Perceiving the shape and material of an object from a single image is inherently ambiguous, especially when lighting is unknown and unconstrained. Despite this, humans can often disentangle shape and material, and when they are uncertain, they often move their head slightly or rotate the object to help resolve the ambiguities. Inspired by this behavior, we introduce a novel conditional denoising-diffusion model that generates samples of shape-and-material maps from a short video of an object undergoing differential motions. Our parameter-efficient architecture allows training directly in pixel-space, and it generates many disentangled attributes of an object simultaneously. Trained on a modest number of synthetic object-motion videos with supervision on shape and material, the model exhibits compelling emergent behavior: For static observations, it produces diverse, multimodal predictions of plausible shape-and-material maps that capture the inherent ambiguities; and when objects move, the distributions converge to more accurate explanations. The model also produces high-quality shape-and-material estimates for less ambiguous, real-world objects. By moving beyond single-view to continuous motion observations, and by using generative perception to capture visual ambiguities, our work suggests ways to improve visual reasoning in physically-embodied systems.

Neural Radiance Fields (NeRF) is a popular view synthesis technique that represents a scene as a continuous volumetric function, parameterized by multilayer perceptrons that provide the volume density and view-dependent emitted radiance at each location. While NeRF-based techniques excel at representing fine geometric structures with smoothly varying view-dependent appearance, they often fail to accurately capture and reproduce the appearance of glossy surfaces. We address this limitation by introducing Ref-NeRF, which replaces NeRF's parameterization of view-dependent outgoing radiance with a representation of reflected radiance and structures this function using a collection of spatially-varying scene properties. We show that together with a regularizer on normal vectors, our model significantly improves the realism and accuracy of specular reflections. Furthermore, we show that our model's internal representation of outgoing radiance is interpretable and useful for scene editing.

Decomposing an object's appearance into representations of its materials and the surrounding illumination is difficult, even when the object's 3D shape is known before-hand. This problem is especially challenging for diffuse objects: it is ill-conditioned because diffuse materials severely blur incoming light, and it is ill-posed because diffuse materials under high-frequency lighting can be indistinguishable from shiny materials under low-frequency lighting. We show that it is possible to recover precise materials and illumination-even from diffuse objects-by exploiting un-intended shadows, like the ones cast onto an object by the photographer who moves around it. These shadows are a nuisance in most previous inverse rendering pipelines, but here we exploit them as signals that improve conditioning and help resolve material-lighting ambiguities. We present a method based on differentiable Monte Carlo ray tracing that uses images of an object to jointly recover its spatially-varying materials, the surrounding illumination environment, and the shapes of the unseen light occluders who in-advertently cast shadows upon it.

Models for inferring monocular shape of surfaces with diffuse reflection---shape from shading---ought to produce distributions of outputs, because there are fundamental mathematical ambiguities of both continuous (e.g., bas-relief) and discrete (e.g., convex/concave) types that are also experienced by humans. Yet, the outputs of current models are limited to point estimates or tight distributions around single modes, which prevent them from capturing these effects. We introduce a model that reconstructs a multimodal distribution of shapes from a single shading image, which aligns with the human experience of multistable perception. We train a small denoising diffusion process to generate surface normal fields from $16\times 16$ patches of synthetic images of everyday 3D objects. We deploy this model patch-wise at multiple scales, with guidance from inter-patch shape consistency constraints. Despite its relatively small parameter count and predominantly bottom-up structure, we show that multistable shape explanations emerge from this model for ambiguous test images that humans experience as being multistable. At the same time, the model produces veridical shape estimates for object-like images that include distinctive occluding contours and appear less ambiguous. This may inspire new architectures for stochastic 3D shape perception that are more efficient and better aligned with human experience.

Abstract Let $$\textbf{p}$$ p be a configuration of n points in $$\mathbb R^d$$ R d for some n and some $$d \ge 2$$ d ≥ 2 . Each pair of points defines an edge, which has a Euclidean length in the configuration. A path is an ordered sequence of the points, and a loop is a path that begins and ends at the same point. A path or loop, as a sequence of edges, also has a Euclidean length, which is simply the sum of its Euclidean edge lengths. We are interested in reconstructing $$\textbf{p}$$ p given a set of edge, path and loop lengths. In particular, we consider the unlabeled setting where the lengths are given simply as a set of real numbers, and are not labeled with the combinatorial data describing which paths or loops gave rise to these lengths. In this paper, we study the question of when $$\textbf{p}$$ p will be uniquely determined (up to an unknowable Euclidean transform) from some given set of path or loop lengths through an exhaustive trilateration process. Such a process has already been used for the simpler problem of reconstruction using unlabeled edge lengths. This paper also provides a complete proof that this process must work in that edge-setting when given a sufficiently rich set of edge measurements and assuming that $$\textbf{p}$$ p is generic.

Optical metasurfaces composed of precisely engineered nanostructures have gained significant attention for their ability to manipulate light and implement distinct functionalities based on the properties of the incident field. Computational imaging systems have started harnessing this capability to produce sets of coded measurements that benefit certain tasks when paired with digital post-processing. Inspired by these works, we introduce a new system that uses a birefringent metasurface with a polarizer-mosaicked photosensor to capture four optically-coded measurements in a single exposure. We apply this system to the task of incoherent opto-electronic filtering, where digital spatial-filtering operations are replaced by simpler, per-pixel sums across the four polarization channels, independent of the spatial filter size. In contrast to previous work on incoherent opto-electronic filtering that can realize only one spatial filter, our approach can realize a continuous family of filters from a single capture, with filters being selected from the family by adjusting the post-capture digital summation weights. To find a metasurface that can realize a set of user-specified spatial filters, we introduce a form of gradient descent with a novel regularizer that encourages light efficiency and a high signal-to-noise ratio. We demonstrate several examples in simulation and with fabricated prototypes, including some with spatial filters that have prescribed variations with respect to depth and wavelength.

