Perception of shape and space across rigid transformations

Shape configuration of mental targets representation as a holistic measure in a 3D real world pointing test for spatial orientation

Deficits in spatial memory are often early signs of neurological disorders. Here, we analyzed the geometrical shape configuration of 2D-projections of pointing performances to a memorized array of spatially distributed targets in order to assess the feasibility of this new holistic analysis method. The influence of gender differences and cognitive impairment was taken into account in this methodological study. 56 right-handed healthy participants (28 female, mean age 48.89 ± 19.35 years) and 22 right-handed patients with heterogeneous cognitive impairment (12 female, mean age 71.73 ± 7.41 years) underwent a previously validated 3D-real-world pointing test (3D-RWPT). Participants were shown a 9-dot target matrix and afterwards asked to point towards each target in randomized order with closed eyes in different body positions relative to the matrix. Two-dimensional projections of these pointing vectors (i.e., the shapes resulting from the individual dots) were then quantified using morphological analyses. Shape configurations in healthy volunteers largely reflected the real-world target pattern with gender-dependent differences (ANCOVA area males vs. females F(1,73) = 9.00, p 3.69 × 10-3, partial η2 = 0.10, post-hoc difference = 38,350.43, pbonf=3.69 × 10-3**, Cohen's d 0.76, t 3.00). Patients with cognitive impairment showed distorted rectangularity with more large-scale errors, resulting in decreased overall average diameters and solidity (ANCOVA diameter normal cognition/cognitive impairment F(1,71) = 9.30, p 3.22 × 10-3, partial η2 = 0.09, post-hoc difference = 31.22, pbonf=3.19 × 10-3**, Cohen's d 0.92, t 3.05; solidity normal cognition/cognitive impairment F(1,71) = 7.79, p 6.75 × 10-3, partial η2 = 0.08, post-hoc difference = 0.07, pbonf=6.76 × 10-3** Cohen's d 0.84, t 2.79). Shape configuration analysis of the 3D-RWPT target array appears to be a suitable holistic measure of spatial performance in a pointing task. The results of this methodological investigation support further testing in a clinical study for differential diagnosis of disorders with spatial memory deficits.

Homology judgements of pre-evolutionary naturalists explained by general human shape matching abilities

Many biological homologies were discovered before Darwin and without agreed criteria. Paradigmatic examples include the phylogenetic homology of mammalian forelimb bones and the serial homology of floral organs in waterlilies. It is generally assumed that perceiving similarities intuitively was the first step towards establishing morphological homologies. However, this assumption has never been tested. We hypothesize that pre-evolutionary naturalists relied on the well-established ability of humans to find visual correspondences between differently shaped objects. By using images of homologous organs and applying an experimental paradigm from cognitive psychology, we found that (1) naïve participants utilised this ability when identifying "corresponding" locations. In addition, (2) these locations were statistically indistinguishable from the locations that pre-evolutionary naturalists and contemporary experts considered homologous. Furthermore, (3) presenting naïve participants with images of intermediate organs influenced their correspondence judgements. This influence was in line with historical reports according to which intermediate organs facilitated the pre-evolutionary recognition of homologies.

Dynamic pruning group equivariant network for motor imagery EEG recognition

Introduction: The decoding of the motor imaging electroencephalogram (MI-EEG) is the most critical part of the brain-computer interface (BCI) system. However, the inherent complexity of EEG signals makes it challenging to analyze and model them. Methods: In order to effectively extract and classify the features of EEG signals, a classification algorithm of motor imagery EEG signals based on dynamic pruning equal-variant group convolutional network is proposed. Group convolutional networks can learn powerful representations based on symmetric patterns, but they lack clear methods to learn meaningful relationships between them. The dynamic pruning equivariant group convolution proposed in this paper is used to enhance meaningful symmetric combinations and suppress unreasonable and misleading symmetric combinations. At the same time, a new dynamic pruning method is proposed to dynamically evaluate the importance of parameters, which can restore the pruned connections. Results and Discussion: The experimental results show that the pruning group equivariant convolution network is superior to the traditional benchmark method in the benchmark motor imagery EEG data set. This research can also be transferred to other research areas.

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.

Melting Ice With Your Mind: Representational Momentum for Physical States

When a log burns, it transforms from a block of wood into a pile of ash. Such state changes are among the most dramatic ways objects change, going beyond mere changes of position or orientation. How does the mind represent changes of state? A foundational result in visual cognition is that memory extrapolates the positions of moving objects-a distortion called representational momentum. Here, five experiments (N = 400 adults) exploited this phenomenon to investigate mental representations in state space. Participants who viewed objects undergoing state changes (e.g., ice melting, logs burning, or grapes shriveling) remembered them as more changed (e.g., more melted, burned, or shriveled) than they actually were. This pattern extended to several types of state changes, went beyond their low-level properties, and even adhered to their natural trajectories in state space. Thus, mental representations of objects actively incorporate how they change-not only in their relation to their environment, but also in their essential qualities.

