Abstract The problem of noise in Monte‐Carlo rendering arising from estimator variance is well‐known and well‐studied. In this work, we concentrate on identifying individual light paths as outliers that lead to significant spikes of noise and represent a challenge for existing filtering methods. Most noise‐reduction methods, such as importance sampling and stratification, attempt to generate samples that are expected a priori to have lower variance, but do not take into account actual sample values. While these methods are essential to decrease overall noise, we show that filtering samples a posteriori allows for greater reduction of spiked noise. In particular, given evaluated sample values, outliers can be identified and removed. Conforming with conventions in statistics, we emphasize that the term “outlier” should not be taken as synonymous with “incorrect”, but as referring to samples that distort the empirically‐observed distribution of energy relative to the true underlying distribution. By expressing a path distribution in joint image and color space, we show how outliers can be characterized by their density across the set of all nearby paths in this space. We show that removing these outliers leads to significant improvements in rendering quality.

Recent advances in real-time rendering have allowed the GPU implementation of traditionally CPU-restricted algorithms, often with performance increases of an order of magnitude or greater. Such gains are achieved by leveraging the large-scale parallelism of the GPU towards applications that are well-suited for these streaming architectures. By contrast, mesh simplification has traditionally been viewed as a non-interactive process not readily amenable to GPU acceleration. We demonstrate how it becomes practical for real-time use through our method, and that the use of the GPU even for offline simplification leads to significant increases in performance. Our approach for mesh decimation adopts a vertex-clustering method to the GPU by taking advantage of a new addition to the rendering pipeline - the geometry shader stage. We present a novel general-purpose data structure designed for streaming architectures called the probabilistic octree, which allows for much of the flexibility of offline implementations, including sparse encoding and variable level-of-detail. We demonstrate successful use of this data structure in our GPU implementation of mesh simplification. We can generate adaptive levels of detail by applying non-linear warping functions to the cluster map in order to improve resulting simplification quality. Our GPU-accelerated approach enables simultaneous construction of multiple levels of detail and out-of-core simplification of extremely large polygonal meshes.

In 3D shape classification scenarios with classes arranged in a hierarchy from most general to most specific, the use of an independent classifier for each class can produce predictions that are inconsistent with the parent-child relationships of the hierarchy. To be consistent, an example shape must not be assigned to a class unless it is also assigned to its parent class. This paper presents a Bayesian framework for combining multiple classifiers based on a class hierarchy. Given a set of independent classifiers for an arbitrary type of shape descriptor, we combine their possibly inconsistent predictions in our Bayesian framework to obtain the most probable consistent set of predictions. Such error correction is expected to improve accuracy on the overall classification by utilizing the structure of the hierarchy. Our experiments show that over the 170-class hierarchical Princeton Shape Benchmark using the Spherical Harmonic Descriptor (SHD) our algorithm improves the classification accuracy of the majority of classes, in comparison to independent classifiers. Our method is also more effective than straightforward heuristics for correcting hierarchical inconsistencies.

Recent progress in the measurement of surface reflectance has created a demand for non-parametric appearance representations that are accurate, compact, and easy to use for rendering. Another crucial goal, which has so far received little attention, is editability: for practical use, we must be able to change both the directional and spatial behavior of surface reflectance (e.g., making one material shinier, another more anisotropic, and changing the spatial "texture maps" indicating where each material appears). We introduce an Inverse Shade Tree framework that provides a general approach to estimating the "leaves" of a user-specified shade tree from high-dimensional measured datasets of appearance. These leaves are sampled 1- and 2-dimensional functions that capture both the directional behavior of individual materials and their spatial mixing patterns. In order to compute these shade trees automatically, we map the problem to matrix factorization and introduce a flexible new algorithm that allows for constraints such as non-negativity, sparsity, and energy conservation. Although we cannot infer every type of shade tree, we demonstrate the ability to reduce multi-gigabyte measured datasets of the Spatially-Varying Bidirectional Reflectance Distribution Function (SVBRDF) into a compact representation that may be edited in real time.

Methods for triangle mesh decimation are common; however, most existing techniques operate only on static geometry. In this paper, we present a view- and pose-independent method for the automatic simplification of skeletally articulated meshes. Such meshes have associated kinematic skeletons that are used to control their deformation, with the position of each vertex influenced by a linear combination of bone transformations. Our method extends the commonly-used quadric error metric by incorporating knowledge of potential poses into a probability function. We minimize the average error of the deforming mesh over all possible configurations, weighted by the probability. This is possible by transforming the quadrics from each configuration into a common coordinate system. Our simplification algorithm runs as a preprocess, and the resulting meshes can be seamlessly integrated into existing systems. We demonstrate the effectiveness of this approach for generating highly-simplified models while preserving necessary detail in deforming regions near joints.

In this paper, we present an efficient (topology preserving) multiresolution meshing framework for interactive level-of-detail (LOD) generation and rendering of large triangle meshes. More specifically, the presented approach, called FastMesh, provides view-dependent LOD generation and real-time mesh simplification that minimizes visual artifacts. Multiresolution triangle mesh representations are an important tool for reducing triangle mesh complexity in interactive rendering environments. Ideally, for interactive visualization, a triangle mesh is simplified to the maximal tolerated visible error and, thus, mesh simplification is view-dependent. This paper introduces an efficient hierarchical multiresolution triangulation framework based on a half-edge triangle mesh data structure and presents optimized implementations of several view-dependent or visual mesh simplification heuristics within that framework. Despite being optimized for performance, these error heuristics provide conservative error bounds. The presented framework is highly efficient both in space and time cost and needs only a fraction of the time required for rendering to perform the error calculations and dynamic mesh updates.

We present a novel disk-based multiresolution triangle mesh data structure that supports paging and view-dependent rendering of very large meshes at interactive frame rates from external memory. Our approach, called XFastMesh, is based on a view-dependent mesh simplification framework that represents half-edge collapse operations in a binary hierarchy known as a merge-tree forest. The proposed technique partitions the merge-tree forest into so-called detail blocks, which consist of binary subtrees, that are stored on disk. We present an efficient external memory data structure and file format that stores all detail information of the multiresolution triangulation method using significantly less storage then previously reported approaches. Furthermore, we present a paging algorithm that provides efficient loading and interactive rendering of large meshes from external memory at varying and view-dependent level-of-detail. The presented approach is highly efficient both in terms of space cost and paging performance.