Mapping the perceptual structure of rectangles through goodness-of-fit ratings

Three experiments were carried out to investigate the internal structure of a rectangular frame to test Arnheim's (1974 Art and Visual Perception, 1988 The Power of the Center) proposals about its 'structural skeleton'. Observers made subjective ratings of how well a small probe circle fit within a rectangle at different interior positions. In experiment 1, ratings of 77 locations were highest in the center, decreased with distance from the center, greatly elevated along vertical and horizontal symmetry axes, and somewhat elevated along the local symmetry axes. A linear regression model with six symmetry-related factors accounted for 95% of the variance. In experiment 2 we measured perceived fit along local symmetry axes versus global diagonals near the corners to determine which factor was relevant. 2AFC probabilities were elevated only along the local symmetry axes and were higher when the probe was closer to the vertex. In experiment 3 we examined the effect of dividing a rectangular frame into two rectangular 'subframes' using an additional line. The results show that the primary determinant of good fit is the position of the target circle within the local subframes. In general, the results are consistent with Arnheim's proposals about the internal structure of a rectangular frame, but an alternative interpretation is offered in terms of the Gestalt concept of figural goodness.     

Similarity of rectangles

Krantz and Tversky found that neither (log-) height (y) and width (x), nor area (x + y) and shape (x ? y) qualify as “subjective dimensions of rectangles” because both pairs violate the decomposability condition for their dissimilarity data. However, the data suggest a nonlinear transformation of x, y into a pair of subjective dimensions u(x, y), v(x, y) for which decomposability should be approximately satisfied. An explicit statement of this mapping is given.     

Exploring the mental space of autonomous intentional agents

The ability to infer the intentions of other agents on the basis of their motion is a critical psychological faculty. In the present study, we examine a key question underlying this process, namely: What are the psychologically natural categories of intentional agents and actions? To investigate this question empirically, we use displays containing a number of autonomous, independently programmed agents moving about a two-dimensional environment and interacting with one another. Each agent behaves according to its own simple program, controlled by a small number of parameters that define its "personality." We probe participants' impressions of the similarities among the behaviors of the various agents, and then use multidimensional scaling in an attempt to recover the subjective mental space of agent types. An important variable underlying this space turns out to be a parameter that determines how the agent reacts to a nearby agent at one critical distance. A follow-up experiment suggests that variation along this parameter ultimately contributes to modulating a more fundamental perceptual dimension that reflects how "hostile" or "friendly" the agents appear to be.     

Mapping the color space of saccadic selectivity in visual search

Color coding is used to guide attention in computer displays for such critical tasks as baggage screening or air traffic control. It has been shown that a display object attracts more attention if its color is more similar to the color for which one is searching. However, what does similar precisely mean? Can we predict the amount of attention that a display color will receive during a search for a given target color? To tackle this question, two color‐search experiments measuring the selectivity of saccadic eye movements and mapping out its underlying color space were conducted. A variety of mathematical models, predicting saccadic selectivity for given target and display colors, were devised and evaluated. The results suggest that applying a Gaussian function to a weighted Euclidean distance in a slightly modified HSI color space is the best predictor of saccadic selectivity in the chosen paradigm. Hue and intensity information by itself provides a basis for useful predictors, spanning a possibly spherical color space of saccadic selectivity. Although the current models cannot predict saccadic selectivity values for a wide variety of visual search tasks, they reveal some characteristics of color search that are of both theoretical and applied interest, such as for the design of human–computer interfaces.     

The mean-integral representation of rectangles

To assess perceptual interaction between the height and width of rectangles, we used an accuracy variant of the Garner paradigm. We measured the discriminability of height and width (baseline tasks) and size and shape (correlated tasks). From thed′ values in these conditions, we estimated perceptual distances and inferred amean-integral representation in which height and width corresponded to nonindependent dimensions in a perceptual space. This model accounted well for performance in these two-stimulus conditions, and it also explained 70% –80% of the decline in performance in selective and divided attention. In a second experiment, conducted for purposes of comparison with the rectangle discrimination Experiment, we studied the discrimination of horizontal and vertical line segments connected in an L-shape. In size discrimination, observers were equally good with line pairs and rectangles, suggesting holistic perception; but in shape discrimination, they appeared to combine information from the two line-pair components of the rectangle independently. The mean-integral model was again successful in relating performance in the Garner tasks quantitatively.     

Extending neuropsychological assessments into the primary mental ability space

A battery of 17 neuropsychological tests (including the CERAD battery) and 17 psychometric ability tests were administered to a sample of 499 participants of the Seattle Longitudinal study who had been given the psychometric ability tests seven and 14 years earlier. The neuropsychological tests were projected into a 5-factor psychometric ability space by means of extension analysis. The concurrent regressions of the neuropsychology tests on the psychometric ability tests were then used to estimate neuropsychology test scores from the psychometric ability tests administered in 1984, 1991 and 1998. Neuropsychologists then rated the study participants as either normal, suspect or cognitively impaired in 1998. Changes in estimated test scores were computed over seven and fourteen years. Significant odds ratios between normal and cognitively impaired groups were found for all neuropsychological tests over the proximal period and for most tests over the 14-year period. Similar findings occurred for the odds ratios between the normal and suspect groups for the most proximal 7-year changes.     