Neural Radiance Fields (NeRF) is a popular view synthesis technique that represents a scene as a continuous volumetric function, parameterized by multilayer perceptrons that provide the volume density and view-dependent emitted radiance at each location. While NeRF-based techniques excel at representing fine geometric structures with smoothly varying view-dependent appearance, they often fail to accurately capture and reproduce the appearance of glossy surfaces. We address this limitation by introducing Ref-NeRF, which replaces NeRF's parameterization of view-dependent outgoing radiance with a representation of reflected radiance and structures this function using a collection of spatially-varying scene properties. We show that together with a regularizer on normal vectors, our model significantly improves the realism and accuracy of specular reflections. Furthermore, we show that our model's internal representation of outgoing radiance is interpretable and useful for scene editing.

We introduce a bottom-up model for simultaneously finding many boundary elements in an image, including contours, corners and junctions. The model explains boundary shape in each small patch using a ‘generalized M-junction’ comprising M angles and a freely-moving vertex. Images are analyzed using non-convex optimization to cooperatively find M + 2 junction values at every location, with spatial consistency being enforced by a novel regularizer that reduces curvature while preserving corners and junctions. The resulting ‘field of junctions’ is simultaneously a contour detector, corner/junction detector, and boundary-aware smoothing of regional appearance. Notably, its unified analysis of contours, corners, junctions and uniform regions allows it to succeed at high noise levels, where other methods for segmentation and boundary detection fail.

Localizing stereo boundaries is difficult because matching cues are absent in the occluded regions that are adjacent to them. We introduce an energy and level-set optimizer that improves boundaries by encoding the essential geometry of occlusions: The spatial extent of an occlusion must equal the amplitude of the disparity jump that causes it. In a collection of figure-ground scenes from Middlebury and Falling Things stereo datasets, the model provides more accurate boundaries than previous occlusion-handling techniques.

We present a sufficient condition for recovering unique texture and viewpoints from unknown orthographic projections of a flat texture process. We show that four observations are sufficient in general, and we characterize the ambiguous cases. The results are applicable to shape from texture and texture-based structure from motion.

Under the conventional diffuse shading model with unknown directional lighting, the set of quadratic surface shapes that are consistent with the spatial derivatives of intensity at a single image point is a two-dimensional algebraic variety embedded in the five-dimensional space of quadratic shapes. We describe the geometry of this variety, and we introduce a concise feedforward model that computes an explicit, differentiable approximation of the variety from the intensity and its derivatives at any single image point. The result is a parallelizable processor that operates at each image point and produces a lighting-invariant descriptor of the continuous set of compatible surface shapes at the point. We describe two applications of this processor: two-shot uncalibrated photometric stereo and quadratic-surface shape from shading.

We consider the shape from texture problem, where the input is a single image of a curved, textured surface, and the texture and shape are both a priori unknown. We formulate this task as a three-player game between a shape process, a texture process, and a discriminator. The discriminator adapts a set of non-linear filters to try to distinguish image patches created by the texture process from those created by the shape process, while the shape and texture processes try to create image patches that are indistinguishable from those of the other. An equilibrium of this game yields two things: an estimate of the 2.5D surface from the shape process, and a stochastic texture synthesis model from the texture process. Experiments show that this approach is robust to common non-idealities such as shading, gloss, and clutter. We also find that it succeeds for a wide variety of texture types, including both periodic textures and those composed of isolated textons, which have previously required distinct and specialized processing.

Stereo occlusion boundaries are one-dimensional structures in the visual field that separate foreground regions of a scene that are visible to both eyes (binocular regions) from background regions of a scene that are visible to only one eye (monocular regions). Stereo occlusion boundaries often coincide with object boundaries, and localizing them is useful for tasks like grasping, manipulation, and navigation. This paper describes the local signatures for stereo occlusion boundaries that exist in a stereo cost volume, and it introduces a local detector for them based on a simple feedforward network with relatively small receptive fields. The local detector produces better boundaries than many other stereo methods, even without incorporating explicit stereo matching, top-down contextual cues, or single-image boundary cues based on texture and intensity.

The focal track sensor is a monocular and computationally efficient depth sensor that is based on defocus controlled by a liquid membrane lens. It synchronizes small lens oscillations with a photosensor to produce real-time depth maps by means of differential defocus, and it couples these oscillations with bigger lens deformations that adapt the defocus working range to track objects over large axial distances. To create the focal track sensor, we derive a texture-invariant family of equations that relate image derivatives to scene depth when a lens changes its focal length differentially. Based on these equations, we design a feed-forward sequence of computations that: robustly incorporates image derivatives at multiple scales; produces confidence maps along with depth; and can be trained endto- end to mitigate against noise, aberrations, and other non-idealities. Our prototype with 1-inch optics produces depth and confidence maps at 100 frames per second over an axial range of more than 75cm.

Two types of information exist in a stereo pair: correlation (matching) and decorrelation (half-occlusion). Vision science has shown that both types of information are used in the visual cortex, and that people can perceive depth even when correlation cues are absent or very weak, a capability that remains absent from most computational stereo systems. As a step toward stereo algorithms that are more consistent with these perceptual phenomena, we re-examine the topic of scanline stereo as energy minimization. We represent a disparity profile as a piecewise smooth function with explicit breakpoints between its smooth pieces, and we show this allows correlation and decorrelation to be integrated into an objective that requires only two types of local information: the correlation and its spatial gradient. Experimentally, we show the global optimum of this objective matches human perception on a broad collection of wellknown perceptual stimuli, and that it also provides reasonable piecewise-smooth interpretations of depth in natural images, even without exploiting monocular boundary cues.

Many patch-based image denoising algorithms can be formulated as applying a smoothing filter to the noisy image. Expressed as matrices, the smoothing filters must be row normalized, so that each row sums to unity. Surprisingly, if we apply a column normalization before the row normalization, the performance of the smoothing filter can often be significantly improved. Prior works showed that such performance gain is related to the Sinkhorn-Knopp balancing algorithm, an iterative procedure that symmetrizes a row-stochastic matrix to a doubly stochastic matrix. However, a complete understanding of the performance gain phenomenon is still lacking. In this paper, we study the performance gain phenomenon from a statistical learning perspective. We show that Sinkhorn-Knopp is equivalent to an expectation-maximization (EM) algorithm of learning a Gaussian mixture model of the image patches. By establishing the correspondence between the steps of Sinkhorn-Knopp and the EM algorithm, we provide a geometrical interpretation of the symmetrization process. This observation allows us to develop a new denoising algorithm called Gaussian mixture model symmetric smoothing filter (GSF). GSF is an extension of the Sinkhorn-Knopp and is a generalization of the original smoothing filters. Despite its simple formulation, GSF outperforms many existing smoothing filters and has a similar performance compared with several state-of-the-art denoising algorithms.

