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.

We present a method for measurement and reconstruction of second order approximations of light fields in closed spaces. We visualized their structure using light tubes and rendered objects at several points along a tube.

The theory of illuminance flow estimation by structure tensors is generalized for oblique viewing of anisotropic texture. Previous theory is revised using general matrix formulations and predictions are compared with results on rendered images.

The appearance of objects is determined by their surface reflectance and roughness and by the light field. Conversely, human observers might derive properties of the light field from the appearance of objects. The inverse problem has no unique solution, so perceptual interactions between reflectance, roughness, and light field are to be expected. In two separate experiments, we tested whether observers are able to match the illumination of spheres under collimated illumination only (matching of illumination direction) and under more or less diffuse illumination (matching of illumination direction and directedness of the beam). We found that observers are quite able to match collimated illumination directions of two rendered Lambertian spheres. Matching of the collimated beam directions of a Lambertian sphere and that of a real object with arbitrary reflectance and roughness properties resulted in similar results for the azimuthal angle, but in higher variance for the polar angle. Translucent objects and a tennis ball were found to be systematic outliers. If the directedness of the beam was also varied, the direction settings showed larger variance for more diffuse illumination. The directedness settings showed an overall quite large variance and, interestingly, interacted with the polar angle settings. We discuss possible photometrical mechanisms behind these effects.

The structure of light fields of natural scenes is highly complex due to high frequencies in the radiance distribution function. However it is the low-order properties of light that determine the appearance of common matte materials. We describe the local light field in terms of spherical harmonics and analyze the qualitative properties and physical meaning of the low-order components. We take a first step in the further development of Gershun's classical work on the light field by extending his description beyond the 3D vector field, toward a more complete description of the illumination using tensors. We show that the three first components, namely, the monopole (density of light), the dipole (light vector), and the quadrupole (squash tensor) suffice to describe a wide range of qualitatively different light fields. In this paper we address a related issue, namely, the spatial properties of light fields within natural scenes. We want to find out to what extent local light fields change from point to point and how different orders behave. We found experimentally that the low-order components of the light field are rather constant over the scenes whereas high-order components are not. Using very simple models, we found a strong relationship between the low-order components and the geometrical layouts of the scenes.

Light fields [Gershun 1939] of natural scenes are highly complex and vary within a scene from point to point. However, in many applications complex lighting can be successfully replaced by its low order approximation [Ramamoorthi and Hanrahan 2001]. The purpose of this research was to investigate the spatial behavior of light fields in natural scenes. We describe the light fields in terms of spherical harmonics and analyze their qualitative properties. We show that low order approximations of natural light fields vary smoothly and systematically, in accordance with very simple models. This finding has important implications for graphics, visualization, architectural design and scene perception research.

Current reflectance models for glossy surfaces assume that the reflectance from such objects can be represented by a linear combination of specular and diffuse reflectance functions. This assumption is based on the physics of reflectance of smooth dielectric materials such as plastic and holds quite well for perfectly smooth convex dielectric objects such as billiard balls. In this paper, however, we demonstrate visually and semi-quantitatively that linear combinations of body and interface scattering do not apply to rough surfaces (concavities on a meso scale) and to concave shapes (concavities on a macro scale), because the linearity is destroyed by multiple scattering. Using a physical model of a canonical case of rough opaque surfaces, namely a hemispherical pit, we demonstrate that the mechanism of multiple specular and diffuse reflexes causes a discrepancy between a linear superposition of specular and diffuse cases and the real glossy model. We discuss how the reflectance from locally glossy pitted surfaces may be calculated on the basis of two exact descriptions of the complete bidirectional reflectance distribution functions for locally specular and locally matte "thoroughly pitted surfaces."

