"Warm," "cool," and the colors.

Participants judged affective cooler/warmer gradients around a 12-step color circle. Each pair of adjacent colors was presented twice (left-right reversed), all in random order. Participants readily performed the task, but their settings do not correlate very well. Individual responses were compared with a small number of canonical templates. For a little less than one-half of the participants responses or judgements correlate with such a template. We find a warm pole (in the orange environment) and a cool pole (in the teal environment) connected with two tracks that tend to have one or more gaps or weak, even inverted links. We conclude that the common artistic cool-warm polarity is only weakly reflected in responses of our observers. If it does, the observers apparently use categorical warm and cool poles and may be uncertain in relating adjacent hue steps along the 12-step color circle.

Looking behavior and potential human interactions during locomotion.

As humans move through parts of their environment, they meet others that may or may not try to interact with them. Where do people look when they meet others? We had participants wearing an eye tracker walk through a university building. On the way, they encountered nine "walkers." Walkers were instructed to e.g. ignore the participant, greet him or her, or attempt to hand out a flyer. The participant's gaze was mostly directed to the currently relevant body parts of the walker. Thus, the participants gaze depended on the walker's action. Individual differences in participant's looking behavior were consistent across walkers. Participants who did not respond to the walker seemed to look less at that walker, although this difference was not statistically significant. We suggest that models of gaze allocation should take social motivation into account.

The well-tempered color circle: A chromatic Gestalt.

The "Color Circle" is an important chromatic Gestalt in the visual arts. There is not really a formal equivalent in conventional colorimetry. The fact that the hues can be linearly ordered and that such an order is necessarily periodic was intuited by artists in the early 19th century, but only formally explained by Ostwald and later Schrödinger a century later. As with musical keys, various metrical orders are in common use. Is there such a thing as a "well tempered" order? We consider this an issue for experimental phenomenology. We discuss an attempt based on observations by 30 (nonartist) observers.

Eye contact avoidance in crowds: A large wearable eye-tracking study.

Eye contact is essential for human interactions. We investigated whether humans are able to avoid eye contact while navigating crowds. At a science festival, we fitted 62 participants with a wearable eye tracker and instructed them to walk a route. Half of the participants were further instructed to avoid eye contact. We report that humans can flexibly allocate their gaze while navigating crowds and avoid eye contact primarily by orienting their head and eyes towards the floor. We discuss implications for crowd navigation and gaze behavior. In addition, we address a number of issues encountered in such field studies with regard to data quality, control of the environment, and participant adherence to instructions. We stress that methodological innovation and scientific progress are strongly interrelated.

Light fields and shape from shading.

From a theoretical point of view, the use of the shading cue involves estimates of the light field and thus observers need to judge the light field and the shape simultaneously. The conventional stimulus in perceptual experiments, a circular disk filled with a monotonic gradient on a uniform surround, represents a local shading or tonal gradient. In typical scenes, such gradients vary smoothly from point to point over large areas, whereas light fields are globally defined and tend to be invariant over large parts of the scene. Hence, it is hardly surprising that multi-local shape estimates tend to synchronize although previous reports of such synchronies involved uniform, homogeneous light fields. Here, we consider more complicated and more realistic light fields. We present extensive, highly structured, quantitative observations using novel paradigms. Human observers are able to deal with some structured light fields but totally fail in others, even though these may be formally similar (like radial and circular fields). Observers respond very differently in some cases where the light fields differ only by sign, like converging and diverging fields. These results can be qualitatively understood on the basis of a few simple assumptions, mainly global top-down template matching of peripheral local data.

Perception of the Potential for Interaction in Social Scenes.

In urban environments, humans often encounter other people that may engage one in interaction. How do humans perceive such invitations to interact at a glance? We briefly presented participants with pictures of actors carrying out one of 11 behaviors (e.g., waving or looking at a phone) at four camera-actor distances. Participants were asked to describe what they might do in such a situation, how they decided, and what stood out most in the photograph. In addition, participants rated how likely they deemed interaction to take place. Participants formulated clear responses about how they might act. We show convincingly that what participants would do depended on the depicted behavior, but not the camera-actor distance. The likeliness to interact ratings depended both on the depicted behavior and the camera-actor distance. We conclude that humans perceive the "gist" of photographs and that various aspects of the actor, action, and context depicted in photographs are subjectively available at a glance. Our conclusions are discussed in the context of scene perception, social robotics, and intercultural differences.