We introduce a multi-scale framework for low-level vision, where the goal is estimating physical scene values from image data—such as depth from stereo image pairs. The framework uses a dense, overlapping set of image regions at multiple scales and a “local model,” such as a slanted-plane model for stereo disparity, that is expected to be valid piecewise across the visual field. Estimation is cast as optimization over a dichotomous mixture of variables, simultaneously determining which regions are inliers with respect to the local model (binary variables) and the correct co-ordinates in the local model space for each inlying region (continuous variables). When the regions are organized into a multi-scale hierarchy, optimization can occur in an efficient and parallel architecture, where distributed computational units iteratively perform calculations and share information through sparse connections between parents and children. The framework performs well on a standard benchmark for binocular stereo, and it produces a distributional scene representation that is appropriate for combining with higher-level reasoning and other low-level cues.

Edges in images of translucent objects are very different from edges in images of opaque objects. The physical causes for these differences are hard to characterize analytically and are not well understood. This paper considers one class of translucency edges-those caused by a discontinuity in surface orientation-and describes the physical causes of their appearance. We simulate thousands of translucency edge profiles using many different scattering material parameters, and we explain the resulting variety of edge patterns by qualitatively analyzing light transport. We also discuss the existence of shape and material metamers, or combinations of distinct shape or material parameters that generate the same edge profile. This knowledge is relevant to visual inference tasks that involve translucent objects, such as shape or material estimation.

In this paper we explore interactions between the appearance of an outdoor scene and the ambient temperature. By studying statistical correlations between image sequences from outdoor cameras and temperature measurements we identify two interesting interactions. First, semantically meaningful regions such as foliage and reflective oriented surfaces are often highly indicative of the temperature. Second, small camera motions are correlated with the temperature in some scenes. We propose simple scene-specific temperature prediction algorithms which can be used to turn a camera into a crude temperature sensor. We find that for this task, simple features such as local pixel intensities outperform sophisticated, global features such as from a semantically-trained convolutional neural network.

We study a class of smoothing filters for image denoising. Expressed as matrices, these smoothing filters must be row normalized so that each row sums to unity. Surprisingly, if one applies a column normalization to the matrix before the row normalization, the denoising quality can often be significantly improved. This column-row normalization corresponds to one iteration of a symmetrization process called the Sinkhorn-Knopp balancing algorithm. However, a complete understanding of the performance gain phenomenon is lacking. In this paper, we analyze the performance gain from a Gaussian mixture model (GMM) perspective. We show that the symmetrization is equivalent to an expectation-maximization (EM) algorithm for learning the GMM. Moreover, we make modifications to the symmetrization procedure and present a new denoising algorithm. Experimental results show that the new algorithm achieves comparable denoising results to some state-of-the-art methods.

We develop a framework for extracting a concise representation of the shape information available from diffuse shading in a small image patch. This produces a mid-level scene descriptor, comprised of local shape distributions that are inferred separately at every image patch across multiple scales. The framework is based on a quadratic representation of local shape that, in the absence of noise, has guarantees on recovering accurate local shape and lighting. And when noise is present, the inferred local shape distributions provide useful shape information without over-committing to any particular image explanation. These local shape distributions naturally encode the fact that some smooth diffuse regions are more informative than others, and they enable efficient and robust reconstruction of object-scale shape. Experimental results show that this approach to surface reconstruction compares well against the state-of-art on both synthetic images and captured photographs.

We present a computational imaging system, inspired by the optical coherence tomography (OCT) framework, that uses interferometry to produce decompositions of light transport in small scenes or volumes. The system decomposes transport according to various attributes of the paths that photons travel through the scene, including where on the source the paths originate, their pathlengths from source to camera through the scene, their wavelength, and their polarization. Since it uses interference, the system can achieve high pathlength resolutions, with the ability to distinguish paths whose lengths differ by as little as ten microns. We describe how to construct and optimize an optical assembly for this technique, and we build a prototype to measure and visualize three-dimensional shape, direct and indirect reflection components, and properties of scattering, refractive/dispersive, and birefringent materials.

Digital color cameras make sub-sampled measurements of color at alternating pixel locations, and then “demosaick” these measurements to create full color images by up-sampling. This allows traditional cameras with restricted processing hardware to produce color images from a single shot, but it requires blocking a majority of the incident light and is prone to aliasing artifacts. In this paper, we introduce a computational approach to color photography, where the sampling pattern and reconstruction process are co-designed to enhance sharpness and photographic speed. The pattern is made predominantly panchromatic, thus avoiding excessive loss of light and aliasing of high spatial-frequency intensity variations. Color is sampled at a very sparse set of locations and then propagated throughout the image with guidance from the un-aliased luminance channel. Experimental results show that this approach often leads to significant reductions in noise and aliasing artifacts, especially in low-light conditions.

To produce images that are suitable for display, tone-mapping is widely used in digital cameras to map linear color measurements into narrow gamuts with limited dynamic range. This introduces non-linear distortion that must be undone, through a radiometric calibration process, before computer vision systems can analyze such photographs radiometrically. This paper considers the inherent uncertainty of undoing the effects of tone-mapping. We observe that this uncertainty varies substantially across color space, making some pixels more reliable than others. We introduce a model for this uncertainty and a method for fitting it to a given camera or imaging pipeline. Once fit, the model provides for each pixel in a tone-mapped digital photograph a probability distribution over linear scene colors that could have induced it. We demonstrate how these distributions can be useful for visual inference by incorporating them into estimation algorithms for a representative set of vision tasks.

