Development of differential sensitivity for shape changes resulting from linear and nonlinear planar transformations

Visual foundations of Euclidean geometry

Geometry defines entities that can be physically realized in space, and our knowledge of abstract geometry may therefore stem from our representations of the physical world. Here, we focus on Euclidean geometry, the geometry historically regarded as "natural". We examine whether humans possess representations describing visual forms in the same way as Euclidean geometry - i.e., in terms of their shape and size. One hundred and twelve participants from the U.S. (age 3-34 years), and 25 participants from the Amazon (age 5-67 years) were asked to locate geometric deviants in panels of 6 forms of variable orientation. Participants of all ages and from both cultures detected deviant forms defined in terms of shape or size, while only U.S. adults drew distinctions between mirror images (i.e. forms differing in "sense"). Moreover, irrelevant variations of sense did not disrupt the detection of a shape or size deviant, while irrelevant variations of shape or size did. At all ages and in both cultures, participants thus retained the same properties as Euclidean geometry in their analysis of visual forms, even in the absence of formal instruction in geometry. These findings show that representations of planar visual forms provide core intuitions on which humans' knowledge in Euclidean geometry could possibly be grounded.

Sensitivity to Nonaccidental Configurations of Two-Line Stimuli

According to Recognition-By-Components theory, object recognition relies on a specific subset of three-dimensional shapes called geons. In particular, these configurations constitute a powerful cue to three-dimensional object reconstruction because their two-dimensional projection remains viewpoint-invariant. While a large body of literature has demonstrated sensitivity to changes in these so-called nonaccidental configurations, it remains unclear what information is used in establishing such sensitivity. In this study, we explored the possibility that nonaccidental configurations can already be inferred from the basic constituents of objects, namely, their edges. We constructed a set of stimuli composed of two lines corresponding to various nonaccidental properties and configurations underlying the distinction between geons, including collinearity, alignment, curvature of contours, curvature of configuration axis, expansion, cotermination, and junction type. Using a simple visual search paradigm, we demonstrated that participants were faster at detecting targets that differed from distractors in a nonaccidental property than in a metric property. We also found that only some but not all of the observed sensitivity could have resulted from simple low-level properties of our stimuli. Given that such sensitivity emerged from a configuration of only two lines, our results support the view that nonaccidental configurations could be encoded throughout the visual processing hierarchy even in the absence of object context.

Visual perception of complex shape-transforming processes

Morphogenesis-or the origin of complex natural form-has long fascinated researchers from practically every branch of science. However, we know practically nothing about how we perceive and understand such processes. Here, we measured how observers visually infer shape-transforming processes. Participants viewed pairs of objects ('before' and 'after' a transformation) and identified points that corresponded across the transformation. This allowed us to map out in spatial detail how perceived shape and space were affected by the transformations. Participants' responses were strikingly accurate and mutually consistent for a wide range of non-rigid transformations including complex growth-like processes. A zero-free-parameter model based on matching and interpolating/extrapolating the positions of high-salience contour features predicts the data surprisingly well, suggesting observers infer spatial correspondences relative to key landmarks. Together, our findings reveal the operation of specific perceptual organization processes that make us remarkably adept at identifying correspondences across complex shape-transforming processes by using salient object features. We suggest that these abilities, which allow us to parse and interpret the causally significant features of shapes, are invaluable for many tasks that involve 'making sense' of shape.

Deep Neural Networks as a Computational Model for Human Shape Sensitivity

Theories of object recognition agree that shape is of primordial importance, but there is no consensus about how shape might be represented, and so far attempts to implement a model of shape perception that would work with realistic stimuli have largely failed. Recent studies suggest that state-of-the-art convolutional ‘deep’ neural networks (DNNs) capture important aspects of human object perception. We hypothesized that these successes might be partially related to a human-like representation of object shape. Here we demonstrate that sensitivity for shape features, characteristic to human and primate vision, emerges in DNNs when trained for generic object recognition from natural photographs. We show that these models explain human shape judgments for several benchmark behavioral and neural stimulus sets on which earlier models mostly failed. In particular, although never explicitly trained for such stimuli, DNNs develop acute sensitivity to minute variations in shape and to non-accidental properties that have long been implicated to form the basis for object recognition. Even more strikingly, when tested with a challenging stimulus set in which shape and category membership are dissociated, the most complex model architectures capture human shape sensitivity as well as some aspects of the category structure that emerges from human judgments. As a whole, these results indicate that convolutional neural networks not only learn physically correct representations of object categories but also develop perceptually accurate representational spaces of shapes. An even more complete model of human object representations might be in sight by training deep architectures for multiple tasks, which is so characteristic in human development.

Shape plays an important role in object recognition. Despite years of research, no models of vision could account for shape understanding as found in human vision of natural images. Given recent successes of deep neural networks (DNNs) in object recognition, we hypothesized that DNNs might in fact learn to capture perceptually salient shape dimensions. Using a variety of stimulus sets, we demonstrate here that the output layers of several DNNs develop representations that relate closely to human perceptual shape judgments. Surprisingly, such sensitivity to shape develops in these models even though they were never explicitly trained for shape processing. Moreover, we show that these models also represent categorical object similarity that follows human semantic judgments, albeit to a lesser extent. Taken together, our results bring forward the exciting idea that DNNs capture not only objective dimensions of stimuli, such as their category, but also their subjective, or perceptual, aspects, such as shape and semantic similarity as judged by humans.

