Global shape versus local feature: An angle illusion

Towards the most prägnant Gestalt: Leveling and sharpening as contextually dependent adaptive strategies

Gestalt psychologists posited that we always organize our visual input in the best way possible under the given conditions. Both weakening or removing unnecessary details (i.e., leveling) and exaggerating distinctive features (i.e., sharpening) can contribute to achieving a better organization. When is a feature leveled or sharpened, however? We investigated whether the importance of a feature for discrimination among alternatives influences which organizational tendency occurs. Participants were simultaneously presented with four figures composed of simple geometrical shapes, and asked to reconstruct one of these figures in such a way that another participant would be able to recognize it among the alternatives. The four figures differed either qualitatively or only quantitatively (i.e., far or close context). Regarding quantitative differences, two feature dimensions were varied, with one manifesting a wider range of variability across the alternatives than the other. In case of a smaller variability range, the target figure was either at the extreme of the range or had an in-between value. As expected, the results indicated that sharpening occurred more often for the feature with an extreme value, for the feature exhibiting more variability, and for the features of figures presented in the close context, than for the feature with a non-extreme value, exhibiting less variability, or in the far context. In line with Metzger's (1941) definition of prägnant Gestalts, the essence of a Gestalt is context-dependent, and this will influence whether leveling or sharpening of a feature will lead to the best organization in the specific context.

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.

Optimizing the strength of the Bourdon effect by varying the triangle arrangement

The Bourdon illusion refers to the perceived bentness of the straight collinear edges when two right-angled triangles are placed apex to apex. We studied this illusion using a cancellation method. In the first of three experiments, we manipulated the apex angle, with six different angles ranging from 4° to 45°. Results indicated that the Bourdon illusion is strongest when the angle is around 12°. In the second experiment, we compared four scalene triangles with a right-angled triangle. The angular shift was most salient when the shape corresponded to a right-angled triangle. In the third experiment, the patterns were created by varying the size of one right-angled triangle while holding the size of the second right-angled triangle constant. Results indicated that the Bourdon illusion was strongest when both right-angled triangles were of equal size. Our data suggest that the Bourdon illusion depends critically upon the specific arrangement of shapes in the display.

Curvature Blindness Illusion

We report a novel illusion––curvature blindness illusion: a wavy line is perceived as a zigzag line. The following are required for this illusion to occur. First, the luminance contrast polarity of the wavy line against the background is reversed at the turning points. Second, the curvature of the wavy line is somewhat low; the right angle is too steep to be perceived as an illusion. This illusion implies that, in order to perceive a gentle curve, it is necessary to satisfy more conditions––constant contrast polarity––than perceiving an obtuse corner. It is notable that observers exactly “see” an illusory zigzag line against a physically wavy line, rather than have an impaired perception. We propose that the underlying mechanisms for the gentle curve perception and those of obtuse corner perception are competing with each other in an imbalanced way and the percepts of corner might be dominant in the visual system.

Adaptation to Skew Distortions of Natural Scenes and Retinal Specificity of Its Aftereffects

Image skew is one of the prominent distortions that exist in optical elements, such as in spectacle lenses. The present study evaluates adaptation to image skew in dynamic natural images. Moreover, the cortical levels involved in skew coding were probed using retinal specificity of skew adaptation aftereffects. Left and right skewed natural image sequences were shown to observers as adapting stimuli. The point of subjective equality (PSE), i.e., the skew amplitude in simple geometrical patterns that is perceived to be unskewed, was used to quantify the aftereffect of each adapting skew direction. The PSE, in a two-alternative forced choice paradigm, shifted toward the adapting skew direction. Moreover, significant adaptation aftereffects were obtained not only at adapted, but also at non-adapted retinal locations during fixation. Skew adaptation information was transferred partially to non-adapted retinal locations. Thus, adaptation to skewed natural scenes induces coordinated plasticity in lower and higher cortical areas of the visual pathway.

Observational drawing biases are predicted by biases in perception: Empirical support of the misperception hypothesis of drawing accuracy with respect to two angle illusions

We tested the misperception hypothesis of drawing errors, which states that drawing accuracy is strongly influenced by the perceptual encoding of a to-be-drawn stimulus. We used a highly controlled experimental paradigm in which nonartist participants made perceptual judgements and drawings of angles under identical stimulus exposure conditions. Experiment 1 examined the isosceles/scalene triangle angle illusion; congruent patterns of bias in the perception and drawing tasks were found for 40 and 60° angles, but not for 20 or 80° angles, providing mixed support for the misperception hypothesis. Experiment 2 examined shape constancy effects with respect to reproductions of single acute or obtuse angles; congruent patterns of bias in the perception and drawing tasks were found across a range of angles from 29 to 151°, providing strong support for the misperception hypothesis. In both experiments, perceptual and drawing biases were positively correlated. These results are largely consistent with the misperception hypothesis, suggesting that inaccurate perceptual encoding of angles is an important reason that nonartists err in drawing angles from observation.