We propose a randomized version of the nonlocal means (NLM) algorithm for large-scale image filtering. The new algorithm, called Monte Carlo nonlocal means (MCNLM), speeds up the classical NLM by computing a small subset of image patch distances, which are randomly selected according to a designed sampling pattern. We make two contributions. First, we analyze the performance of the MCNLM algorithm and show that, for large images or large external image databases, the random outcomes of MCNLM are tightly concentrated around the deterministic full NLM result. In particular, our error probability bounds show that, at any given sampling ratio, the probability for MCNLM to have a large deviation from the original NLM solution decays exponentially as the size of the image or database grows. Second, we derive explicit formulas for optimal sampling patterns that minimize the error probability bound by exploiting partial knowledge of the pairwise similarity weights. Numerical experiments show that MCNLM is competitive with other state-of-the-art fast NLM algorithms for single-image denoising. When applied to denoising images using an external database containing ten billion patches, MCNLM returns a randomized solution that is within 0.2 dB of the full NLM solution while reducing the runtime by three orders of magnitude.

We present a reflectance display: a dynamic digital display capable of showing images and videos with spatially-varying, user-defined reflectance functions. Our display is passive: it operates by phase-modulation of reflected light. As such, it does not rely on any illumination recording sensors, nor does it require expensive on-the-fly rendering. It reacts to lighting changes instantaneously and consumes only a minimal amount of energy. Our work builds on the wave optics approach to BRDF fabrication of Levin et al. shortciteLevinBRDFFab13. We replace their expensive one-time hardware fabrication with a programable liquid crystal spatial light modulator, retaining high resolution of approximately 160 dpi. Our approach enables the display of a much wider family of angular reflectances, and it allows the display of dynamic content with time varying reflectance properties---"reflectance videos". To facilitate these new capabilities we develop novel reflectance design algorithms with improved resolution tradeoffs. We demonstrate the utility of our display with a diverse set of experiments including display of custom reflectance images and videos, interactive reflectance editing, display of 3D content reproducing lighting and depth variation, and simultaneous display of two independent channels on one screen.

We consider the problem of finding distinctive social interactions involving groups of agents embedded in larger social gatherings. Given a pre-defined gallery of short exemplar interaction videos, and a long input video of a large gathering (with approximately-tracked agents), we identify within the gathering small sub-groups of agents exhibiting social interactions that resemble those in the exemplars. The participants of each detected group interaction are localized in space, the extent of their interaction is localized in time, and when the gallery of exemplars is annotated with group-interaction categories, each detected interaction is classified into one of the pre-defined categories. Our approach represents group behaviors by dichotomous collections of descriptors for (a) individual actions, and (b) pair-wise interactions, and it includes efficient algorithms for optimally distinguishing participants from by-standers in every temporal unit and for temporally localizing the extent of the group interaction. Most importantly, the method is generic and can be applied whenever numerous interacting agents can be approximately tracked over time. We evaluate the approach using three different video collections, two that involve humans and one that involves mice.

Non-local means (NLM) is a popular denoising scheme. Conceptually simple, the algorithm is computationally intensive for large images. We propose to speed up NLM by using random sampling. Our algorithm picks, uniformly at random, a small number of columns of the weight matrix, and uses these “representatives” to compute an approximate result. It also incorporates an extra column-normalization of the sampled columns, a form of symmetrization that often boosts the denoising performance on real images. Using statistical large deviation theory, we analyze the proposed algorithm and provide guarantees on its performance. We show that the probability of having a large approximation error decays exponentially as the image size increases. Thus, for large images, the random estimates generated by the algorithm are tightly concentrated around their limit values, even if the sampling ratio is small. Numerical results confirm our theoretical analysis: the proposed algorithm reduces the run time of NLM, and thanks to the symmetrization step, actually provides some improvement in peak signal-to-noise ratios.

Achieving computer vision on microscale devices is a challenge. On these platforms, the power and mass constraints are severe enough for even the most common computations (matrix manipulations, convolution, etc.) to be difficult. This paper proposes and analyzes a class of miniature vision sensors that can help overcome these constraints. These sensors reduce power requirements through template-based optical convolution, and they enable a wide field-of-view within a small form through a refractive optical design. We describe the tradeoffs between the field-of-view, volume, and mass of these sensors and we provide analytic tools to navigate the design space. We demonstrate milliscale prototypes for computer vision tasks such as locating edges, tracking targets, and detecting faces. Finally, we utilize photolithographic fabrication tools to further miniaturize the optical designs and demonstrate fiducial detection onboard a small autonomous air vehicle.

Multiple scattering contributes critically to the characteristic translucent appearance of food, liquids, skin, and crystals; but little is known about how it is perceived by human observers. This article explores the perception of translucency by studying the image effects of variations in one factor of multiple scattering: the phase function. We consider an expanded space of phase functions created by linear combinations of Henyey-Greenstein and von Mises-Fisher lobes, and we study this physical parameter space using computational data analysis and psychophysics. Our study identifies a two-dimensional embedding of the physical scattering parameters in a perceptually meaningful appearance space. Through our analysis of this space, we find uniform parameterizations of its two axes by analytical expressions of moments of the phase function, and provide an intuitive characterization of the visual effects that can be achieved at different parts of it. We show that our expansion of the space of phase functions enlarges the range of achievable translucent appearance compared to traditional single-parameter phase function models. Our findings highlight the important role phase function can have in controlling translucent appearance, and provide tools for manipulating its effect in material design applications.

Translucent materials are ubiquitous, and simulating their appearance requires accurate physical parameters. However, physically-accurate parameters for scattering materials are difficult to acquire. We introduce an optimization framework for measuring bulk scattering properties of homogeneous materials (phase function, scattering coefficient, and absorption coefficient) that is more accurate, and more applicable to a broad range of materials. The optimization combines stochastic gradient descent with Monte Carlo rendering and a material dictionary to invert the radiative transfer equation. It offers several advantages: (1) it does not require isolating single-scattering events; (2) it allows measuring solids and liquids that are hard to dilute; (3) it returns parameters in physically-meaningful units; and (4) it does not restrict the shape of the phase function using Henyey-Greenstein or any other low-parameter model. We evaluate our approach by creating an acquisition setup that collects images of a material slab under narrow-beam RGB illumination. We validate results by measuring prescribed nano-dispersions and showing that recovered parameters match those predicted by Lorenz-Mie theory. We also provide a table of RGB scattering parameters for some common liquids and solids, which are validated by simulating color images in novel geometric configurations that match the corresponding photographs with less than 5% error.