Task-related gaze control in human crowd navigation.

Human crowds provide an interesting case for research on the perception of people. In this study, we investigate how visual information is acquired for (1) navigating human crowds and (2) seeking out social affordances in crowds by studying gaze behavior during human crowd navigation under different task instructions. Observers (n = 11) wore head-mounted eye-tracking glasses and walked two rounds through hallways containing walking crowds (n = 38) and static objects. For round one, observers were instructed to avoid collisions. For round two, observers furthermore had to indicate with a button press whether oncoming people made eye contact. Task performance (walking speed, absence of collisions) was similar across rounds. Fixation durations indicated that heads, bodies, objects, and walls maintained gaze comparably long. Only crowds in the distance maintained gaze relatively longer. We find no compelling evidence that human bodies and heads hold one's gaze more than objects while navigating crowds. When eye contact was assessed, heads were fixated more often and for a total longer duration, which came at the cost of looking at bodies. We conclude that gaze behavior in crowd navigation is task-dependent, and that not every fixation is strictly necessary for navigating crowds. When explicitly tasked with seeking out potential social affordances, gaze is modulated as a result. We discuss our findings in the light of current theories and models of gaze behavior. Furthermore, we show that in a head-mounted eye-tracking study, a large degree of experimental control can be maintained while many degrees of freedom on the side of the observer remain.

Wide distribution of external local sign in the normal population.

The extent of the apparent visual field was determined for a group of 78 naïve visual observers. We find that there exists a minority (less than 10%) that is essentially veridical, but that the majority of the population experiences an apparent visual field of only about 90 degrees, thus much narrower than the dioptrics of the eye would suggest (a little over 180 degrees). This is in good accordance with available (albeit mainly anecdotal) evidence, though formal data have been lacking thus far. The finding is discussed in the context of metrical calibration of the topological structure of the visual field, an aspect of "local sign".

Exocentric pointing in depth.

An exocentric pointing task was used to compare the indicated pointing directions under exchange of target and pointer. Such a pair of pointing directions, together with the pointer and target locations, specifies a unique cubic arc. Such an arc may assume one of two qualitatively different shapes, namely a "C-arc" (constant sign of curvature) or an "S-arc" (containing a point of inflection between the endpoints). We show that human observers most often produce S-curves. This is of fundamental importance, since-in case one interprets the curve as an empirically determined "pregeodesic" ("shortest connection", or "straight" connection in visual space)-it would imply that "visual space" in the strict geometrical sense is a non-entity. The experiments were performed in the outside environment, under normal daylight conditions, for distances ranging from one to over thirty meters. The implications of these data are discussed and possible ways to extend the restricted notion of "visual space" (e.g., as advocated by Luneburg) such as to allow one to account for the present results are suggested. Such extensions of the visual space concept include the local adjustment of geometrical structure in regions adjacent to the fixation direction.

Geometry of Pictorial Relief.

Pictorial relief is a quality of visual awareness that happens when one looks into (as opposed to at) a picture. It has no physical counterpart of a geometrical nature. It takes account of cues, mentally identified in the tonal gradients of the physical picture-pigments distributed over a planar substrate. Among generally recognized qualities of relief are color, pattern, texture, shape, and depth. This review focuses on geometrical properties, the spatial variation of depth. To be aware of an extended quality like relief implies a "depth" dimension, a nonphysical spatial entity that may smoothly vary in a surface-like manner. The conceptual understanding is in terms of formal geometry. The review centers on pertinent facts and formal models. The facts are necessarily so-called brute facts (i.e., they cannot be explained scientifically). This review is a foray into the speculative and experimental phenomenology of the visual field.

Estimating the Illumination Direction From Three-Dimensional Texture of Brownian Surfaces.

