Jay Friedenberg

Detection of symmetry and perceptual organization: The way a lock-and-key process works

We studied the speed with which observers could detect symmetry in drawings that incorporated symmetric contours--related by reflection or translation--within single objects or across different objects. We asked observers to perform a speeded decision whether pairs of contours are the same, i.e., related by reflection or by translation, or different. When the contours belong to a single object, observers are faster to see the relation between contours when they are related by reflection than by translation. When the contours belong to different objects, observers are faster to see the relation between the contours when they are related by translation than by reflection. We tested whether this advantage of translation is due to a lock-and-key process. We first tested our hypothesis by manipulating the correspondence of the features, so as to make matching more difficult. This change did not produce the predicted pattern of results. We performed a second manipulation to change the appearance of the objects: we increased the prägnanz of the objects by changing the type of lines used to connect the contours. Results indicate that perceptual organization can alter detectability of symmetry.

Mapping the similarity space of paintings: Image statistics and visual perception

What makes two images look similar? Here we test the hypothesis that perceived similarity of artwork is related to basic image statistics to which the early visual system is attuned. In two experiments, we employ multidimensional scaling (MDS) analysis of paired-image similarity ratings from observers for paintings. Two sets of images, classified as “landscapes” and “portraits/still-life”, are tested separately. For the landscapes, we find that one of the first two MDS scales of similarity is strongly correlated with a basic greyscale image statistic, whereas the other dimension can be accounted for by a semantic variable (representation of people). For portrait/still-life, the first two MDS scales of similarity are most highly correlated with semantic variables. Linear combinations of statistical and nonstatistical features achieve improved predictive values for the first two MDS scales for both sets. The statistics that play the largest role in shaping similarity judgements in our tests are the activity fraction measure of sparseness and the log-log slope of the spatial frequency amplitude spectrum. We discuss these results in the context of scene perception and in terms of efficient coding of statistical regularities in scenes.

No within-object advantage for detection of rotation

It is known that in a detection task the type of rigid transformation to be detected (reflection vs. translation) interacts with the type of display (closed vs. open contours). The advantage for closed contours found with reflection is believed to be a general within-object advantage, whilst the advantage for open contours found with translation is an exception, described as a lock-and-key process (Acta Psychol. 95 (1997) 119). We tested rotation, using a reaction time paradigm, and found the same result as for translation. Moreover, we found that the critical factor is not the number of objects present, rather it is whether the comparison is made across a surface or across an aperture between surfaces. Post-experiment interviews did not confirm any difference for observers who reported using a conscious lock-and-key mental transformation. We speculate that seeing a translation or a rotation across a closed figure is difficult because the closure of the figure emphasises the mismatch of the contour polarities on the two sides of the figure. That is, there may be a closed object advantage for detecting a difference in polarity which interferes with the task of detecting a regularity in shape. Evidence from the analysis of foil rejection trials supports such a speculation.

Efficient visual system processing of spatial and luminance statistics in representational and non-representational art

An emerging body of research suggests that artists consistently seek modes of representation that are efficiently processed by the human visual system, and that these shared properties could leave statistical signatures. In earlier work, we showed evidence that perceived similarity of representational art could be predicted using intensity statistics to which the early visual system is attuned, though semantic content was also found to be an important factor. Here we report two studies that examine the visual perception of similarity. We test a collection of non-representational art, which we argue possesses useful statistical and semantic properties, in terms of the relationship between image statistics and basic perceptual responses. We find two simple statistics-both expressed as single values-that predict nearly a third of the overall variance in similarity judgments of abstract art. An efficient visual system could make a quick and reasonable guess as to the relationship of a given image to others (i.e., its context) by extracting these basic statistics early in the visual stream, and this may hold for natural scenes as well as art. But a major component of many types of art is representational content. In a second study, we present findings related to efficient representation of natural scene luminances in landscapes by a well-known painter. We show empirically that elements of contemporary approaches to high-dynamic range tone-mapping-which are themselves deeply rooted in an understanding of early visual system coding-are present in the way Vincent Van Gogh transforms scene luminances into painting luminances. We argue that global tone mapping functions are a useful descriptor of an artists perceptual goals with respect to global illumination and we present evidence that mapping the scene to a painting with different implied lighting properties produces a less efficient mapping. Together, these studies suggest that statistical regularities in art can shed light on visual processing.

