Abstract Triple product integrals evaluate the shading at a point by factoring the reflection equation into incident illumination, visibility, and BRDF. By densely sampling the space of incident directions, this approach is capable of highly accurate rendering scenes lit by high‐frequency environment lighting, containing complex materials and featuring intricate shadows. Efficient evaluation of triple product integrals using Haar wavelets enables near‐interactive rendering of such scenes, while dynamically changing the lighting and the view. Although faster methods have been proposed in the recent real‐time rendering literature, the approximations employed in these methods typically limit them to lower frequency phenomena. In this paper, we present a new approach for high‐frequency scene relighting within the triple product framework. Our approach breaks the computation to smaller solid angles (blocks) over most of which the triple product degenerates to a dot product. We introduce a lossless, yet compact, differential representation of the visibility function over each block, and sample the BRDF on the fly, eliminating the need to store multiple rotated copies of each BRDF. By combining these ideas, we are able to achieve true interactive performance even when running on a CPU, while supporting high frequency effects in scenes with high vertex counts.

We present a novel approach for rapid numerical approximation of convolutions with filters of large support. Our approach consists of a multiscale scheme, fashioned after the wavelet transform, which computes the approximation in linear time. Given a specific large target filter to approximate, we first use numerical optimization to design a set of small kernels, which are then used to perform the analysis and synthesis steps of our multiscale transform. Once the optimization has been done, the resulting transform can be applied to any signal in linear time. We demonstrate that our method is well suited for tasks such as gradient field integration, seamless image cloning, and scattered data interpolation, outperforming existing state-of-the-art methods.

This paper presents a method for reducing undesirable tonal fluctuations in video: minute changes in tonal characteristics, such as exposure, color temperature, brightness and contrast in a sequence of frames, which are easily noticeable when the sequence is viewed. These fluctuations are typically caused by the camera's automatic adjustment of its tonal settings while shooting. Our approach operates on a continuous video shot by first designating one or more frames as anchors . We then tonally align a sequence of frames with each anchor: for each frame, we compute an adjustment map that indicates how each of its pixels should be modified in order to appear as if it was captured with the tonal settings of the anchor. The adjustment map is efficiently updated between successive frames by taking advantage of temporal video coherence and the global nature of the tonal fluctuations. Once a sequence has been aligned, it is possible to generate smooth tonal transitions between anchors, and also further control its tonal characteristics in a consistent and principled manner, which is difficult to do without incurring strong artifacts when operating on unstable sequences. We demonstrate the utility of our method using a number of clips captured with a variety of video cameras, and believe that it is well-suited for integration into today's non-linear video editing tools.

Edge-aware operations, such as edge-preserving smoothing and edge-aware interpolation, require assessing the degree of similarity between pairs of pixels, typically defined as a simple monotonic function of the Euclidean distance between pixel values in some feature space. In this work we introduce the idea of replacing these Euclidean distances with diffusion distances , which better account for the global distribution of pixels in their feature space. These distances are approximated using diffusion maps : a set of the dominant eigenvectors of a large affinity matrix, which may be computed efficiently by sampling a small number of matrix columns (the Nyström method). We demonstrate the benefits of using diffusion distances in a variety of image editing contexts, and explore the use of diffusion maps as a tool for facilitating the creation of complex selection masks. Finally, we present a new analysis that establishes a connection between the spatial interaction range between two pixels, and the number of samples necessary for accurate Nyström approximations.

Seamless cloning of a source image patch into a target image is an important and useful image editing operation, which has received considerable research attention in recent years. This operation is typically carried out by solving a Poisson equation with Dirichlet boundary conditions, which smoothly interpolates the discrepancies between the boundary of the source patch and the target across the entire cloned area. In this paper we introduce an alternative, coordinate-based approach, where rather than solving a large linear system to perform the aforementioned interpolation, the value of the interpolant at each interior pixel is given by a weighted combination of values along the boundary. More specifically, our approach is based on Mean-Value Coordinates (MVC). The use of coordinates is advantageous in terms of speed, ease of implementation, small memory footprint, and parallelizability, enabling real-time cloning of large regions, and interactive cloning of video streams. We demonstrate a number of applications and extensions of the coordinate-based framework.

Many recent computational photography techniques decompose an image into a piecewise smooth base layer, containing large scale variations in intensity, and a residual detail layer capturing the smaller scale details in the image. In many of these applications, it is important to control the spatial scale of the extracted details, and it is often desirable to manipulate details at multiple scales, while avoiding visual artifacts. In this paper we introduce a new way to construct edge-preserving multi-scale image decompositions. We show that current basedetail decomposition techniques, based on the bilateral filter, are limited in their ability to extract detail at arbitrary scales. Instead, we advocate the use of an alternative edge-preserving smoothing operator, based on the weighted least squares optimization framework, which is particularly well suited for progressive coarsening of images and for multi-scale detail extraction. After describing this operator, we show how to use it to construct edge-preserving multi-scale decompositions, and compare it to the bilateral filter, as well as to other schemes. Finally, we demonstrate the effectiveness of our edge-preserving decompositions in the context of LDR and HDR tone mapping, detail enhancement, and other applications.

This paper presents a new interactive tool for making local adjustments of tonal values and other visual parameters in an image. Rather than carefully selecting regions or hand-painting layer masks, the user quickly indicates regions of interest by drawing a few simple brush strokes and then uses sliders to adjust the brightness, contrast, and other parameters in these regions. The effects of the user's sparse set of constraints are interpolated to the entire image using an edge-preserving energy minimization method designed to prevent the propagation of tonal adjustments to regions of significantly different luminance. The resulting system is suitable for adjusting ordinary and high dynamic range images, and provides the user with much more creative control than existing tone mapping algorithms. Our tool is also able to produce a tone mapping automatically, which may serve as a basis for further local adjustments, if so desired. The constraint propagation approach developed in this paper is a general one, and may also be used to interactively control a variety of other adjustments commonly performed in the digital darkroom.