The visual light field

Transparent layer constancy improves with increased naturalness of the scene

The extent to which hue, saturation, and transmittance of thin light-transmitting layers are perceived as constant when the illumination changes (transparent layer constancy, TLC) has previously been investigated with simple stimuli in asymmetric matching tasks. In this task, a target filter is presented under one illumination and a second filter is matched under a second illumination. Although two different illuminations are applied in the stimulus generation, there is no guarantee that the stimulus will be interpreted appropriately by the visual system. In previous work, we found a higher degree of TLC when both illuminations were presented alternately than when they were presented simultaneously, which could be explained, for example, by an increased plausibility of an illumination change. In this work, we test whether TLC can also be increased in simultaneous presentation when the filter's belonging to a particular illumination context is made more likely by additional cues. To this end, we presented filters in differently lit areas of complex, naturalistically rendered 3D scenes containing different types of cues to the prevailing illumination, such as scene geometry, object shading, and cast shadows. We found higher degrees of TLC in such complex scenes than in colorimetrically similar simple 2D color mosaics, which is consistent with the results of similar studies in the area of color constancy. To test which of the illumination cues available in the scenes are actually used, the different types of cues were successively removed from the naturalistically rendered complex scene. A total of eight levels of scene complexity were examined. As expected, TLC decreased the more cues were removed. Object shading and illumination gradients due to shadow cast were both found to have a positive effect on TLC. A second filter had a small positive effect on TLC when added in strongly reduced scenes, but not in the complex scenes that already provide many cues about the illumination context of the filter.

Estimating lighting direction in scenes with multiple objects

To recover the reflectance and shape of an object in a scene, the human visual system must account for the properties of the light illuminating the object. Here, we examine the extent to which multiple objects within a scene are utilised to estimate the direction of lighting in a scene. In Experiment 1, we presented participants with rendered scenes that contained 1, 9, or 25 unfamiliar blob-like objects and measured their capacity to discriminate whether a directional light source was left or right of the participants' vantage point. Trends reported for ensemble perception suggest that the number of utilised objects-and, consequently, discrimination sensitivity-would increase with set size. However, we find little indication that increasing the number of objects in a scene increased discrimination sensitivity. In Experiment 2, an equivalent noise analysis was used to measure participants' internal noise and the number of objects used to judge the average light source direction in a scene, finding that participants relied on 1 or 2 objects to make their judgement regardless of whether 9 or 25 objects were present. In Experiment 3, participants completed a shape identification task that required an implicit judgement of light source direction, rather than an explicit judgement as in Experiments 1 and 2. We find that sensitivity for identifying surface shape was comparable for scenes containing 1, 9, and 25 objects. Our results suggest that the visual system relied on a small number of objects to estimate the direction of lighting in our rendered scenes.

The art of the float

For more than 2000 years, artists have exploited cast shadows to influence how objects appear to be positioned in a scene. A contact cast shadow can anchor an object to the ground and a detached cast shadow can make an object appear to float. However, there is a period of approximately 1000 years when there were virtually no cast shadows in art. How were states of contact versus floating depicted by artists without cast shadows? Here, we survey various techniques used by artists to anchor relative position with and without cast shadows. We then conduct experimental tests of the hypothesized surface attraction principles that underlie these techniques. In the absence of cast shadows, an object (a wooden box) was often seen as resting on a surface as long as that surface offered information about ground orientation and support (a tiled floor). When the ground surface was ambiguous and cloud-like (1/f noise), the box was more likely to be seen to float. The presence of cast shadows made the box appear to contact the ground whether it was well-defined or ambiguous. Both shadows and surface support also increased the accuracy with which participants detected when the box was tilted up from the ground. These results indicate that artists long ago discovered the important power of support relationships to anchor objects to surfaces in the absence of shadows.

Quantifying the spatial, temporal, angular and spectral structure of effective daylight in perceptually meaningful ways

We present a method to capture the 7-dimensional light field structure, and translate it into perceptually-relevant information. Our spectral cubic illumination method quantifies objective correlates of perceptually relevant diffuse and directed light components, including their variations over time, space, in color and direction, and the environment's response to sky and sunlight. We applied it "in the wild", capturing how light on a sunny day differs between light and shadow, and how light varies over sunny and cloudy days. We discuss the added value of our method for capturing nuanced lighting effects on scene and object appearance, such as chromatic gradients.