Recent attempts to fabricate surfaces with custom reflectance functions boast impressive angular resolution, yet their spatial resolution is limited. In this paper we present a method to construct spatially varying reflectance at a high resolution of up to 220dpi, orders of magnitude greater than previous attempts, albeit with a lower angular resolution. The resolution of previous approaches is limited by the machining, but more fundamentally, by the geometric optics model on which they are built. Beyond a certain scale geometric optics models break down and wave effects must be taken into account. We present an analysis of incoherent reflectance based on wave optics and gain important insights into reflectance design. We further suggest and demonstrate a practical method, which takes into account the limitations of existing micro-fabrication techniques such as photolithography to design and fabricate a range of reflection effects, based on wave interference.

We propose an approach for cross-view action recognition by way of `virtual views' that connect the action descriptors extracted from one (source) view to those extracted from another (target) view. Each virtual view is associated with a linear transformation of the action descriptor, and the sequence of transformations arising from the sequence of virtual views aims at bridging the source and target views while preserving discrimination among action categories. Our approach is capable of operating without access to labeled action samples in the target view and without access to corresponding action instances in the two views, and it also naturally incorporate and exploit corresponding instances or partial labeling in the target view when they are available. The proposed approach achieves improved or competitive performance relative to existing methods when instance correspondences or target labels are available, and it goes beyond the capabilities of these methods by providing some level of discrimination even when neither correspondences nor target labels exist.

Consumer digital cameras use tone-mapping to produce compact, narrow-gamut images that are nonetheless visually pleasing. In doing so, they discard or distort substantial radiometric signal that could otherwise be used for computer vision. Existing methods attempt to undo these effects through deterministic maps that de-render the reported narrow-gamut colors back to their original wide-gamut sensor measurements. Deterministic approaches are unreliable, however, because the reverse narrow-to-wide mapping is one-to-many and has inherent uncertainty. Our solution is to use probabilistic maps, providing uncertainty estimates useful to many applications. We use a non-parametric Bayesian regression technique - local Gaussian process regression - to learn for each pixel's narrow-gamut color a probability distribution over the scene colors that could have created it. Using a variety of consumer cameras we show that these distributions, once learned from training data, are effective in simple probabilistic adaptations of two popular applications: multi-exposure imaging and photometric stereo. Our results on these applications are better than those of corresponding deterministic approaches, especially for saturated and out-of-gamut colors.

We introduce an efficient maximum likelihood approach for one part of the color constancy problem: removing from an image the color cast caused by the spectral distribution of the dominating scene illuminant. We do this by developing a statistical model for the spatial distribution of colors in white balanced images (i.e., those that have no color cast), and then using this model to infer illumination parameters as those being most likely under our model. The key observation is that by applying spatial band-pass filters to color images one unveils color distributions that are unimodal, symmetric, and well represented by a simple parametric form. Once these distributions are fit to training data, they enable efficient maximum likelihood estimation of the dominant illuminant in a new image, and they can be combined with statistical prior information about the illuminant in a very natural manner. Experimental evaluation on standard data sets suggests that the approach performs well.

We explore a polar representation of optical flow in which each element of the brightness motion field is represented by its magnitude and orientation instead of its Cartesian projections. This seemingly small change in representation provides more direct access to the intrinsic structure of a flow field, and when used with existing variational inference procedures it provides a framework in which regularizers can be intuitively tailored for very different classes of motion. Our evaluations reveal that a flow estimation algorithm that is based on a polar representation can perform as well or better than the state-of-the-art when applied to traditional optical flow problems concerning camera or rigid scene motion, and at the same time, it facilitates both qualitative and quantitative improvements for non-traditional cases such as fluid flows and specular flows, whose structure is very different.

Hyperspectral images provide higher spectral resolution than typical RGB images by including per-pixel irradiance measurements in a number of narrow bands of wavelength in the visible spectrum. The additional spectral resolution may be useful for many visual tasks, including segmentation, recognition, and relighting. Vision systems that seek to capture and exploit hyperspectral data should benefit from statistical models of natural hyperspectral images, but at present, relatively little is known about their structure. Using a new collection of fifty hyperspectral images of indoor and outdoor scenes, we derive an optimized “spatio-spectral basis” for representing hyperspectral image patches, and explore statistical models for the coefficients in this basis.

Achieving computer vision on micro-scale devices is a challenge. On these platforms, the power and mass constraints are severe enough for even the most common computations (matrix manipulations, convolution, etc.) to be difficult. This paper proposes and analyzes a class of miniature vision sensors that can help overcome these constraints. These sensors reduce power requirements through template-based optical convolution, and they enable a wide field-of-view within a small form through a novel optical design. We describe the trade-offs between the field of view, volume, and mass of these sensors and we provide analytic tools to navigate the design space. We also demonstrate milli-scale prototypes for computer vision tasks such as locating edges, tracking targets, and detecting faces.

Color is known to be highly discriminative for many object recognition tasks, but is difficult to infer from uncontrolled images in which the illuminant is not known. Traditional methods for color constancy can improve surface reflectance estimates from such uncalibrated images, but their output depends significantly on the background scene. In many recognition and retrieval applications, we have access to image sets that contain multiple views of the same object in different environments; we show in this paper that correspondences between these images provide important constraints that can improve color constancy. We introduce the multi-view color constancy problem, and present a method to recover estimates of underlying surface reflectance based on joint estimation of these surface properties and the illuminants present in multiple images. The method can exploit image correspondences obtained by various alignment techniques, and we show examples based on matching local region features. Our results show that multi-view constraints can significantly improve estimates of both scene illuminants and object color (surface reflectance) when compared to a baseline single-view method.

Specular flow is the motion field induced on the image plane by the movement of points reflected by a curved, mirror-like surface. This flow provides information about surface shape, and when the camera and surface move as a fixed pair, shape can be recovered by solving linear differential equations along integral curves of flow. Previous analysis has shown that two distinct motions (i.e., two flow fields) are generally sufficient to guarantee a unique solution without externally-provided initial conditions. In this work, we show that we can often succeed with only one flow. The key idea is to exploit the fact that smooth surfaces induce integrability constraints on the surface normal field. We show that this induces a new differential equation that facilitates the propagation of shape information between integral curves of flow, and that combining this equation with known methods often permits the recovery of unique shape from a single specular flow given only a single seed point.