Three dimensional surface corrugations on globally smooth surfaces give rise to brightness modulations of global shading patterns. We study systematic variations of such 3D image texture as a function of illumination and viewing geometry. The 3D texture is especially noticeable near the shadow terminator (for collimated illumination) or near the dark pole (for hemispherical diffuse illumination). We find that a simple micro-facet model, assuming locally Lambertian scattering, suffices to robustly describe texture contrast gradients of a large variety (measured and rendered textures; laboratory and field conditions) in a semi-quantitative manner. Robust statistical measures of the texture allows one to draw inferences concerning the nature of the light field (collimated to diffuse) and of surface roughness parameters, which can be used as input to the simplest BRDF models.

We studied image texture due to the shading of corrugated (3D textured) surfaces, which are Lambertian on the micro scale. Our theory applies to physically canonical cases of isotropic Gaussian random surfaces, under collimated illumination. In this investigation we analyze effects of oblique viewing, extending our theory which applied to normal viewing conditions only [5]. The theory for normal views predicts the structure tensors from either the gradient or the Hessian of the image intensity and allows for inferences of the orientation of irradiation of the surface. Even for surfaces that are not at all Gaussian, the BRDF [10] far from Lambertian, with vignetting and multiple scattering present, such inferences of the orientation of irradiation were accurate up to a few degrees. In this paper we derive predictions for oblique viewing conditions, for which the inferences of the irradiation orientation will deviate from the veridical value in a systematic manner, depending on the viewing and illumination directions. Theoretical predictions are compared with empirical data, for rendered and for real rough surfaces, and found to be in good agreement. We discuss issues of scale selection and robustness.

Three human observers estimated the illumination direction for samples of random Gaussian surfaces illuminated by a collimated beam from random directions. These stimuli appear as 'texture' due to shading and shadowing (the surface on the microscale was Lambertian of uniform albedo; thus texture appears only through shading and shadowing). We found that observers were able to estimate the azimuth of the source with remarkable accuracy. In the shading regime (no shadows) the observers committed 180° azimuth errors with 50% probability, whereas in the shadow-dominated regime they were able to avoid this convex/concave confusion to a large extent. They evidently relied on second-order statistics in the shading regime and used an unidentified first-order cue in the shadow regime. The elevations of the source were also estimated with remarkable precision. We attribute this to the statistical homogeneity of the sample which can apparently be exploited by the observers. Likely cues are the fraction of shadowed surface, average intensity and rms contrast. The ability of human observers to estimate the illumination direction from surface texture no doubt contributes to the ability to estimate the light field in scenes, which is a prerequisite to the photometric parsing of scenes (shape from shading, and so forth).

We measured radiance distributions for black lining cloth and copper gauze using the convenient technique of wrapping the materials around a circular cylinder, irradiating it with a parallel light source and collecting the scattered radiance by a digital camera. One family of parallel threads (weave or weft) was parallel to the cylinder generator. The most salient features for such glossy plane weaves are a splitting up of the reflection peak due to the wavy variations in local slopes of the threads around the cylinders and a surface scattering lobe due to the threads that run along the cylinder. These scattering characteristics are quite different from the (off-)specular peaks and lobes that were found before for random rough specular surfaces, The split off-specular reflection is due to the regular structures in our samples of man-made materials. We derived simple approximations for these reflectance characteristics using geometrical optics.

In an image of a scene illuminated by a single source, such as a landscape in sun light, the light field is approximately the same at all locations in the scene. This is apparent from the common direction of cast shadows, the common polarity of illuminated and shaded parts of convex objects, and so forth. Here we concentrate upon the statistics of texture due to 3D surface corrugations. We show that patches of roughly uniform texture reveal the local direction of the illumination. In this way we are able to map the global structure of the "illuminance flow" through simple image processing techniques. We propose a theoretical treatment of texture due to illuminaton of rough surfaces and we present experiments on real textures and scenes. The illuminance flow is a robust indicator of the light field and thus reveals global structure in a scene. It is an important entity for many subsequent inferences from the image such as shape from shading.

