Multi‐Class Anisotropic Electrostatic Halftoning

Electrostatic halftoning, a sampling algorithm based on electrostatic principles, is among the leading methods for stippling, dithering and sampling. However, this approach is only applicable for a single class of dots with a uniform size and colour. In our work, we complement these ideas by advanced features for real‐world applications. We propose a versatile framework for colour halftoning, hatching and multi‐class importance sampling with individual weights. Our novel approach is the first method that globally optimizes the distribution of different objects in varying sizes relative to multiple given density functions. The quality, versatility and adaptability of our approach is demonstrated in various experiments.     

Spectralization: Reconstructing spectra from sparse data

Traditional RGB reflectance and light data suffers from the problem of metamerism and is not suitable for rendering purposes where exact color reproduction under many different lighting conditions is needed. Nowadays many setups for cheap and fast acquisition of RGB or similar trichromatic datasets are available. In contrast to this, multi‐ or even hyper‐spectral measurements require costly hardware and have severe limitations in many cases. In this paper, we present an approach to combine efficiently captured RGB data with spectral data that can be captured with small additional effort for example by scanning a single line of an image using a spectral line‐scanner. Our algorithm can infer spectral reflectances and illumination from such sparse spectral and dense RGB data. Unlike other approaches, our method reaches acceptable perceptual errors with only three channels for the dense data and thus enables further use of highly efficient RGB capture systems. This way, we are able to provide an easier and cheaper way to capture spectral textures, BRDFs and environment maps for the use in spectral rendering systems.     

Efficient Computation of Blue Noise Point Sets through Importance Sampling

Dart‐throwing can generate ideal Poisson‐disk distributions with excellent blue noise properties, but is very computationally expensive if a maximal point set is desired. In this paper, we observe that the Poisson‐disk sampling problem can be posed in terms of importance sampling by representing the available space to be sampled as a probability density function (pdf). This allows us to develop an efficient algorithm for the generation of maximal Poisson‐disk distributions with quality similar to naïve dart‐throwing but without rejection of samples. In our algorithm, we first position samples in one dimension based on its marginal cumulative distribution function (cdf). We then throw samples in the other dimension only in the regions which are available for sampling. After each 2D sample is placed, we update the cdf and data structures to keep track of the available regions. In addition to uniform sampling, our method is able to perform variable‐density sampling with small modifications. Finally, we also propose a new min‐conflict metric for variable‐density sampling which results in better adaptation of samples to the underlying importance field.     

Electrostatic Halftoning

We introduce a new global approach for image dithering, stippling, screening and sampling. It is inspired by the physical principles of electrostatics. Repelling forces between equally charged particles create a homogeneous distribution in flat areas, while attracting forces from the image brightness values ensure a high approximation quality. Our model is transparent and uses only two intuitive parameters: One steers the granularity of our halftoning approach, and the other its regularity. We evaluate two versions of our algorithm: A discrete version for dithering that ties points to grid positions, as well as a continuous one which does not have this restriction, and can thus be used for stippling or sampling density functions. Our methods create very few visual artefacts, reveal favourable blue‐noise behaviour in the frequency domain, and have a lower approximation error under Gaussian convolution than state‐of‐the‐art methods.     

Matrix Trees

We propose a new data representation for octrees and kd‐trees that improves upon memory size and algorithm speed of existing techniques. While pointerless approaches exploit the regular structure of the tree to facilitate efficient data access, their memory footprint becomes prohibitively large as the height of the tree increases. Pointerbased trees require memory consumption proportional to the number of tree nodes, thus exploiting the typical sparsity of large trees. Yet, their traversal is slowed by the need to follow explicit pointers across the different levels. Our solution is a pointerless approach that represents each tree level with its own matrix, as opposed to traditional pointerless trees that use only a single vector. This novel data organization allows us to fully exploit the tree's regular structure and improve the performance of tree operations. By using a sparse matrix data structure we obtain a representation that is suited for sparse and dense trees alike. In particular, it uses less total memory than pointer‐based trees even when the data set is extremely sparse. We show how our approach is easily implemented on the GPU and illustrate its performance in typical visualization scenarios.     

Silhouette‐Aware Warping for Image‐Based Rendering

Image‐based rendering (IBR) techniques allow capture and display of 3D environments using photographs. Modern IBR pipelines reconstruct proxy geometry using multi‐view stereo, reproject the photographs onto the proxy and blend them to create novel views. The success of these methods depends on accurate 3D proxies, which are difficult to obtain for complex objects such as trees and cars. Large number of input images do not improve reconstruction proportionally; surface extraction is challenging even from dense range scans for scenes containing such objects. Our approach does not depend on dense accurate geometric reconstruction; instead we compensate for sparse 3D information by variational image warping. In particular, we formulate silhouette‐aware warps that preserve salient depth discontinuities. This improves the rendering of difficult foreground objects, even when deviating from view interpolation. We use a semi‐automatic step to identify depth discontinuities and extract a sparse set of depth constraints used to guide the warp. Our framework is lightweight and results in good quality IBR for previously challenging environments.     