Diffuseness of illumination suitable for reproducing a faithful and ideal appearance of an object

We investigated the diffuseness of illumination to examine which diffuseness condition faithfully reproduces the surface appearance of an object as seen in a natural environment. We also examined the diffuseness condition which produces the ideal appearance of the object. Observers first memorized the appearance of various objects in daily environments, and then evaluated the appearance of the objects under different diffuseness conditions. The observers reported that the moderate diffuseness condition best reproduced a faithful and ideal appearance of the objects, compared with the low and high diffuseness conditions. This indicates that a very low or high diffuseness, which is unfamiliar, is not suitable for reproducing an object's surface appearance faithfully and ideally. Our results suggest that it is possible to determine a suitable diffuseness condition for reproducing the appearance of objects.

Effects of light map orientation and shape on the visual perception of canonical materials

We previously presented a systematic optics-based canonical approach to test material-lighting interactions in their full natural ecology, combining canonical material and lighting modes. Analyzing the power of the spherical harmonics components of the lighting allowed us to predict the lighting effects on material perception for generic natural illumination environments. To further understand how material properties can be brought out or communicated visually, in the current study, we tested whether and how light map orientation and shape affect these interactions in a rating experiment: For combinations of four materials, three shapes, and three light maps, we rotated the light maps in 15 different configurations. For the velvety objects, there were main and interaction effects of lighting and light map orientation. The velvety ratings decreased when the main light source was coming from the back of the objects. For the specular objects, there were main and interaction effects of lighting and shape. The specular ratings increased when the environment in the specular reflections was clearly visible in the stimuli. For the glittery objects, there were main and interaction effects of shape and light map orientation. The glittery ratings correlated with the coverage of the glitter reflections as the shape and light map orientation varied. For the matte objects, results were robust across all conditions. Last, we propose combining the canonical modes approach with so-called importance maps to analyze the appearance features of the proximal stimulus, the image, in contradistinction to the physical parameters as an approach for optimization of material communication.

Temporal dynamics of daylight perception: Detection thresholds

Temporal changes in illumination are ubiquitous; natural light, for example, varies in color temperature and irradiance throughout the day. Yet little is known about human sensitivity to temporal changes in illumination spectra. Here, we aimed to determine the minimum detectable velocity of chromaticity change of daylight metamers in an immersive environment. The main stimulus was a continuous, monotonic change in global illumination chromaticity along the daylight locus in warmer (toward lower correlated color temperatures [CCTs]) or cooler directions, away from an adapting base light (CCT: 13,000 K, 6500 K, 4160 K, or 2000 K). All lights were generated by spectrally tunable overhead lamps as smoothest-possible metamers of the desired chromaticities. Mean detection thresholds (for 22 participants) for a fixed duration of 10 seconds ranged from 15 to 2 CIELUV ΔE units, depending significantly on base light CCT and with a significant interaction between CCT and direction of change. Cool changes become less noticeable for progressively warmer base lights and vice versa. For the two extreme base lights, sensitivity to changes toward neutral is significantly lower than for the opposite direction. The results suggest a “neutral bias” in illumination change discriminability, and that typical temporal changes in daylight chromaticity are likely to be below threshold detectability, at least where there are no concomitant overall illuminance changes. These factors may contribute to perceptual stability of natural scenes and color constancy.

On the Ambient Optic Array: James Gibson's Insights About the Phenomenon of Chiaroscuro

In 1966, James Gibson first presented his theory of the ambient optic array, and he proposed a new field of ecological optics that he hoped would advance our knowledge on this topic. This study will consider how his ideas have largely come to fruition over the past 50 years. It reviews the research on the visual perception of three-dimensional shape from shading, the effects of ambient light from surface interreflections on observers' perceptions, the perception of the light field, and the perception of surface materials. Finally, it also considers Gibson's impact on these developments.

Light: Toward a Transdisciplinary Science of Appearance and Atmosphere

To understand the processes behind seeing light, we need to integrate knowledge about the incoming optical structure, its perception, and how light interacts with material, shape, and space-objectively and subjectively. To that end, we need a novel approach to the science of light, namely, a transdisciplinary science of appearance, integrating optical, perceptual, and design knowledge and methods. In this article, I review existing literature as a basis for such a synthesis, which should discuss light in its full complexity, including its spatial properties and interactions with materials, shape, and space. I propose to investigate this by representing the endless variety of light, materials, shapes, and space as canonical modes and their combinations.