Perception of two-body center of mass

Participants estimated the perceptual center of mass between two horizontally oriented black dots varying in size and distance. Experiment 1 showed that estimates, measured as distance from the larger dots center, decreased with an increase in size ratio between the dots and a decrease in the distance between them, as predicted by the physical center-of-mass equation. The results were replicated and extended in further experiments with different ratios and distances. In all experiments, the true center was consistently overestimated, either because the stimuli were perceived in a low dimensionality or because of a hesitancy to place estimates near the larger dots edge. In Experiment 4, the center was deliberately placed near this edge for one- and two-dimensional solutions. Participants still overestimated, indicating an “edge effect” as responsible.

Aesthetic Preference for Polygon Shape

Abstract shapes can vary in how much they are preferred by observers, but the key factors are still not well understood. In Experiment 1, observers rated the attractiveness of octagonal polygons that varied in contour length but had approximate constant area. Thus, the shapes differed in compactness. Shapes with partial symmetry were judged to be more attractive as were those with greater total contour length. In a second experiment, participants judged polygons with different numbers of concavities but with constant contour length. Shapes with more concavities were considered more attractive. The data demonstrate a preference for greater complexity—both in terms of contour length and as changes in the number of concavities.

Aesthetic Judgment of Triangular Shape: Compactness and Not the Golden Ratio Determines Perceived Attractiveness

Many studies over a period of more than a century have investigated the influence of the golden ratio on perceived geometric beauty. Surprisingly, very few of these studies used triangular shapes. In Experiment 1, we presented right triangles that differed in regard to their elongation determined by increasing the length of one side relative to another. Attractiveness ratings did not peak at the golden ratio, but there was a very strong influence of axis ratio overall. Participant ratings were a negative decreasing function of ratio. Triangles that pointed upward were judged as significantly more attractive than those that pointed down. We interpret these results according to a compactness hypothesis: triangles that are more compact are less likely to move or break and are thus considered more pleasing. Orientation also affects aesthetics. Upward-pointing triangles with a base parallel to the ground, regardless of their compactness, are also considered more perceptually stable and attractive. These findings were replicated across stimulus type in a second experiment with isosceles triangles and across testing procedure in a third experiment using a paired comparison technique.

Perceiving the Center of Three-Body Displays: The Role of Size-Ratio, Symmetry, Elongation, and Gravity

Participants judged the perceived center of three-dot displays at different orientations. In Experiment 1, the dots formed an equilateral triangle. The direction of the response distribution aligned with the largest dot, along axes of reflec- tional symmetry and with the gravitational down. In Experiment 2, we created isosceles triangles where the distance be- tween one of the dot pairs was varied. Errors were higher for configurations where the symmetry axis was horizontal and a virtual elongation axis was vertical. The results of Experiment 3 replicate this finding and show that response direction is an accommodation to gravity and other shape factors.

Visual estimation of three- and four-body center of mass.

Center-of-mass perception in dot patterns arranged into triangular and quadrilateral configurations was investigated. In Exp. 1, the length, orientation, and direction of dots forming right triangles were varied. Errors in center-of-mass perception by 19 participants increased with the length of the triangles. In Exp. 2,27 participants estimated the centers of squares and rectangles made up of four dots. Accuracy was best for squares that contained greater reflective and rotational symmetry. The orientation of responses was generally downward in both experiments, indicating a gravitational influence. The results are consistent with a process model by which observers use internal pattern structure like medians and axes when estimating the center of an object.

Lateral Feature Displacement and Perceived Facial Attractiveness

Pairs of vertically adjacent facial features were laterally displaced in the same or opposite direction. Undergraduates rated the resulting images on attractiveness. Displacements were first made on normal faces. Symmetric faces were not rated more attractive than normal controls. Faces with two alternating adjacent pairs were rated lower than faces with one or no alternating pairs. In Exp. 2, the same displacements were made from symmetrical faces to control for distance. Symmetric faces again were not rated higher than normal ones, and both conditions were considered more attractive than faces with any type of displacement. This latter result suggests a greater sensitivity to feature displacement when performed from symmetry.