Using the axis of elongation to align shapes: developmental changes between 18 and 24 months of age

An object's axis of elongation serves as an important frame of reference for forming three-dimensional representations of object shape. By several recent accounts, the formation of these representations is also related to experiences of acting on objects. Four experiments examined 18- to 24-month-olds' (N=103) sensitivity to the elongated axis in action tasks that required extracting, comparing, and physically rotating an object so that its major axis was aligned with that of a visual standard. In Experiments 1 and 2, the older toddlers precisely rotated both simple and complexly shaped three-dimensional objects in insertion tasks where the visual standard was the rectangular contour defining the opening in a box. The younger toddlers performed poorly. Experiments 3 and 4 provide evidence on emerging abilities in extracting and using the most extended axis as a frame of reference for shape comparison. Experiment 3 showed that 18-month-olds could rotate an object to align its major axis with the direction of their own hand motion, and Experiment 4 showed that they could align the major axis of one object with that of another object of the exact same three-dimensional shape. The results are discussed in terms of theories of the development of three-dimensional shape representations, visual object recognition, and the role of action in these developments.

Greater sensitivity to nonaccidental than metric shape properties in preschool children

Nonaccidental properties (NAPs) are image properties that are invariant over orientation in depth and allow facile recognition of objects at varied orientations. NAPs are distinguished from metric properties (MPs) that generally vary continuously with changes in orientation in depth. While a number of studies have demonstrated greater sensitivity to NAPs in human adults, pigeons, and macaque IT cells, the few studies that investigated sensitivities in preschool children did not find significantly greater sensitivity to NAPs. However, these studies did not provide a principled measure of the physical image differences for the MP and NAP variations. We assessed sensitivity to NAP vs. MP differences in a nonmatch-to-sample task in which 14 preschool children were instructed to choose which of two shapes was different from a sample shape in a triangular display. Importantly, we scaled the shape differences so that MP and NAP differences were roughly equal (although the MP differences were slightly larger), using the Gabor-Jet model of V1 similarity (Lades & et al., 1993). Mean reaction times (RTs) for every child were shorter when the target shape differed from the sample in a NAP than an MP. The results suggest that preschoolers, like adults, are more sensitive to NAPs, which could explain their ability to rapidly learn new objects, even without observing them from every possible orientation.

A Developmental Difference in Shape Processing and Word-Shape Associations between 4 and 6.5 Year Olds

In distinguishing individual shapes (defined by their contours), older children (6.5 years of age on average) performed better than younger children (4 years of age on average), and, although the task did not involve any categorization or generalization, the error pattern was qualitatively affected by shape differences that are generally common distinctions between objects belonging to different categories. The influence of these shape differences was also observed for unfamiliar shapes, demonstrating that the influence of categorization experience was not modulated by the retrieval of shape features from known categories but rather related to a different perception of shape by age. The results suggest a direct influence of categorization experience on more abstract shape processing. When children were distinguishing shapes, new words were paired with the target shapes, and in 2 additional tasks, the acquired name–shape associations were tested. The younger age group was able to remember more words correctly.

Sensitivity to nonaccidental properties across various shape dimensions

Nonaccidental properties (NAPs) are image properties that are invariant over orientation in depth and are distinguished from metric properties (MPs) that can change continuously with variations over depth orientation. To a large extent NAPs allow facile recognition of objects at novel viewpoints. Two match-to-sample experiments with 2D or 3D appearing geons assessed sensitivity to NAP vs. MP differences. A matching geon was always identical to the sample and the distractor differed from the matching geon in either a NAP or an MP on a single generalized cone dimension. For example, if the sample was a cylinder with a slightly curved axis, the NAP distractor would have a straight axis and the MP distractor would have an axis of greater curvature than the sample. Critically, the NAP and MP differences were scaled so that the MP differences were slightly greater according to pixel energy and Gabor wavelet measures of dissimilarity. Exp. 1 used a staircase procedure to determine the threshold presentation time required to achieve 75% accuracy. Exp. 2 used a constant, brief display presentation time with reaction times and error rates as dependent measures. Both experiments revealed markedly greater sensitivity to NAP over MP differences, and this was generally true for the individual dimensions. The NAP advantage was not reflected in the similarity computations of the C2 stage of HMAX, a widely cited model of later stage cortical ventral stream processing.

Towards a new kind of experimental psycho-aesthetics? Reflections on the Parallellepipeda project

Experimental psycho-aesthetics-the science aimed at understanding the factors that determine aesthetic experience-is reviewed briefly as background to describe the Parallellepipeda project, a cross-over project between artists and scientists in Leuven. In particular, I sketch how it started and developed further, with close interactions between the participating artists and scientists. A few examples of specific research projects are mentioned to illustrate the kind of research questions we address and the methodological approach we have taken. We often found an effect of providing participants with additional information, a difference between novice and expert participants, and a shift with increasing experience with an artwork, in the direction of tolerating more complexity and acquiring more order from it. By establishing more connections between parts of an artwork and more associations to the artwork, it becomes a stronger Gestalt, which is more easily mastered by the viewer and leads to increased appreciation. In the final part of the paper, I extract some general lessons from the project regarding a possible new way of doing psycho-aesthetics research, which is able to solve some of the problems of traditional experimental psycho-aesthetics (eg, trade-off between experimental control and ecological validity).