We propose an approach for linear unsupervised dimensionality reduction, based on the sparse linear model that has been used to probabilistically interpret sparse coding. We formulate an optimization problem for learning a linear projection from the original signal domain to a lower-dimensional one in a way that approximately preserves, in expectation, pairwise inner products in the sparse domain. We derive solutions to the problem, present nonlinear extensions, and discuss relations to compressed sensing. Our experiments using facial images, texture patches, and images of object categories suggest that the approach can improve our ability to recover meaningful structure in many classes of signals.

Different materials reflect light in different ways, and this reflectance interacts with shape, lighting, and viewpoint to determine an object's image. Common materials exhibit diverse reflectance effects, and this is a significant source of difficulty for image analysis. One strategy for dealing with this diversity is to build computational tools that exploit reflectance symmetries, such as reciprocity and isotropy, that are exhibited by broad classes of materials. By building tools that exploit these symmetries, one can create vision systems that are more likely to succeed in real-world, non-Lambertian environments. In this paper, we develop a framework for representing and exploiting reflectance symmetries. We analyze the conditions for distinct surface points to have local view and lighting conditions that are equivalent under these symmetries, and we represent these conditions in terms of the geometric structure they induce on the Gaussian sphere and its abstraction, the projective plane. We also study the behavior of these structures under perturbations of surface shape and explore applications to both calibrated and uncalibrated photometric stereo.

Blur is caused by a pixel receiving light from multiple scene points, and in many cases, such as object motion, the induced blur varies spatially across the image plane. However, the seemingly straight-forward task of estimating spatially-varying blur from a single image has proved hard to accomplish reliably. This work considers such blur and makes two contributions: a local blur cue that measures the likelihood of a small neighborhood being blurred by a candidate blur kernel; and an algorithm that, given an image, simultaneously selects a motion blur kernel and segments the region that it affects. The methods are shown to perform well on a diversity of images.

Abstract We present a new Precomputed Radiance Transfer (PRT) algorithm based on a two dimensional representation of isotropic BRDFs. Our approach involves precomputing matrices that allow quickly mapping environment lighting, which is represented in the global coordinate system, and the surface BRDFs, which are represented in a bivariate domain, to the local hemisphere at a surface location where the reflection integral is evaluated. When the lighting and BRDFs are represented in a wavelet basis, these rotation matrices are sparse and can be efficiently stored and combined with pre‐computed visibility at run‐time. Compared to prior techniques that also precompute wavelet rotation matrices, our method allows full control over the lighting and materials due to the way the BRDF is represented. Furthermore, this bivariate parameterization preserves sharp specular peaks and grazing effects that are attenuated in conventional parameterizations. We demonstrate a prototype rendering system that achieves real‐time framerates while lighting and materials are edited.

An image of a specular (mirror-like) object is nothing but a distorted reflection of its environment. When the environment is unknown, reconstructing shape from such an image can be very difficult. This reconstruction task can be made tractable when, instead of a single image, one observes relative motion between the specular object and its environment, and therefore, a motion field-or specular flow-in the image plane. In this paper, we study the shape from specular flow problem and show that observable specular flow is directly related to surface shape through a nonlinear partial differential equation. This equation has the key property of depending only on the relative motion of the environment while being independent of its content. We take first steps toward understanding and exploiting this PDE, and we examine its qualitative properties in relation to shape geometry. We analyze several cases in which the surface shape can be recovered in closed form, and we show that, under certain conditions, specular shape can be reconstructed when both the relative motion and the content of the environment are unknown. We discuss numerical issues related to the proposed reconstruction algorithms, and we validate our findings using both real and synthetic data.

Personal photographs are being captured in digital form at an accelerating rate, and our computational tools for searching, browsing, and sharing these photos are struggling to keep pace. One promising approach is automatic face recognition, which would allow photos to be organized by the identities of the individuals they contain. However, achieving accurate recognition at the scale of the Web requires discriminating among hundreds of millions of individuals and would seem to be a daunting task. This paper argues that social network context may be the key for large-scale face recognition to succeed. Many personal photographs are shared on the Web through online social network sites, and we can leverage the resources and structure of such social networks to improve face recognition rates on the images shared. Drawing upon real photo collections from volunteers who are members of a popular online social network, we asses the availability of resources to improve face recognition and discuss techniques for applying these resources.

We present a novel optical setup and processing pipeline for measuring the 3D geometry and spatially-varying surface reflectance of physical objects. Central to our design is a digital camera and a high frequency spatially-modulated light source aligned to share a common focal point and optical axis. Pairs of such devices allow capturing a sequence of images from which precise measurements of geometry and reflectance can be recovered. Our approach is enabled by two technical contributions: a new active multiview stereo algorithm and an analysis of light descattering that has important implications for image-based reflectometry. We show that the geometry measured by our scanner is accurate to within 50 microns at a resolution of roughly 200 microns and that the reflectance agrees with reference data to within 5.5%. Additionally, we present an image relighting application and show renderings that agree very well with reference images at light and view positions far from those that were initially measured.

Images harvested from the Web are proving to be useful for many visual tasks, including recognition, geo-location, and three-dimensional reconstruction. These images are captured under a variety of lighting conditions by consumer-level digital cameras, and these cameras have color processing pipelines that are diverse, complex, and scenedependent. As a result, the color information contained in these images is difficult to exploit. In this paper, we analyze the factors that contribute to the color output of a typical camera, and we explore the use of parametric models for relating these output colors to meaningful scenes properties. We evaluate these models using a database of registered images captured with varying camera models, camera settings, and lighting conditions. The database is available online at

Different materials reflect light in different ways, and reflectance interacts with shape, lighting, and viewpoint to determine an object's image. Common materials exhibit diverse reflectance effects, and this is a significant source of difficulty for radiometric image analysis. One strategy for dealing with this diversity is to build computational tools that exploit reflectance symmetries, such as reciprocity and isotropy, that are exhibited by broad classes of materials. In this paper, we advocate the real projective plane as a tool for representing and exploiting these symmetries. In this approach, each point in the plane represents a surface normal that is visible from a fixed viewpoint, and reflectance symmetries are analyzed in terms of the geometric structures that they induce. We provide an overview of these structures and explore applications to both calibrated and uncalibrated photometric stereo.