We studied whether human observers can estimate the illumination direction from 3D textures of random Brownian surfaces, containing undulations over a range of scales. The locally Lambertian surfaces were illuminated with a collimated beam from random directions. The surfaces had a uniform albedo and thus texture appeared only through shading and shadowing. The data confirm earlier results with Gaussian surfaces, containing undulations of a single scale. Observers were able to accurately estimate the source azimuth. If shading dominated the images, the observers committed 180° errors. If cast shadows were present, they resolved this convex-concave-ambiguity almost completely. Thus, observers relied on second-order statistics in the shading regime and used an unidentified first-order cue in the shadow regime. The source elevations could also be estimated, which can be explained by the observers' exploitation of the statistical homogeneity of the stimulus set. The fraction of the surface that is in shadow and the median intensity are likely cues for these elevation estimates.

Reference Frames and 3-D Shape Perception of Pictured Objects: On Verticality and Viewpoint-From-Above.

Research on the influence of reference frames has generally focused on visual phenomena such as the oblique effect, the subjective visual vertical, the perceptual upright, and ambiguous figures. Another line of research concerns mental rotation studies in which participants had to discriminate between familiar or previously seen 2-D figures or pictures of 3-D objects and their rotated versions. In the present study, we disentangled the influence of the environmental and the viewer-centered reference frame, as classically done, by comparing the performances obtained in various picture and participant orientations. However, this time, the performance is the pictorial relief: the probed 3-D shape percept of the depicted object reconstructed from the local attitude settings of the participant. Comparisons between the pictorial reliefs based on different picture and participant orientations led to two major findings. First, in general, the pictorial reliefs were highly similar if the orientation of the depicted object was vertical with regard to the environmental or the viewer-centered reference frame. Second, a viewpoint-from-above interpretation could almost completely account for the shears occurring between the pictorial reliefs. More specifically, the shears could largely be considered as combinations of slants generated from the viewpoint-from-above, which was determined by the environmental as well as by the viewer-centered reference frame.

Exocentric pointing to opposite targets.

We use an exocentric pointing task to study exocentric visual directions to targets that are opposite to a pointer relative to the observer. (The apparent distance between the target and the pointer always exceeded 90 degrees of visual angle.) All pointing takes place in the horizontal plane at eye height. Observers could not see both target and pointer at a single glance. They had to look back and forth between them, using combinations of eye movements, head turns, twists at the waist and turning on the feet. In the limit of diametrically opposite targets we find that the observers pick either one of two distinct orientations of the pointer as equally "visually correct". Which one results depends on the stance assumed by the observer. The difference between the two equally acceptable pointings is between 5 degrees and 10 degrees. Such a result is predicted from earlier measurements in the context of a model that describes the geometry of the horizon as a Riemannian space with varying intrinsic curvature. The present results thus fit--perhaps surprisingly--very well in such a picture.

Perception of length to width relations of city squares.

In this paper, we focus on how people perceive the aspect ratio of city squares. Earlier research has focused on distance perception but not so much on the perceived aspect ratio of the surrounding space. Furthermore, those studies have focused on "open" spaces rather than urban areas enclosed by walls, houses and filled with people, cars, etc. In two experiments, we therefore measured, using a direct and an indirect method, the perceived aspect ratio of five city squares in the historic city center of Delft, the Netherlands. We also evaluated whether the perceived aspect ratio of city squares was affected by the position of the observer on the square. In the first experiment, participants were asked to set the aspect ratio of a small rectangle such that it matched the perceived aspect ratio of the city square. In the second experiment, participants were asked to estimate the length and width of the city square separately. In the first experiment, we found that the perceived aspect ratio was in general lower than the physical aspect ratio. However, in the second experiment, we found that the calculated ratios were close to veridical except for the most elongated city square. We conclude therefore that the outcome depends on how the measurements are performed. Furthermore, although indirect measurements are nearly veridical, the perceived aspect ratio is an underestimation of the physical aspect ratio when measured in a direct way. Moreover, the perceived aspect ratio also depends on the location of the observer. These results may be beneficial to the design of large open urban environments, and in particular to rectangular city squares.