Importance Sampling Techniques for Path Tracing in Participating Media

We introduce a set of robust importance sampling techniques which allow efficient calculation of direct and indirect lighting from arbitrary light sources in both homogeneous and heterogeneous media. We show how to distribute samples along a ray proportionally to the incoming radiance for point and area lights. In heterogeneous media, we decouple ray marching from light calculations by computing a representation of the transmittance function that can be quickly evaluated during sampling, at the cost of a small amount of bias. This representation also allows the calculation of another probability density function which can direct samples to regions most likely to scatter light. These techniques are orthogonal and can be combined via multiple importance sampling to further reduce variance. Our method has very modest per‐ray memory requirements and does not require any preprocessing, making it simple to integrate into production ray tracing based renderers.     

Fast and Robust Normal Estimation for Point Clouds with Sharp Features

This paper presents a new method for estimating normals on unorganized point clouds that preserves sharp features. It is based on a robust version of the Randomized Hough Transform (RHT). We consider the filled Hough transform accumulator as an image of the discrete probability distribution of possible normals. The normals we estimate corresponds to the maximum of this distribution. We use a fixed‐size accumulator for speed, statistical exploration bounds for robustness, and randomized accumulators to prevent discretization effects. We also propose various sampling strategies to deal with anisotropy, as produced by laser scans due to differences of incidence. Our experiments show that our approach offers an ideal compromise between precision, speed, and robustness: it is at least as precise and noise‐resistant as state‐of‐the‐art methods that preserve sharp features, while being almost an order of magnitude faster. Besides, it can handle anisotropy with minor speed and precision losses.     

Intrinsic Images by Clustering

Decomposing an input image into its intrinsic shading and reflectance components is a long‐standing ill‐posed problem. We present a novel algorithm that requires no user strokes and works on a single image. Based on simple assumptions about its reflectance and luminance, we first find clusters of similar reflectance in the image, and build a linear system describing the connections and relations between them. Our assumptions are less restrictive than widely‐adopted Retinex‐based approaches, and can be further relaxed in conflicting situations. The resulting system is robust even in the presence of areas where our assumptions do not hold. We show a wide variety of results, including natural images, objects from the MIT dataset and texture images, along with several applications, proving the versatility of our method.     

Flexible and Accurate Transparent‐Object Matting and Compositing Using Refractive Vector Field

In digital image editing, environment matting and compositing are fundamental and interesting operations that can capture and simulate the refraction and reflection effects of light from an environment. The state‐of‐the‐art real‐time environment matting and compositing method is short of flexibility, in the sense that it has to repeat the entire complex matte acquisition process if the distance between the object and the background is different from that in the acquisition stage, and also lacks accuracy, in the sense that it can only remove noises but not errors. In this paper, we introduce the concept of refractive vector and propose to use a refractive vector field as a new representation for environment matte. Such refractive vector field provides great flexibility for transparent‐object environment matting and compositing. Particularly, with only one process of the matte acquisition and the refractive vector field extraction, we are able to composite the transparent object into an arbitrary background at any distance. Furthermore, we introduce a piecewise vector field fitting algorithm to simultaneously remove both noises and errors contained in the extracted matte data. Experimental results show that our method is less sensitive to artefacts and can generate perceptually good composition results for more general scenarios.     

Turning a Digital Camera into an Absolute 2D Tele‐Colorimeter

We present a simple and effective technique for absolute colorimetric camera characterization, invariant to changes in exposure/aperture and scene irradiance, suitable in a wide range of applications including image‐based reflectance measurements, spectral pre‐filtering and spectral upsampling for rendering, to improve colour accuracy in high dynamic range imaging. Our method requires a limited number of acquisitions, an off‐the‐shelf target and a commonly available projector, used as a controllable light source, other than the reflected radiance to be known. The characterized camera can be effectively used as a 2D tele‐colorimeter, providing the user with an accurate estimate of the distribution of luminance and chromaticity in a scene, without requiring explicit knowledge of the incident lighting power spectra. We validate the approach by comparing our estimated absolute tristimulus values (XYZ data in ) with the measurements of a professional 2D tele‐colorimeter, for a set of scenes with complex geometry, spatially varying reflectance and light sources with very different spectral power distribution.     

Efficient GPU Data Structures and Methods to Solve Sparse Linear Systems in Dynamics Applications

We present graphics processing unit (GPU) data structures and algorithms to efficiently solve sparse linear systems that are typically required in simulations of multi‐body systems and deformable bodies. Thereby, we introduce an efficient sparse matrix data structure that can handle arbitrary sparsity patterns and outperforms current state‐of‐the‐art implementations for sparse matrix vector multiplication. Moreover, an efficient method to construct global matrices on the GPU is presented where hundreds of thousands of individual element contributions are assembled in a few milliseconds. A finite‐element‐based method for the simulation of deformable solids as well as an impulse‐based method for rigid bodies are introduced in order to demonstrate the advantages of the novel data structures and algorithms. These applications share the characteristic that a major computational effort consists of building and solving systems of linear equations in every time step. Our solving method results in a speed‐up factor of up to 13 in comparison to other GPU methods.     