The Limiting Case of Amodal Completion: The Phenomenal Salience and the Role of Contrast Polarity

In this work, we demonstrated unique and relevant visual properties imparted by contrast polarity in perceptual organization and in eliciting amodal completion, which is the vivid completion of a single continuous object of the visible parts of an occluded shape despite portions of its boundary contours not actually being seen. T-junction, good continuation, and closure are considered the main principles involved according to relevant explanations of amodal completion based on the simplicity–Prägnanz principle, Helmholtz’s likelihood, and Bayesian inference. The main interest of these approaches is to explain how the occluded object is completed, what is the amodal shape, and how contours of partially visible fragments are relatable behind an occluder. Different from these perspectives, amodal completion was considered here as a visual phenomenon and not as a process, i.e., the final outcome of perceptual processes and grouping principles. Therefore, the main question we addressed through our stimuli was “What is the role of shape formation and perceptual organization in inducing amodal completion?” To answer this question, novel stimuli, similar to limiting cases and instantiae crucis, were studied through Gestalt experimental phenomenology. The results demonstrated the domination of the contrast polarity against good continuation, T-junctions, and regularity. Moreover, the limiting conditions explored revealed a new kind of junction next to the T- and Y-junctions, respectively responsible for amodal completion and tessellation. We called them I-junctions. The results were theoretically discussed in relation to the previous approaches and in the light of the phenomenal salience imparted by contrast polarity.

Shape from shading under inconsistent illumination

People are able to perceive the 3D shape of illuminated surfaces using image shading cues. Theories about how we accomplish this often assume that the human visual system estimates a single lighting direction and interprets shading cues in accord with that estimate. In natural scenes, however, lighting can be much more complex than this, with multiple nearby light sources. Here we show that the human visual system can successfully judge 3D surface shape even when the lighting direction varies from place to place over a surface, provided the scale at which these lighting changes occur is similar to, or larger than, the size of the shape features being judged. Furthermore, we show that despite being able to accommodate rapid changes in lighting direction when judging shape, observers are generally unable to detect these changes. We conclude that, rather than relying on a single estimated illumination direction, the human visual system can accommodate illumination that varies substantially and rapidly across a surface.

Asymmetric perceptual confounds between canonical lightings and materials

To better understand the interactions between material perception and light perception, we further developed our material probe MatMix 1.0 into MixIM 1.0, which allows optical mixing of canonical lighting modes. We selected three canonical lighting modes (ambient, focus, and brilliance) and created scenes to represent the three illuminations. Together with four canonical material modes (matte, velvety, specular, glittery), this resulted in 12 basis images (the "bird set"). These images were optically mixed in our probing method. Three experiments were conducted with different groups of observers. In Experiment 1, observers were instructed to manipulate MixIM 1.0 and match optically mixed lighting modes while discounting the materials. In Experiment 2, observers were shown a pair of stimuli and instructed to simultaneously judge whether the materials and lightings were the same or different in a four-category discrimination task. In Experiment 3, observers performed both the matching and discrimination tasks in which only the ambient and focus light were implemented. Overall, the matching and discrimination results were comparable as (a) robust asymmetric perceptual confounds were found and confirmed in both types of tasks, (b) performances were consistent and all above chance levels, and (c) observers had higher sensitivities to our canonical materials than to our canonical lightings. The latter result may be explained in terms of a generic insensitivity for naturally occurring variations in light conditions. Our findings suggest that midlevel image features are more robust across different materials than across different lightings and, thus, more diagnostic for materials than for lightings, causing the asymmetric perceptual confounds.