When a curved mirror-like surface moves relative to its environment, it induces a motion field-or specular flow- on the image plane that observes it. This specular flow is related to the mirror's shape through a non-linear partial differential equation, and there is interest in understanding when and how this equation can be solved for surface shape. Existing analyses of this `shape from specular flow equation' have focused on closed-form solutions, and while they have yielded insight, their critical reliance on externally-provided initial conditions and/or specific motions makes them difficult to apply in practice. This paper resolves these issues. We show that a suitable reparameterization leads to a linear formulation of the shape from specular flow equation. This formulation radically simplifies the reconstruction process and allows, for example, both motion and shape to be recovered from as few as two specular flows even when no externally-provided initial conditions are available. Our analysis moves us closer to a practical method for recovering shape from specular flow that operates under arbitrary, unknown motions in unknown illumination environments and does not require additional shape information from other sources.

We present a method for simultaneously recovering shape and spatially varying reflectance of a surface from photometric stereo images. The distinguishing feature of our approach is its generality; it does not rely on a specific parametric reflectance model and is therefore purely ldquodata-drivenrdquo. This is achieved by employing novel bi-variate approximations of isotropic reflectance functions. By combining this new approximation with recent developments in photometric stereo, we are able to simultaneously estimate an independent surface normal at each point, a global set of non-parametric ldquobasis materialrdquo BRDFs, and per-point material weights. Our experimental results validate the approach and demonstrate the utility of bi-variate reflectance functions for general non-parametric appearance capture.

Estimating the color of a scene illuminant often plays a central role in computational color constancy. While this problem has received significant attention, the methods that exist do not maximally leverage spatial dependencies between pixels. Indeed, most methods treat the observed color (or its spatial derivative) at each pixel independently of its neighbors. We propose an alternative approach to illuminant estimation-one that employs an explicit statistical model to capture the spatial dependencies between pixels induced by the surfaces they observe. The parameters of this model are estimated from a training set of natural images captured under canonical illumination, and for a new image, an appropriate transform is found such that the corrected image best fits our model.

In an extended image sequence of an outdoor scene, one observes changes in color induced by variations in the spectral composition of daylight. This paper proposes a model for these temporal color changes and explores its use for the analysis of outdoor scenes from time-lapse video data. We show that the time-varying changes in direct sunlight and ambient skylight can be recovered with this model, and that an image sequence can be decomposed into two corresponding components. The decomposition provides access to both radiometric and geometric information about a scene, and we demonstrate how this can be exploited for a variety of visual tasks, including color-constancy, background subtraction, shadow detection, scene reconstruction, and camera geo-location.

The inference of specular (mirror-like) shape is a particularly difficult problem because an image of a specular object is nothing but a distortion of the surrounding environment. Consequently, when the environment is unknown, such an image would seem to convey little information about the shape itself. It has recently been suggested (Adato et al., ICCV 2007) that observations of relative motion between a specular object and its environment can dramatically simplify the inference problem and allow one to recover shape without explicit knowledge of the environment content. However, this approach requires solving a non-linear PDE (the dasiashape from specular flow equationpsila) and analytic solutions are only known to exist for very constrained motions. In this paper, we consider the recovery of shape from specular flow under general motions. We show that while the dasiashape from specular flowpsila PDE for a single motion is non-linear, we can combine observations of multiple specular flows from distinct relative motions to yield a linear set of equations. We derive necessary conditions for this procedure, discuss several numerical issues with their solution, and validate our results quantitatively using image data.

Motivated by perceptual principles, we derive a new color space in which the associated metric approximates perceived distances and color displacements capture relationships that are robust to spectral changes in illumination. The resulting color space can be used with existing image processing algorithms with little or no change to the methods.

This paper presents a technique for acquiring the shape of real-world objects with complex isotropic and anisotropic reflectance. Our method estimates the local normal and tangent vectors at each pixel in a reference view from a sequence of images taken under varying point lighting. We show that for many real-world materials and a restricted set of light positions, the 2D slice of the BRDF obtained by fixing the local view direction is symmetric under reflections of the halfway vector across the normal-tangent and normal-binormal planes. Based on this analysis, we develop an optimization that estimates the local surface frame by identifying these planes of symmetry in the measured BRDF. As with other photometric methods, a key benefit of our approach is that the input is easy to acquire and is less sensitive to calibration errors than stereo or multi-view techniques. Unlike prior work, our approach allows estimating the surface tangent in the case of anisotropic reflectance. We confirm the accuracy and reliability of our approach with analytic and measured data, present several normal and tangent fields acquired with our technique, and demonstrate applications to appearance editing.

A set of images of a Lambertian surface under varying lighting directions defines its shape up to a three-parameter generalized bas-relief (GBR) ambiguity. In this paper, we examine this ambiguity in the context of surfaces having an additive non-Lambertian reflectance component, and we show that the GBR ambiguity is resolved by any non-Lambertian reflectance function that is isotropic and spatially invariant. The key observation is that each point on a curved surface under directional illumination is a member of a family of points that are in isotropic or reciprocal configurations. We show that the GBR can be resolved in closed form by identifying members of these families in two or more images. Based on this idea, we present an algorithm for recovering full Euclidean geometry from a set of uncalibrated photometric stereo images, and we evaluate it empirically on a number of examples.

The image of a curved, specular (mirror-like) surface is a distorted reflection of the environment. The goal of our work is to develop a framework for recovering general shape from such distortions when the environment is neither calibrated nor known. To achieve this goal we consider far-field illumination, where the object-environment distance is relatively large, and we examine the dense specular flow that is induced on the image plane through relative object-environment motion. We show that under these very practical conditions the observed specular flow can be related to surface shape through a pair of coupled nonlinear partial differential equations. Importantly, this relationship depends only on the environment's relative motion and not its content. We examine the qualitative properties of these equations, present analytic methods for recovery of the shape in several special cases, and empirically validate our results using captured data. We also discuss the relevance to both computer vision and human perception.