Adding rotation to translation: percepts and illusions

This study investigated how the perception of a translating object is affected by rotation. Observers were asked to judge the motion and trajectory of objects that rotated around their centroid while linearly translating. The expected percept, consistent with the actual dynamics used to generate the movie sequences, is that of a translating and rotating object, akin to a tumbling rugby ball. Observers, however, do not always report this and, under certain circumstances, perceive the object to translate on an illusory curved trajectory, similar to a car driving on a curved road. The prevalence of veridical versus nonveridical percepts depends on a number of factors. First, if the object's orientation remains within a limited range relative to the axis of translation, the illusory, curved percept dominates. If the orientation, at any point of the movie sequence, differs sufficiently from the axis of translation, the percept switches to linear translation with rotation. The angle at which the switch occurs is dependent upon a number of factors that relate to an object's elongation and, with it, the prominence of its orientation. For an ellipse with an aspect ratio of 3, the switch occurs at approximately 45 degrees. Higher aspect ratios increase the range; lower ratios decrease it. This applies similarly to rectangular shapes. A line is more likely to be perceived on a curved trajectory than an elongated rectangle, which, in turn, is more likely seen on a curved path than a square. This is largely independent of rotational and translational speeds. Measuring perceived directions of motion at different instants in time allows the shape of the perceived illusory curved path to be extrapolated. This results in a trajectory that is independent of object size and corresponds closely to the actual object orientation at different points during the movie sequence. The results provide evidence for a perceptual transition from an illusory curved trajectory to a veridical linear trajectory (with rotation) for the same object. Both are consistent with special real-world cases such as objects rotating around a centre outside of the object so that their orientation remains tangent to the trajectory (cheetahs running along a curve, sailboats) or objects tumbling along simple trajectories (a monkey spinning in air, spinning cars on ice). In certain cases, the former is an illusion.

Geometrical illusions are not always where you think they are: a review of some classical and less classical illusions, and ways to describe them

Geometrical illusions are known through a small core of classical illusions that were discovered in the second half of the nineteenth century. Most experimental studies and most theoretical discussions revolve around this core of illusions, as though all other illusions were obvious variants of these. Yet, many illusions, mostly described by German authors at the same time or at the beginning of the twentieth century have been forgotten and are awaiting their rehabilitation. Recently, several new illusions were discovered, mainly by Italian authors, and they do not seem to take place into any current classification. Among the principles that are invoked to explain the illusions, there are principles relating to the metric aspects (contrast, assimilation, shrinkage, expansion, attraction of parallels) principles relating to orientations (regression to right angles, orthogonal expansion) or, more recently, to gestalt effects. Here, metric effects are discussed within a measurement framework, in which the geometric illusions are the outcome of a measurement process. There would be a main "convexity" bias in the measures: the measured value m(x) of an extant x would grow more than proportionally with x. This convexity principle, completed by a principle of compromise for conflicting measures can replace, for a large number of patterns, both the assimilation and the contrast effects. We know from evolutionary theory that the most pertinent classification criteria may not be the most salient ones (e.g., a dolphin is not a fish). In order to obtain an objective classification of illusions, I initiated with Kevin O'Regan systematic work on "orientation profiles" (describing how the strength of an illusion varies with its orientation in the plane). We showed first that the Zöllner illusion already exists at the level of single stacks, and that it does not amount to a rotation of the stacks. Later work suggested that it is best described by an "orthogonal expansion"-an expansion of the stacks applied orthogonally to the oblique segments of the stacks, generating an apparent rotation effect. We showed that the Poggendorff illusion was mainly a misangulation effect. We explained the hierarchy of the illusion magnitudes found among variants of the Poggendorff illusion by the existence of control devices that counteract the loss of parallelism or the loss of collinearity produced by the biased measurements. I then studied the trapezium illusion. The oblique sides, but not the bases, were essential to the trapezium illusion, suggesting the existence of a common component between the trapezium and the Zöllner illusion. Unexpectedly, the trapeziums sometimes appeared as twisted surfaces in 3d. It also appeared impossible, using a nulling procedure, to make all corresponding sides of two trapeziums simultaneously equal. The square-diamond illusion is usually presented with one apex of the diamond pointing toward the square. I found that when the figures were displayed more symmetrically, the illusion was significantly reduced. Furthermore, it is surpassed, for all subjects, by an illusion that goes in the opposite direction, in which the diagonal of a small diamond is underestimated with respect to the side of a larger square. In general, the experimental work generated many unexpected results. Each illusory stimulus was compared to a number of control variants, and often, I measured larger distortions in a variant than in the standard stimulus. In the Discussion, I will stress what I think are the main ordering principle in the metric and the orientation domains for illusory patterns. The convexity bias principle and the orthogonal expansion principles help to establish unsuspected links between apparently unrelated stimuli, and reduce their apparently extreme heterogeneity. However, a number of illusions (e.g., those of the twisted cord family, or the Poggendorff illusions) remain unpredicted by the above principles. Finally, I will develop the idea that the brain is constructing several representations, and the one that is commonly used for the purpose of shape perception generates distortions inasmuch as it must satisfy a number of conflicting constraints, such as the constraint of producing a stable shape despite the changing perspectives produced by eye movements.

Arc length-based aspect ratio selection

The aspect ratio of a plot has a dramatic impact on our ability to perceive trends and patterns in the data. Previous approaches for automatically selecting the aspect ratio have been based on adjusting the orientations or angles of the line segments in the plot. In contrast, we recommend a simple, effective method for selecting the aspect ratio: minimize the arc length of the data curve while keeping the area of the plot constant. The approach is parameterization invariant, robust to a wide range of inputs, preserves visual symmetries in the data, and is a compromise between previously proposed techniques. Further, we demonstrate that it can be effectively used to select the aspect ratio of contour plots. We believe arc length should become the default aspect ratio selection method.