The many facets of shape

Shape is an interesting property of objects because it is used in ordinary discourse in ways that seem to have little connection to how it is typically defined in mathematics. The present article describes how the concept of shape can be grounded within Euclidean and non-Euclidean geometry and also to human perception. It considers the formal methods that have been proposed for measuring the differences among shapes and how the performance of those methods compares with shape difference thresholds of human observers. It discusses how different types of shape change can be perceptually categorized. It also evaluates the specific data structures that have been used to represent shape in models of both human and machine vision, and it reviews the psychophysical evidence about the extent to which those models are consistent with human perception. Based on this review of the literature, we argue that shape is not one thing but rather a collection of many object attributes, some of which are more perceptually salient than others. Because the relative importance of these attributes can be context dependent, there is no obvious single definition of shape that is universally applicable in all situations.

The causal future: The influence of shape features caused by external transformation on visual attention

Previous studies have validated that participants can distinguish different origins of objects’ shape features, teasing apart features caused by transformation (causal history) from those of the original shape. Considering bite as a transformation example, two experiments were designed to investigate the effect of causal history on the allocation of visual attention. Participants were presented with regular and familiar complete or bitten shapes in Experiment 1 and unfamiliar and irregular complete or bitten shapes in Experiment 2 over a range of stimulus onset asynchronies (SOAs). The task was to identify different probes (i.e., punctuation marks) that equally appeared at four positions around these shapes. The results showed that complete regular shapes had no impact on participants’ reaction times to identify probes that appeared at the four different positions (Experiment 1), whereas complete irregular shapes would facilitate participants’ responses to the probes that appeared at the positions around the “head” of the irregular shape (Experiment 2) regardless of SOAs. When presented with bitten shapes, in the earlier phase of visual processing, participants’ response patterns resembled those found when complete shapes were presented. However, with longer SOAs, participants were faster in identifying probes that appeared at those positions that were around the nontransformed region of the bitten shapes. The results revealed that information about shape features caused by causal history could be incorporated, albeit relatively later, into the allocation of visual attention. The role of causal history in the speculation about one object's future development is discussed.

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.

Searching for Strangely Shaped Cookies - Is Taking a Bite Out of a Cookie Similar to Occluding Part of It?

Does recognizing the transformations that gave rise to an object’s retinal image contribute to early object recognition? It might, because finding a partially occluded object among similar objects that are not occluded is more difficult than finding an object that has the same retinal image shape without evident occlusion. If this is because the occlusion is recognized as such, we might see something similar for other transformations. We confirmed that it is difficult to find a cookie with a section missing when this was the result of occlusion. It is not more difficult to find a cookie from which a piece has been bitten off than to find one that was baked in a similar shape. On the contrary, the bite marks help detect the bitten cookie. Thus, biting off a part of a cookie has very different effects on visual search than occluding part of it. These findings do not support the idea that observers rapidly and automatically compensate for the ways in which objects’ shapes are transformed to give rise to the objects’ retinal images. They are easy to explain in terms of detecting characteristic features in the retinal image that such transformations may hide or create.

The role of semantics in the perceptual organization of shape

Establishing correspondence between objects is fundamental for object constancy, similarity perception and identifying transformations. Previous studies measured point-to-point correspondence between objects before and after rigid and non-rigid shape transformations. However, we can also identify 'similar parts' on extremely different objects, such as butterflies and owls or lizards and whales. We measured point-to-point correspondence between such object pairs. In each trial, a dot was placed on the contour of one object, and participants had to place a dot on 'the corresponding location' of the other object. Responses show correspondence is established based on similarities between semantic parts (such as head, wings, or legs). We then measured correspondence between ambiguous objects with different labels (e.g., between 'duck' and 'rabbit' interpretations of the classic ambiguous figure). Despite identical geometries, correspondences were different across the interpretations, based on semantics (e.g., matching 'Head' to 'Head', 'Tail' to 'Tail'). We present a zero-parameter model based on labeled semantic part data (obtained from a different group of participants) that well explains our data and outperforms an alternative model based on contour curvature. This demonstrates how we establish correspondence between very different objects by evaluating similarity between semantic parts, combining perceptual organization and cognitive processes.