Sensual Light? Subjective Dimensions of Ambient Illumination

This work concerns the subjective impression of perceived illumination. The purpose of the study is to test attributes expressing qualitative experiences referring to ambient lighting that can be applied as descriptors. Seventy participants viewed an actual model room, with the fourth wall removed (viewing booth). Walls, floor, and ceiling were achromatic. Two achromatic cubes were placed inside the room: One was a reflectance increment to the walls, the other a decrement. The room was illuminated by two different light sources, Artificial Daylight (D65) or Tungsten Filament (F), the order of which was randomized across participants. The participants' task was to evaluate ambient illumination for each light source. A semantic differential method was employed with 27 pairs of adjectives on 1 to 7 rating scales, categorized in three groups: characteristics of atmosphere, time, and cross-modal. Only the ratings of nine pairs of adjectives were not influenced by the type of illumination. The most differentiated couples under different illuminants were hot/cold and modern/old, but large differences also appeared with the following couples: hard/soft, technological/primitive, summery/wintry, warm/cool, sensual/frigid, natural/artificial, and hospitable/inhospitable. The hypothesis that there would be consistency among the subjects in evaluations of the characteristics tested and that these would be differently perceived under different illuminants was confirmed. The results show that it is possible to identify subjective perceived illumination as a phenomenon endowed with specific filling-in qualities and that as a perceptual experience it can be categorized, with implications for application in architecture and design.

Illumination discrimination in the absence of a fixed surface-reflectance layout

Previous studies have shown that humans can discriminate spectral changes in illumination and that this sensitivity depends both on the chromatic direction of the illumination change and on the ensemble of surfaces in the scene. These studies, however, always used stimulus scenes with a fixed surface-reflectance layout. Here we compared illumination discrimination for scenes in which the surface reflectance layout remains fixed (fixed-surfaces condition) to those in which surface reflectances were shuffled randomly across scenes, but with the mean scene reflectance held approximately constant (shuffled-surfaces condition). Illumination discrimination thresholds in the fixed-surfaces condition were commensurate with previous reports. Thresholds in the shuffled-surfaces condition, however, were considerably elevated. Nonetheless, performance in the shuffled-surfaces condition exceeded that attainable through random guessing. Analysis of eye fixations revealed that in the fixed-surfaces condition, low illumination discrimination thresholds (across observers) were predicted by low overall fixation spread and high consistency of fixation location and fixated surface reflectances across trial intervals. Performance in the shuffled-surfaces condition was not systematically related to any of the eye-fixation characteristics we examined for that condition, but was correlated with performance in the fixed-surfaces condition.

Visual Light Zones

In this article, we studied perception of a particular case of light fields that is characterized by a difference in its consistent structure between parts of a scene. In architectural lighting design, such a consistent structure in a part of a light field is called a light zone. First, we explored whether human observers are sensitive to light zones, that is, zones determined primarily by light flow differences, for a natural-looking scene. We found that observers were able to distinguish the light conditions between the zones. The results suggested an effect of light zones' orientation. Therefore, in Experiment 2, we systematically examined how the orientation of light zones (left-right or front-back) with respect to a viewer influences light inferences in symmetric scenes. We found that observers are quite sensitive to the difference in the light flow of the light zones. In addition, we found that participants showed idiosyncratic behavior, especially for front-back-oriented light zones. Our findings show that observers are sensitive to differences in light field structure between two parts of a scene, which we call visual light zones.

Increasing the Complexity of the Illumination May Reduce Gloss Constancy

We examined in which way gradual changes in the geometric structure of the illumination affect the perceived glossiness of a surface. The test stimuli were computer-generated three-dimensional scenes with a single test object that was illuminated by three point light sources, whose relative positions in space were systematically varied. In the first experiment, the subjects were asked to adjust the microscale smoothness of a match object illuminated by a single light source such that it has the same perceived glossiness as the test stimulus. We found that small changes in the structure of the light field can induce dramatic changes in perceived glossiness and that this effect is modulated by the microscale smoothness of the test object. The results of a second experiment indicate that the degree of overlap of nearby highlights plays a major role in this effect: Whenever the degree of overlap in a group of highlights is so large that they perceptually merge into a single highlight, the glossiness of the surface is systematically underestimated. In addition, we examined the predictability of the smoothness settings by a linear model that is based on a set of four different global image statistics.

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.