Space-time disarray and visual awareness.

Local space-time scrambling of optical data leads to violent jerks and dislocations. On masking these, visual awareness of the scene becomes cohesive, with dislocations discounted as amodally occluding foreground. Such cohesive space-time of awareness is technically illusory because ground truth is jumbled whereas awareness is coherent. Apparently the visual field is a construction rather than a (veridical) perception.

Awareness of the light field: the case of deformation.

Human observers group local shading patterns into global super-patterns that appear to be illuminated in some unitary fashion. Many years ago, this was noticed for the case of uniform, unidirectional illumination. Recently, we found that it also applies to convergent and divergent illumination flows, but that human observers are blind to rotational light flow patterns (in the sense of being unable to group the local shading patterns). We now report that human observers are also blind to deformation patterns. This is perhaps interesting because convergent, divergent, rotational, and deformation patterns all occur in natural light fields. This is an idiosyncrasy of the human visual system, on par with the fact that visual awareness fails to present the observer with saddle shapes.

Interaction of depth probes and style of depiction.

We study the effect of stylistic differences on the nature of pictorial spaces as they appear to an observer when looking into a picture. Four pictures chosen from diverse styles of depiction were studied by 2 different methods. Each method addresses pictorial depth but draws on a different bouquet of depth cues. We find that the depth structures are very similar for 8 observers, apart from an idiosyncratic depth scaling (up to a factor of 3). The differences between observers generalize over (very different) pictures and (very different) methods. They are apparently characteristic of the person. The differences between depths as sampled by the 2 methods depend upon the style of the picture. This is the case for all observers except one.

Depth in box spaces.

Human observers adjust the frontal view of a wireframe box on a computer screen so as to look equally deep and wide, so that in the intended setting the box looks like a cube. Perspective cues are limited to the size-distance effect, since all angles are fixed. Both the size on the screen, and the viewing distance from the observer to the screen were varied. All observers prefer a template view of a cube over a veridical rendering, independent of picture size and viewing distance. If the rendering shows greater or lesser foreshortening than the template, the box appears like a long corridor or a shallow slab, that is, like a 'deformed' cube. Thus observers ignore 'veridicality'. This does not fit an 'inverse optics' model. We discuss a model of 'vision as optical user interface'.

Measuring 3D point configurations in pictorial space.

We propose a novel method to probe the depth structure of the pictorial space evoked by paintings. The method involves an exocentric pointing paradigm that allows one to find the slope of the geodesic connection between any pair of points in pictorial space. Since the locations of the points in the picture plane are known, this immediately yields the depth difference between the points. A set of depth differences between all pairs of points from an N-point (N > 2) configuration then yields the configuration in depth up to an arbitrary depth offset. Since an N-point configuration implies N(N-1) (ordered) pairs, the number of observations typically far exceeds the number of inferred depths. This yields a powerful check on the geometrical consistency of the results. We report that the remaining inconsistencies are fully accounted for by the spread encountered in repeated observations. This implies that the concept of 'pictorial space' indeed has an empirical significance. The method is analyzed and empirically verified in considerable detail. We report large quantitative interobserver differences, though the results of all observers agree modulo a certain affine transformation that describes the basic cue ambiguities. This is expected on the basis of a formal analysis of monocular optical structure. The method will prove useful in a variety of potential applications.

Depth.

Depth is the feeling of remoteness, or separateness, that accompanies awareness in human modalities like vision and audition. In specific cases depths can be graded on an ordinal scale, or even measured quantitatively on an interval scale. In the case of pictorial vision this is complicated by the fact that human observers often appear to apply mental transformations that involve depths in distinct visual directions. This implies that a comparison of empirically determined depths between observers involves pictorial space as an integral entity, whereas comparing pictorial depths as such is meaningless. We describe the formal structure of pictorial space purely in the phenomenological domain, without taking recourse to the theories of optics which properly apply to physical space-a distinct ontological domain. We introduce a number of general ways to design and implement methods of geodesy in pictorial space, and discuss some basic problems associated with such measurements. We deal mainly with conceptual issues.