Summary. This paper proposes a unified and consistent set of flexible tools to approximate important geometric attributes, including normal vectors and curvatures on arbitrary triangle meshes. We present a consistent derivation of these first and second order differential properties using averaging Voronoi cells and the mixed Finite-Element/Finite-Volume method, and compare them to existing formulations. Building upon previous work in discrete geometry, these operators are closely related to the continuous case, guaranteeing an appropriate extension from the continuous to the discrete setting: they respect most intrinsic properties of the continuous differential operators. We show that these estimates are optimal in accuracy under mild smoothness conditions, and demonstrate their numerical quality. We also present applications of these operators, such as mesh smoothing, enhancement, and quality checking, and show results of denoising in higher dimensions, such as for tensor images.

In this paper, we develop methods to rapidly remove rough features from irregularly triangulated data intended to portray a smooth surface. The main task is to remove undesirable noise and uneven edges while retaining desirable geometric features. The problem arises mainly when creating high-fidelity computer graphics objects using imperfectly-measured data from the real world.Our approach contains three novel features: an implicit integration method to achieve efficiency, stability, and large time-steps; a scale-dependent Laplacian operator to improve the diffusion process; and finally, a robust curvature flow operator that achieves a smoothing of the shape itself, distinct from any parameterization. Additional features of the algorithm include automatic exact volume preservation, and hard and soft constraints on the positions of the points in the mesh.We compare our method to previous operators and related algorithms, and prove that our curvature and Laplacian operators have several mathematically-desirable qualities that improve the appearance of the resulting surface. In consequence, the user can easily select the appropriate operator according to the desired type of fairing. Finally, we provide a series of examples to graphically and numerically demonstrate the quality of our results.

Parameterization of discrete surfaces is a fundamental and widely‐used operation in graphics, required, for instance, for texture mapping or remeshing. As 3D data becomes more and more detailed, there is an increased need for fast and robust techniques to automatically compute least‐distorted parameterizations of large meshes. In this paper, we present new theoretical and practical results on the parameterization of triangulated surface patches. Given a few desirable properties such as rotation and translation invariance, we show that the only admissible parameterizations form a two‐dimensional set and each parameterization in this set can be computed using a simple, sparse, linear system. Since these parameterizations minimize the distortion of different intrinsic measures of the original mesh, we call them Intrinsic Parameterizations. In addition to this partial theoretical analysis, we propose robust, efficient and tunable tools to obtain least‐distorted parameterizations automatically. In particular, we give details on a novel, fast technique to provide an optimal mapping without fixing the boundary positions, thus providing a unique Natural Intrinsic Parameterization. Other techniques based on this parameterization family, designed to ease the rapid design of parameterizations, are also proposed.

networks on production data and observe improvements over state-of-theart MC denoisers, showing that our methods generalize well to a variety of scenes. We conclude by analyzing various components of our architecture and identify areas of further research in deep learning for MC denoising.

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We present a modular convolutional architecture for denoising rendered images. We expand on the capabilities of kernel-predicting networks by combining them with a number of task-specific modules, and optimizing the assembly using an asymmetric loss. The source-aware encoder---the first module in the assembly---extracts low-level features and embeds them into a common feature space, enabling quick adaptation of a trained network to novel data. The spatial and temporal modules extract abstract, high-level features for kernel-based reconstruction, which is performed at three different spatial scales to reduce low-frequency artifacts. The complete network is trained using a class of asymmetric loss functions that are designed to preserve details and provide the user with a direct control over the variance-bias trade-off during inference. We also propose an error-predicting module for inferring reconstruction error maps that can be used to drive adaptive sampling. Finally, we present a theoretical analysis of convergence rates of kernel-predicting architectures, shedding light on why kernel prediction performs better than synthesizing the colors directly, complementing the empirical evidence presented in this and previous works. We demonstrate that our networks attain results that compare favorably to state-of-the-art methods in terms of detail preservation, low-frequency noise removal, and temporal stability on a variety of production and academic datasets.

Immune correlates of protection against intracellular bacterial pathogens are largely thought to be cell-mediated, although a reasonable amount of data supports a role for antibody-mediated protection. To define a role for antibody-mediated immunity against an intracellular pathogen, Rhodococcus equi, that causes granulomatous pneumonia in horse foals, we devised and tested an experimental system relying solely on antibody-mediated protection against this host-specific etiologic agent. Immunity was induced by vaccinating pregnant mares 6 and 3 weeks prior to predicted parturition with a conjugate vaccine targeting the highly conserved microbial surface polysaccharide, poly-N-acetyl glucosamine (PNAG). We ascertained antibody was transferred to foals via colostrum, the only means for foals to acquire maternal antibody. Horses lack transplacental antibody transfer. Next, a randomized, controlled, blinded challenge was conducted by inoculating at ~4 weeks of age ~106 cfu of R. equi via intrabronchial challenge. Eleven of 12 (91%) foals born to immune mares did not develop clinical R. equi pneumonia, whereas 6 of 7 (86%) foals born to unvaccinated controls developed pneumonia (P = 0.0017). In a confirmatory passive immunization study, infusion of PNAG-hyperimmune plasma protected 100% of 5 foals against R. equi pneumonia whereas all 4 recipients of normal horse plasma developed clinical disease (P = 0.0079). Antibodies to PNAG mediated killing of extracellular and intracellular R. equi and other intracellular pathogens. Killing of intracellular organisms depended on antibody recognition of surface expression of PNAG on infected cells, along with complement deposition and PMN-assisted lysis of infected macrophages. Peripheral blood mononuclear cells from immune and protected foals released higher levels of interferon-γ in response to PNAG compared to controls, indicating vaccination also induced an antibody-dependent cellular release of this critical immune cytokine. Overall, antibody-mediated opsonic killing and interferon-γ release in response to PNAG may protect against diseases caused by intracellular bacterial pathogens.