Separate and Simultaneous Adjustment of Light Qualities in a Real Scene

Humans are able to estimate light field properties in a scene in that they have expectations of the objects’ appearance inside it. Previously, we probed such expectations in a real scene by asking whether a “probe object” fitted a real scene with regard to its lighting. But how well are observers able to interactively adjust the light properties on a “probe object” to its surrounding real scene? Image ambiguities can result in perceptual interactions between light properties. Such interactions formed a major problem for the “readability” of the illumination direction and diffuseness on a matte smooth spherical probe. We found that light direction and diffuseness judgments using a rough sphere as probe were slightly more accurate than when using a smooth sphere, due to the three-dimensional (3D) texture. We here extended the previous work by testing independent and simultaneous (i.e., the light field properties separated one by one or blended together) adjustments of light intensity, direction, and diffuseness using a rough probe. Independently inferred light intensities were close to the veridical values, and the simultaneously inferred light intensity interacted somewhat with the light direction and diffuseness. The independently inferred light directions showed no statistical difference with the simultaneously inferred directions. The light diffuseness inferences correlated with but contracted around medium veridical values. In summary, observers were able to adjust the basic light properties through both independent and simultaneous adjustments. The light intensity, direction, and diffuseness are well “readable” from our rough probe. Our method allows “tuning the light” (adjustment of its spatial distribution) in interfaces for lighting design or perception research.

Is the perception of 3D shape from shading based on assumed reflectance and illumination?

The research described in the present article was designed to compare three types of image shading: one generated with a Lambertian BRDF and homogeneous illumination such that image intensity was determined entirely by local surface orientation irrespective of position; one that was textured with a linear intensity gradient, such that image intensity was determined entirely by local surface position irrespective of orientation; and another that was generated with a Lambertian BRDF and inhomogeneous illumination such that image intensity was influenced by both position and orientation. A gauge figure adjustment task was used to measure observers' perceptions of local surface orientation on the depicted surfaces, and the probe points included 60 pairs of regions that both had the same orientation. The results show clearly that observers' perceptions of these three types of stimuli were remarkably similar, and that probe regions with similar apparent orientations could have large differences in image intensity. This latter finding is incompatible with any process for computing shape from shading that assumes any plausible reflectance function combined with any possible homogeneous illumination.

The visual light field in real scenes

Human observers' ability to infer the light field in empty space is known as the “visual light field.” While most relevant studies were performed using images on computer screens, we investigate the visual light field in a real scene by using a novel experimental setup. A “probe” and a scene were mixed optically using a semitransparent mirror. Twenty participants were asked to judge whether the probe fitted the scene with regard to the illumination intensity, direction, and diffuseness. Both smooth and rough probes were used to test whether observers use the additional cues for the illumination direction and diffuseness provided by the 3D texture over the rough probe. The results confirmed that observers are sensitive to the intensity, direction, and diffuseness of the illumination also in real scenes. For some lighting combinations on scene and probe, the awareness of a mismatch between the probe and scene was found to depend on which lighting condition was on the scene and which on the probe, which we called the “swap effect.” For these cases, the observers judged the fit to be better if the average luminance of the visible parts of the probe was closer to the average luminance of the visible parts of the scene objects. The use of a rough instead of smooth probe was found to significantly improve observers' abilities to detect mismatches in lighting diffuseness and directions.

We infer light in space

In studies of lightness and color constancy, the terms lightness and brightness refer to the qualia corresponding to perceived surface reflectance and perceived luminance, respectively. However, what has rarely been considered is the fact that the volume of space containing surfaces appears neither empty, void, nor black, but filled with light. Helmholtz (1866/1962) came closest to describing this phenomenon when discussing inferred illumination, but previous theoretical treatments have fallen short by restricting their considerations to the surfaces of objects. The present work is among the first to explore how we infer the light present in empty space. It concludes with several research examples supporting the theory that humans can infer the differential levels and chromaticities of illumination in three-dimensional space.

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.

Fechner, information, and shape perception

How do retinal images lead to perceived environmental objects? Vision involves a series of spatial and material transformations--from environmental objects to retinal images, to neurophysiological patterns, and finally to perceptual experience and action. A rationale for understanding functional relations among these physically different systems occurred to Gustav Fechner: Differences in sensation correspond to differences in physical stimulation. The concept of information is similar: Relationships in one system may correspond to, and thus represent, those in another. Criteria for identifying and evaluating information include (a) resolution, or the precision of correspondence; (b) uncertainty about which input (output) produced a given output (input); and (c) invariance, or the preservation of correspondence under transformations of input and output. We apply this framework to psychophysical evidence to identify visual information for perceiving surfaces. The elementary spatial structure shared by objects and images is the second-order differential structure of local surface shape. Experiments have shown that human vision is directly sensitive to this higher-order spatial information from interimage disparities (stereopsis and motion parallax), boundary contours, texture, shading, and combined variables. Psychophysical evidence contradicts other common ideas about retinal information for spatial vision and object perception.

