve this remains mysterious. State-of-the-art theories suggest observers rely on internal 'generative models', which not only describe observed objects, but can also synthesize novel variations. However, compelling evidence for generative models in human one-shot learning remains sparse. In most studies, participants merely compare candidate objects created by the experimenters, rather than generating their own ideas. Here, we overcame this key limitation by presenting participants with 2D 'Exemplar' shapes and asking them to draw their own 'Variations' belonging to the same class. The drawings reveal that participants inferred-and synthesized-genuine novel categories that were far more varied than mere copies. Yet, there was striking agreement between participants about which shape features were most distinctive, and these tended to be preserved in the drawn Variations. Indeed, swapping distinctive parts caused objects to swap apparent category. Our findings suggest that internal generative models are key to how humans generalize from single exemplars. When observers see a novel object for the first time, they identify its most distinctive features and infer a generative model of its shape, allowing them to mentally synthesize plausible variants.

Constant curvature modeling of abstract shape representation

How abstract shape is perceived and represented poses crucial unsolved problems in human perception and cognition. Recent findings suggest that the visual system may encode contours as sets of connected constant curvature segments. Here we describe a model for how the visual system might recode a set of boundary points into a constant curvature representation. The model includes two free parameters that relate to the degree to which the visual system encodes shapes with high fidelity vs. the importance of simplicity in shape representations. We conducted two experiments to estimate these parameters empirically. Experiment 1 tested the limits of observers’ ability to discriminate a contour made up of two constant curvature segments from one made up of a single constant curvature segment. Experiment 2 tested observers’ ability to discriminate contours generated from cubic splines (which, mathematically, have no constant curvature segments) from constant curvature approximations of the contours, generated at various levels of precision. Results indicated a clear transition point at which discrimination becomes possible. The results were used to fix the two parameters in our model. In Experiment 3, we tested whether outputs from our parameterized model were predictive of perceptual performance in a shape recognition task. We generated shape pairs that had matched physical similarity but differed in representational similarity (i.e., the number of segments needed to describe the shapes) as assessed by our model. We found that pairs of shapes that were more representationally dissimilar were also easier to discriminate in a forced choice, same/different task. The results of these studies provide evidence for constant curvature shape representation in human visual perception and provide a testable model for how abstract shape descriptions might be encoded.