Color constancy is almost exclusively modeled with diagonal transforms. However, the choice of basis under which diagonal transforms are taken is traditionally ad hoc. Attempts to remedy the situation have been hindered by the fact that no joint characterization of the conditions for {sensors, illuminants, reflectances} to support diagonal color constancy has previously been achieved. In this work, we observe that the von Kries compatibility conditions are impositions only on the sensor measurements, not the physical spectra. This allows us to formulate the von Kries compatibility conditions succinctly as rank constraints on an order 3 measurement tensor. Given this, we propose an algorithm that computes a (locally) optimal choice of color basis for diagonal color constancy and compare the results against other proposed choices.

Helmholtz stereopsis is a surface reconstruction method that exploits reciprocity for the recovery of 3D shape without an assumed BRDF model, and it has been shown to yield high quality results when the cameras and light sources are carefully calibrated. In many practical cases, however, accurate off-line calibration is difficult (or impossible) to achieve. We address this issue by exploring widebaseline matching in Helmholtz stereo images. We identify two classes of local image interest regions (‘features’) that can be reliably detected and matched between views in a Helmholtz stereo dataset; and by exploiting reciprocity, we show how these regions can be used to recover both geometric and radiometric calibration information. When used in conjunction with existing methods for dense reconstruction, this provides an automated shape recovery pipeline that operates independent of reflectance and does not require the acquisition of additional calibration images off-line.

Complex reflectance phenomena such as specular reflections confound many vision problems since they produce image ‘features’ that do not correspond directly to intrinsic surface properties such as shape and spectral reflectance. A common approach to mitigate these effects is to explore functions of an image that are invariant to these photometric events. In this paper we describe two such invariants" one invariant to specular reflections, and the other invariant to both specular reflections and diffuse shading" that result from exploiting color information in images of dichromatic surfaces. These invariants are derived from subspaces of RGB color space, and they enable the application of Lambertian-based vision techniques to a broad class of specular, non-Lambertian scenes. Using implementations of recent algorithms taken from the literature, we demonstrate the practical utility of these invariants for a wide variety of applications, including stereo, shape from shading, material-based segmentation, and motion estimation.

Three-dimensional appearance models consisting of spatially varying reflectance functions defined on a known shape can be used in analysis-by-synthesis approaches to a number of visual tasks. The construction of these models requires the measurement of reflectance, and the problem of recovering spatially varying reflectance from images of known shape has drawn considerable interest. To date, existing methods rely on either: (1) low-dimensional (e.g., parametric) reflectance models, or (2) large data sets involving thousands of images (or more) per object. Appearance models based on the former have limited accuracy and generality since they require the selection of a specific reflectance model a priori, and while approaches based on the latter may be suitable for certain applications, they are generally too costly and cumbersome to be used for image analysis. We present an alternative approach that seeks to combine the benefits of existing methods by enabling the estimation of a nonparametric spatially varying reflectance function from a small number of images. We frame the problem as scattered-data interpolation in a mixed spatial and angular domain, and we present a theory demonstrating that the angular accuracy of a recovered reflectance function can be increased in exchange for a decrease in its spatial resolution. We also present a practical solution to this interpolation problem using a new representation of reflectance based on radial basis functions. This representation is evaluated experimentally by testing its ability to predict appearance under novel view and lighting conditions. Our results suggest that since reflectance typically varies slowly from point to point over much of an object's surface, we can often obtain a nonparametric reflectance function from a sparse set of images. In fact, in some cases, we can obtain reasonable results in the limiting case of only a single input image.

We present a photometric stereo method for non-diffuse materials that does not require an explicit reflectance model or reference object. By computing a data-dependent rotation of RGB color space, we show that the specular reflection effects can be separated from the much simpler, diffuse (approximately Lambertian) reflection effects for surfaces that can be modeled with dichromatic reflectance. Images in this transformed color space are used to obtain photometric reconstructions that are independent of the specular reflectance. In contrast to other methods for highlight removal based on dichromatic color separation (e.g., color histogram analysis and/or polarization), we do not explicitly recover the specular and diffuse components of an image. Instead, we simply find a transformation of color space that yields more direct access to shape information. The method is purely local and is able to handle surfaces with arbitrary texture.

Helmholtz stereopsis has been previously introduced as a surface reconstruction technique that does not assume a model of surface reflectance. This technique relies on the use of multiple cameras and light sources, and it has been shown to be effective when the camera and source positions are known. Here, we take a stratified look at uncalibrated Helmholtz stereopsis. We derive a photometric matching constraint that can be used to establish correspondence without any knowledge of the cameras and sources (except that they are co-located), and we determine conditions under which we can obtain affine and metric reconstructions. An implementation and experimental results are presented.

Helmholtz stereopsis has been introduced recently as a surface reconstruction technique that does not assume a model of surface reflectance. In the reported formulation, correspondence was established using a rank constraint, necessitating at least three viewpoints and three pairs of images. Here, it is revealed that the fundamental Helmholtz stereopsis constraint defines a nonlinear partial differential equation, which can be solved using only two images. It is shown that, unlike conventional stereo, binocular Helmholtz stereopsis is able to establish correspondence (and thereby recover surface depth) for objects having an arbitrary and unknown BRDF and in textureless regions (i.e., regions of constant or slowly varying BRDF). An implementation and experimental results validate the method for specular surfaces with and without texture.

We address an open and hitherto neglected problem in computer vision, how to reconstruct the geometry of objects with arbitrary and possibly anisotropic bidirectional reflectance distribution functions (BRDFs). Present reconstruction techniques, whether stereo vision, structure from motion, laser range finding, etc. make explicit or implicit assumptions about the BRDF. Here, we introduce two methods that were developed by re-examining the underlying image formation process; the methods make no assumptions about the object's shape, the presence or absence of shadowing, or the nature of the BRDF which may vary over the surface. The first method takes advantage of Helmholtz reciprocity, while the second method exploits the fact that the radiance along a ray of light is constant. In particular, the first method uses stereo pairs of images in which point light sources are co-located at the centers of projection of the stereo cameras. The second method is based on double covering a scene's incident light field; the depths of surface points are estimated using a large collection of images in which the viewpoint remains fixed and a point light source illuminates the object. Results from our implementations lend empirical support to both techniques.