Fast Generation of Approximate Blue Noise Point Sets

Poisson‐disk sampling is a popular sampling method because of its blue noise power spectrum, but generation of these samples is computationally very expensive. In this paper, we propose an efficient method for fast generation of a large number of blue noise samples using a small initial patch of Poisson‐disk samples that can be generated with any existing approach. Our main idea is to convolve this set of samples with another to generate our final set of samples. We use the convolution theorem from signal processing to show that the spectrum of the resulting sample set preserves the blue noise properties. Since our method is approximate, we have error with respect to the true Poisson‐disk samples, but we show both mathematically and practically that this error is only a function of the number of samples in the small initial patch and is therefore bounded. Our method is parallelizable and we demonstrate an implementation of it on a GPU, running more than 10 times faster than any previous method and generating more than 49 million 2D samples per second. We can also use the proposed approach to generate multidimensional blue noise samples.     

Estimation and Modeling of Actual Numerical Errors in Volume Rendering

In this paper we study the comprehensive effects on volume rendered images due to numerical errors caused by the use of finite precision for data representation and processing. To estimate actual error behavior we conduct a thorough study using a volume renderer implemented with arbitrary floating‐point precision. Based on the experimental data we then model the impact of floating‐point pipeline precision, sampling frequency and fixed‐point input data quantization on the fidelity of rendered images. We introduce three models, an average model, which does not adapt to different data nor varying transfer functions, as well as two adaptive models that take the intricacies of a new data set and transfer function into account by adapting themselves given a few different images rendered. We also test and validate our models based on new data that was not used during our model building.     

Direct Ray Tracing of Phong Tessellation

There are two major ways of calculating ray and parametric surface intersections in rendering. The first is through the use of tessellated triangles, and the second is to use parametric surfaces together with numerical methods such as Newton's method. Both methods are computationally expensive and complicated to implement. In this paper, we focus on Phong Tessellation and introduce a simple direct ray tracing method for Phong Tessellation. Our method enables rendering smooth surfaces in a computationally inexpensive yet robust way.     

Linkless Octree Using Multi‐Level Perfect Hashing

The standard C/C++ implementation of a spatial partitioning data structure, such as octree and quadtree, is often inefficient in terms of storage requirements particularly when the memory overhead for maintaining parent‐to‐child pointers is significant with respect to the amount of actual data in each tree node. In this work, we present a novel data structure that implements uniform spatial partitioning without storing explicit parent‐to‐child pointer links. Our linkless tree encodes the storage locations of subdivided nodes using perfect hashing while retaining important properties of uniform spatial partitioning trees, such as coarse‐to‐fine hierarchical representation, efficient storage usage, and efficient random accessibility. We demonstrate the performance of our linkless trees using image compression and path planning examples.     

Improved Stochastic Progressive Photon Mapping with Metropolis Sampling

This paper presents an improvement to the stochastic progressive photon mapping (SPPM), a method for robustly simulating complex global illumination with distributed ray tracing effects. Normally, similar to photon mapping and other particle tracing algorithms, SPPM would become inefficient when the photons are poorly distributed. An inordinate amount of photons are required to reduce the error caused by noise and bias to acceptable levels. In order to optimize the distribution of photons, we propose an extension of SPPM with a Metropolis‐Hastings algorithm, effectively exploiting local coherence among the light paths that contribute to the rendered image. A well‐designed scalar contribution function is introduced as our Metropolis sampling strategy, targeting at specific parts of image areas with large error to improve the efficiency of the radiance estimator. Experimental results demonstrate that the new Metropolis sampling based approach maintains the robustness of the standard SPPM method, while significantly improving the rendering efficiency for a wide range of scenes with complex lighting.     

Practical Path Guiding for Efficient Light‐Transport Simulation

We present a robust, unbiased technique for intelligent light‐path construction in path‐tracing algorithms. Inspired by existing path‐guiding algorithms, our method learns an approximate representation of the scene's spatio‐directional radiance field in an unbiased and iterative manner. To that end, we propose an adaptive spatio‐directional hybrid data structure, referred to as SD‐tree, for storing and sampling incident radiance. The SD‐tree consists of an upper part—a binary tree that partitions the 3D spatial domain of the light field—and a lower part—a quadtree that partitions the 2D directional domain. We further present a principled way to automatically budget training and rendering computations to minimize the variance of the final image. Our method does not require tuning hyperparameters, although we allow limiting the memory footprint of the SD‐tree. The aforementioned properties, its ease of implementation, and its stable performance make our method compatible with production environments. We demonstrate the merits of our method on scenes with difficult visibility, detailed geometry, and complex specular‐glossy light transport, achieving better performance than previous state‐of‐the‐art algorithms.     

Parallel Blue‐noise Sampling by Constrained Farthest Point Optimization

We describe a fast sampling algorithm for generating uniformly‐distributed point patterns with good blue noise characteristics. The method, based on constrained farthest point optimization, is provably optimal and may be easily parallelized, resulting in an algorithm whose performance/quality tradeoff is superior to other state‐of‐the‐art approaches.