The color constancy of three-dimensional objects

Human color constancy has been studied for over 100 years, and there is extensive experimental data for the case where a spatially diffuse light source illuminates a set of flat matte surfaces. In natural viewing, however, three-dimensional objects are viewed in three-dimensional scenes. Little is known about color constancy for three-dimensional objects. We used a forced-choice task to measure the achromatic chromaticity of matte disks, matte spheres, and glossy spheres. In all cases, the test stimuli were viewed in the context of stereoscopically viewed graphics simulations of three-dimensional scenes, and we varied the scene illuminant. We studied conditions both where all cues were consistent with the simulated illuminant change (consistent-cue conditions) and where local contrast was silenced as a cue (reduced-cue conditions). We computed constancy indices from the achromatic chromaticities. To first order, constancy was similar for the three test object types. There was, however, a reliable interaction between test object type and cue condition. In the consistent-cue conditions, constancy tended to be best for the matte disks, while in the reduced-cue conditions constancy was best for the spheres. The presence of this interaction presents an important challenge for theorists who seek to generalize models that account for constancy for flat tests to the more general case of three-dimensional objects.

Cast shadows in wide perspective

We investigated the apparent spatial layout of cast shadows up to very wide fields of view. We presented up to 130 degrees wide images in which two 'flat poles' were standing on a green lawn under a cloudless blue sky on a sunny day. The poles threw sharp cast shadows on the green, of which one was fixed. The observer's task was to adjust the azimuth of the shadow of the other pole such that it fitted the scene. The source elevation was kept constant. The two cast shadows are, of course, parallel in physical space, but generically not in the picture plane because of the wide perspective. We found that observers made huge systematic errors, indicating that, generically, they fail to account for these perspective effects. The systematic deviations could be well described by a weighted linear combination of the directions in the picture plane and in the physical space, with weights that depended on the positions of, and distance between, the poles.

Detection of changes in luminance distributions

How well can observers detect the presence of a change in luminance distributions? Performance was measured in three experiments. Observers viewed pairs of grayscale images on a calibrated CRT display. Each image was a checkerboard. All luminances in one image of each pair consisted of random draws from a single probability distribution. For the other image, some patch luminances consisted of random draws from that same distribution, while the rest of the patch luminances (test patches) consisted of random draws from a second distribution. The observers' task was to pick the image with luminances drawn from two distributions. The parameters of the second distribution that led to 75% correct performance were determined across manipulations of (1) the number of test patches, (2) the observers' certainty about test patch location, and (3) the geometric structure of the images. Performance improved with number of test patches and location certainty. The geometric manipulations did not affect performance. An ideal observer model with high efficiency fit the data well and a classification image analysis showed a similar use of information by the ideal and human observers, indicating that observers can make effective use of photometric information in our distribution discrimination task.

The influence of shape cues on the perception of lighting direction

Three scene properties determine the luminances in the image of a shaded object: the material reflectance, the illuminant position, and the object's shape. Because all three properties determine the image, one cannot solve for any one property without knowing the other two. Nevertheless, people perceive consistent 3D shape and consistent lighting in shaded images; they must therefore be making assumptions about the unknown properties. We conducted two psychophysical experiments to determine how viewers use shape information to estimate the lighting direction from shaded images. In the first experiment, we confirmed that observers use 3D shape information when estimating lighting direction. In the second experiment, we investigated how different shape cues affect lighting direction estimates. Observers can accurately determine lighting direction when a host of shape cues specify the objects. When shading is the only cue, observers always set lighting direction to be from above. We modeled the results in a Bayesian framework that included a prior distribution describing the assumed lighting direction. The estimated prior was slightly counterclockwise from above at a ∼30° slant. Our model showed that an assumption of convexity provides an accurate estimate of lighting direction when the shape is globally, but not locally, consistent with convexity.

Representing the light field in finite three-dimensional spaces from sparse discrete samples

We present a method for measurement and reconstruction of light fields in finite spaces. Using a custom-made device called a plenopter, we can measure spatially and directionally varying radiance distribution functions from a real-world scene up to their second-order spherical harmonics approximations. Interpolating between measurement points, we can recover this function for arbitrary points of a scene. We visualized the global structure of the light field using light tubes, which gives an intuitive description of the flux propagation throughout three-dimensional scenes and provides information about the quality of light in the scenes. Our second-order reconstructions are sufficient to render convex matte objects and therefore have a direct interest for computer graphics applications.