We present a theory of image texture resulting from the shading of corrugated (three-dimensional textured) surfaces, Lambertian on the micro scale, in the domain of geometrical optics. The derivation applies to isotropic Gaussian random surfaces, under collimated illumination, in normal view. The theory predicts the structure tensors from either the gradient or the Hessian of the image intensity and allows inferences of the direction of irradiation of the surface. Although the assumptions appear prima facie rather restrictive, even for surfaces that are not at all Gaussian, with the bidirectional reflectance distribution function far from Lambertian and vignetting and multiple scattering present, we empirically recover the direction of irradiation with an accuracy of a few degrees.

We investigate the ability of human observers to judge the direction of illumination from image texture. Photographs of 61 real surfaces were used, taken from the Columbia-Utrecht Reflectance and Texture (Curet) database (http://www.cs.columbia.edu/CAVE/curet). All samples were normally viewed but obliquely illuminated, the elevation of the source being 22.5°, 45.0°, or 67.5°. The illumination was with a collimated, parallel beam. Stimuli were presented in random orientation, and observers had to judge both the elevation and the azimuth of the source. Observers judged the azimuth within approximately 15°, except for the fact that they committed random (with approximately 50% probability) sign flips (180° flips). Connected with this finding is the fact that observers judged the illumination to be from above rather than below in the overwhelming majority of cases, despite the fact that each case occurred with equal probability. The elevation of the illumination can be judged to some extent but is not far above chance level. The data are in good agreement with a simple model that bases the estimate of illumination direction on the second-order statistics of local luminance gradients. This locates the locus of the probable mechanism very early in the visual stream.

We identify a neglected source of information in the 3D texture in images of articulated surfaces. The texture is especially noticeable near the terminator of the body shadow. We provide a very simple model that allows us to describe the 3D texture contrast in detail. Experiments involving the data from the Curet database, laboratory observations, and informal snapshots reveal that the observations follow the theoretical expectations very closely. The 3D texture allows one to draw inferences concerning the nature of the light field (collimated to diffuse) and of parameters of the surface roughness that are the vital input to the simplest BRDF models, namely the range of slopes of surface micro facets, the distribution of heights relative to the fiducial surface, and the width of the surface protrusions. Thus 3D texture is a very useful cue when rerendering or BRDF estimations are to be attempted.

We derive the bidirectional reflectance distribution function for a class of opaque surfaces that are rough on a macroscale and smooth on a microscale. We model this type of surface as a distribution of spherical mirrors. Since our study concerns geometrical optics, it is only the aperture of the concavities that is relevant, not the dimension. The three-dimensional problem is effectively transformed into a much simpler two-dimensional one involving the possibly infinitely many reflections in a spherical mirror. We find that these types of surface show very strong backscattering when the pits are deep but forward scattering when the pits are shallow. Such surfaces also show spectral effects as a result of multiple reflections and polarization effects that are due to the orientation of the effective surface. Both this model and the locally diffuse thoroughly pitted surface model [Int. J. Comput. Vision 31, 129 (1999)] are superior to other models in that they allow for an exact treatment for physically realizable surface geometries.

Image texture due to 3D surface corrugations ("3D texture") differs fundamentally from image texture due to pigmentation variations of a smooth surface ("flat texture"). Flat texture yields no information concerning the way the surface is illuminated, whereas 3D texture is highly dependent upon the illumination. Question: Is the human observer able to perceive the illumination direction from 3D texture? Method: In order to address this question we extracted over sixty 3D textures due to natural materials from the Curet database. Fiducial illumination directions were 22.5°, 45° and 67.5° from the normal direction, all viewing directions were normal. The samples were clipped to circular discs and were randomly rotated in the picture plane. Observers indicated perceived illumination direction by way of an indicator panel showing a hemispherical boss on a plane, viewed normally to the plane. The simulated illumination direction was under the observer's control. Five observers viewed all samples in six different orientations. Result: We find that the azimuth of the illumination direction can be perceived quite veridically except for the fact that 180° confusions are frequent. The elevation cannot be perceived with great certainty (deviations up to 45° occurring frequently) though the increase of perceived elevation with true elevation is significant. We find a number of interesting variations on this pattern that depend critically upon the type of texture.