Softness and weight from shape: Material properties inferred from local shape features

Object shape is an important cue to material identity and for the estimation of material properties. Shape features can affect material perception at different levels: at a microscale (surface roughness), mesoscale (textures and local object shape), or megascale (global object shape) level. Examples for local shape features include ripples in drapery, clots in viscous liquids, or spiraling creases in twisted objects. Here, we set out to test the role of such shape features on judgments of material properties softness and weight. For this, we created a large number of novel stimuli with varying surface shape features. We show that those features have distinct effects on softness and weight ratings depending on their type, as well as amplitude and frequency, for example, increasing numbers and pointedness of spikes makes objects appear harder and heavier. By also asking participants to name familiar objects, materials, and transformations they associate with our stimuli, we can show that softness and weight judgments do not merely follow from semantic associations between particular stimuli and real-world object shapes. Rather, softness and weight are estimated from surface shape, presumably based on learned heuristics about the relationship between a particular expression of surface features and material properties. In line with this, we show that correlations between perceived softness or weight and surface curvature vary depending on the type of surface feature. We conclude that local shape features have to be considered when testing the effects of shape on the perception of material properties such as softness and weight.

Color consistency in the appearance of bleached fabrics

Human observers are remarkably good at perceiving constant object color across illumination changes. However, there are numerous other factors that can modulate surface appearance, such as aging, bleaching, staining, or soaking. Despite this, we are often able to identify material properties across such transformations. Little is known about how and to what extent we can compensate for the accompanying color transformations. Here we investigated whether humans could reproduce the original color of bleached fabrics. We treated 12 different fabric samples with a commercial bleaching product. Bleaching increased luminance and decreased saturation. We presented photographs of the original and bleached samples on a computer screen and asked observers to match the fabric colors to an adjustable matching disk. Different groups of observers produced matches for original and bleached samples. One group of observers were instructed to match the color of the bleached samples as they were before bleaching (i.e., compensate for the effects of bleaching); another, to accurately match color appearance. Observers did compensate significantly for the effects of bleaching when instructed to do so, but not in the appearance match condition. Results of a second experiment suggest that observers achieve color consistency, at least in part, through a strategy based on local spatial differences within the bleached samples. According to the results of a third experiment, these local spatial differences are likely to be the perceptual image cues that allow participants to determine whether a sample is bleached. When the effect of bleaching was limited or uniformly distributed across a sample's surface, observers were uncertain about the bleaching magnitude and seemed to apply cognitive strategies to achieve color consistency.

Visual perception of shape-transforming processes: 'Shape Scission'

Shape-deforming processes (e.g., squashing, bending, twisting) can radically alter objects' shapes. After such a transformation, some features are due to the object's original form, while others are due to the transformation, yet it is challenging to separate the two. We tested whether observers can distinguish the causal origin of different features, teasing apart the characteristics of the original shape from those imposed by transformations, a process we call 'shape scission'. Using computer graphics, we created 8 unfamiliar objects and subjected each to 8 transformations (e.g., "twisted", "inflated", "melted"). One group of participants named transformations consistently. A second group arranged cards depicting the objects into classes according to either (i) the original shape or (ii) the type of transformation. They could do this almost perfectly, suggesting that they readily distinguish the causal origin of shape features. Another group used a digital painting interface to indicate which locations on the objects appeared transformed, with responses suggesting they can localise features caused by transformations. Finally, we parametrically varied the magnitude of the transformations, and asked another group to rate the degree of transformation. Ratings correlated strongly with transformation magnitude with a tendency to overestimate small magnitudes. Responses were predicted by both the magnitude and area affected by the transformation. Together, the findings suggest that observers can scission object shapes into original shape and transformation features and access the resulting representational layers at will.

Visual perception of shape altered by inferred causal history

One of the main functions of vision is to represent object shape. Most theories of shape perception focus exclusively on geometrical computations (e.g., curvatures, symmetries, axis structure). Here, however, we find that shape representations are also profoundly influenced by an object’s causal origins: the processes in its past that formed it. Observers placed dots on objects to report their perceived symmetry axes. When objects appeared ‘complete’—created entirely by a single generative process—responses closely approximated the object’s geometrical axes. However, when objects appeared ‘bitten’—as if parts had been removed by a distinct causal process—the responses deviated significantly from the geometrical axes, as if the bitten regions were suppressed from the computation of symmetry. This suppression of bitten regions was also found when observers were not asked about symmetry axes but about the perceived front and back of objects. The findings suggest that visual shape representations are more sophisticated than previously appreciated. Objects are not only parsed according to what features they have, but also to how or why they have those features.

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.

An overview of quantitative approaches in Gestalt perception

Gestalt psychology is often criticized as lacking quantitative measurements and precise mathematical models. While this is true of the early Gestalt school, today there are many quantitative approaches in Gestalt perception and the special issue of Vision Research "Quantitative Approaches in Gestalt Perception" showcases the current state-of-the-art. In this article we give an overview of these current approaches. For example, ideal observer models are one of the standard quantitative tools in vision research and there is a clear trend to try and apply this tool to Gestalt perception and thereby integrate Gestalt perception into mainstream vision research. More generally, Bayesian models, long popular in other areas of vision research, are increasingly being employed to model perceptual grouping as well. Thus, although experimental and theoretical approaches to Gestalt perception remain quite diverse, we are hopeful that these quantitative trends will pave the way for a unified theory.