Making space: Spirituality and mental health

This paper was the Mary Hemingway Rees Memorial Lecture, delivered at the XXIst World Assembly for Mental Health, Vancouver, Canada, 2001. The author had recently completed a period of appointment as the New Zealand Commissioner for Mental Health. In this lecture, the author puts in a moving plea - as a survivior of mental illness - for considering both spirituality and mental health in terms of the experience of the self. She talks about the value of communication particularly by sharing experiences via personal stories. The author goes on to contrast communication and control, and to emphasize the importance of making space in order to accept our own and others' imperfections and vulnerabilities. Attention is drawn to the work of Baruk (1978, 1998, 1999, 2000). She also discusses the way in which mental illness can lead to spiritual progress, and ultimately to mental health. The original version of the talk contained further pictorial illustrations; for technical reasons it would be difficult to reproduce all of them here in the journal. Most of the illustrative material consisted of photographs by the author, including the two photographs that are reproduced in this paper.     

Improved mental representation of space in beginner orienteers

The purpose of the present study was to monitor any improvement in orienteering skills attributable to acquiring a better mental representation of space. Two groups were examined: the experimental group, who attended 6 mo. of orienteering lessons, versus the control group, who did jogging training instead. Each group, consisting of 20 children, was tested on the Corsi Block-tapping Test, run Forward and Backward, and the Star-Butterfly Test. Pre- and post-tests were administered. In the experimental group, scores increased in mean complexity from pre- to post-test on the Forward and the Backward Corsi tests, while on the Star-Butterfly Test both time and mistakes had decreased after the training. In the control group, mean complexity and Star-Butterfly Test scores were unchanged from pre- to post-test. These results showed that after continual training in orienteering techniques, the orienteering group was able to remember and repeat sequences of events with greater precision than before the training, while these skills were unchanged in the control group after training in jogging.     

Bisecting the mental number line in near and far space

Much evidence suggests that common posterior parietal mechanisms underlie the orientation of attention in physical space and along the mental number line. For example, the small leftward bias (pseudoneglect) found in paper-and-pencil line bisection is also found when participants “bisect” number pairs, estimating (without calculating) the number midway between two others. For bisection of physical lines, pseudoneglect has been found to shift rightward as lines are moved from near space (immediately surrounding the body) to far space. We investigated whether the presentation of stimuli in near or far space also modulated spatial attention for the mental number line. Participants bisected physical lines or number pairs presented at four distances (60, 120, 180, 240 cm). Clear rightward shifts in bias were observed for both tasks. Furthermore, the rate at which this shift occurred in the two tasks, as measured by least-squares regression slopes, was significantly correlated across participants, suggesting that the transition from near to far distances induced a common modulation of lateral attention in physical and numerical space. These results demonstrate a tight coupling between number and physical space, and show that even such prototypically abstract concepts as number are modulated by our on-line interactions with the world.     

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.     

Mapping is not sufficient for specifying position in visual space

The general view is that one knows where an object is located in visual space on the basis of which neurons it activates. But there is reason to believe that a radically different method of specifying position is needed, one which identifies the position using coordinates. Those who study motor systems assume such coordinates, but the question of how the sensory system could derive these values is given no attention.     

Saliency metric for subadditive dissimilarity judgments of rectangles

Previous findings that dissimilarity judgments for rectangles are strongly subadditive, that qualitative individual differences are always present, and that four-parameter psychophysical maps can reproduce the average ratings (Sch?nemann & Lazarte, 1987) are replicated. However, the present study in addition suggests that the metric for bounded response transformation, previously used to restore additivity of responses, has a modest effect on the fits of the psychophysical maps. The differential weighing of the coordinates already incorporates segmental subadditivity predictions into the maps. In fact, the psychophysical maps define a subadditive saliency metric that depends on assigning larger weights to larger coordinates. This constraint on the weights of these maps, together with the response times, allows us to identify a strategy shift when subjects respond to two classes of stimulus pairs: For rectangle-rectangle pairs, subjects center on the shape and size of the rectangles; for square-rectangle pairs, the focus is on height and width.     

Orienting numbers in mental space: Horizontal organization trumps vertical

While research on the spatial representation of number has provided substantial evidence for a horizontally oriented mental number line, recent studies suggest vertical organization as well. Directly comparing the relative strength of horizontal and vertical organization, however, we found no evidence of spontaneous vertical orientation (upward or downward), and horizontal trumped vertical when pitted against each other (Experiment 1). Only when numbers were conceptualized as magnitudes (as opposed to nonmagnitude ordinal sequences) did reliable vertical organization emerge, with upward orientation preferred (Experiment 2). Altogether, these findings suggest that horizontal representations predominate, and that vertical representations, when elicited, may be relatively inflexible. Implications for spatial organization beyond number, and its ontogenetic basis, are discussed.