Browsing by Author "Coeurjolly, David"

Now showing 1 - 6 of 6
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    Analysis of Sample Correlations for Monte Carlo Rendering
    (The Eurographics Association and John Wiley & Sons Ltd., 2019) Singh, Gurprit; Öztireli, Cengiz; Ahmed, Abdalla G. M.; Coeurjolly, David; Subr, Kartic; Deussen, Oliver; Ostromoukhov, Victor; Ramamoorthi, Ravi; Jarosz, Wojciech; Giachetti, Andrea and Rushmeyer, Holly
    Modern physically based rendering techniques critically depend on approximating integrals of high dimensional functions representing radiant light energy. Monte Carlo based integrators are the choice for complex scenes and effects. These integrators work by sampling the integrand at sample point locations. The distribution of these sample points determines convergence rates and noise in the final renderings. The characteristics of such distributions can be uniquely represented in terms of correlations of sampling point locations. Hence, it is essential to study these correlations to understand and adapt sample distributions for low error in integral approximation. In this work, we aim at providing a comprehensive and accessible overview of the techniques developed over the last decades to analyze such correlations, relate them to error in integrators, and understand when and how to use existing sampling algorithms for effective rendering workflows.
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    Fourier Analysis of Correlated Monte Carlo Importance Sampling
    (© 2020 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd, 2020) Singh, Gurprit; Subr, Kartic; Coeurjolly, David; Ostromoukhov, Victor; Jarosz, Wojciech; Benes, Bedrich and Hauser, Helwig
    Fourier analysis is gaining popularity in image synthesis as a tool for the analysis of error in Monte Carlo (MC) integration. Still, existing tools are only able to analyse convergence under simplifying assumptions (such as randomized shifts) which are not applied in practice during rendering. We reformulate the expressions for bias and variance of sampling‐based integrators to unify non‐uniform sample distributions [importance sampling (IS)] as well as correlations between samples while respecting finite sampling domains. Our unified formulation hints at fundamental limitations of Fourier‐based tools in performing variance analysis for MC integration. At the same time, it reveals that, when combined with correlated sampling, IS can impact convergence rate by introducing or inhibiting discontinuities in the integrand. We demonstrate that the convergence of multiple importance sampling (MIS) is determined by the strategy which converges slowest and propose several simple approaches to overcome this limitation. We show that smoothing light boundaries (as commonly done in production to reduce variance) can improve (M)IS convergence (at a cost of introducing a small amount of bias) since it removes discontinuities within the integration domain. We also propose practical integrand‐ and sample‐mirroring approaches which cancel the impact of boundary discontinuities on the convergence rate of estimators.
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    Interpolated Corrected Curvature Measures for Polygonal Surfaces
    (The Eurographics Association and John Wiley & Sons Ltd., 2020) Lachaud, Jacques-Olivier; Romon, Pascal; Thibert, Boris; Coeurjolly, David; Jacobson, Alec and Huang, Qixing
    A consistent and yet practically accurate definition of curvature onto polyhedral meshes remains an open problem. We propose a new framework to define curvature measures, based on the Corrected Normal Current, which generalizes the normal cycle: it uncouples the positional information of the polyhedral mesh from its geometric normal vector field, and the user can freely choose the corrected normal vector field at vertices for curvature computations. A smooth surface is then built in the Grassmannian R3xS2 by simply interpolating the given normal vector field. Curvature measures are then computed using the usual Lipschitz-Killing forms, and we provide closed-form formulas per triangle. We prove a stability result with respect to perturbations of positions and normals. Our approach provides a natural scale-space for all curvature estimations, where the scale is given by the radius of the measuring ball. We show on experiments how this method outperforms state-of-the-art methods on clean and noisy data, and even achieves pointwise convergence on difficult polyhedral meshes like digital surfaces. The framework is also well suited to curvature computations using normal map information.
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    Lightweight Curvature Estimation on Point Clouds with Randomized Corrected Curvature Measures
    (The Eurographics Association and John Wiley & Sons Ltd., 2023) Lachaud, Jacques-Olivier; Coeurjolly, David; Labart, Céline; Romon, Pascal; Thibert, Boris; Memari, Pooran; Solomon, Justin
    The estimation of differential quantities on oriented point cloud is a classical step for many geometry processing tasks in computer graphics and vision. Even if many solutions exist to estimate such quantities, they usually fail at satisfying both a stable estimation with theoretical guarantee, and the efficiency of the associated algorithm. Relying on the notion of corrected curvature measures [LRT22, LRTC20] designed for surfaces, the method introduced in this paper meets both requirements. Given a point of interest and a few nearest neighbours, our method estimates the whole curvature tensor information by generating random triangles within these neighbours and normalising the corrected curvature measures by the corrected area measure. We provide a stability theorem showing that our pointwise curvatures are accurate and convergent, provided the noise in position and normal information has a variance smaller than the radius of neighbourhood. Experiments and comparisons with the state-of-the-art confirm that our approach is more accurate and much faster than alternatives. The method is fully parallelizable, requires only one nearest neighbour request per point of computation, and is trivial to implement.
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    Mumford-Shah Mesh Processing using the Ambrosio-Tortorelli Functional
    (The Eurographics Association and John Wiley & Sons Ltd., 2018) Bonneel, Nicolas; Coeurjolly, David; Gueth, Pierre; Lachaud, Jacques-Olivier; Fu, Hongbo and Ghosh, Abhijeet and Kopf, Johannes
    The Mumford-Shah functional approximates a function by a piecewise smooth function. Its versatility makes it ideal for tasks such as image segmentation or restoration, and it is now a widespread tool of image processing. Recent work has started to investigate its use for mesh segmentation and feature lines detection, but we take the stance that the power of this functional could reach far beyond these tasks and integrate the everyday mesh processing toolbox. In this paper, we discretize an Ambrosio-Tortorelli approximation via a Discrete Exterior Calculus formulation. We show that, combined with a new shape optimization routine, several mesh processing problems can be readily tackled within the same framework. In particular, we illustrate applications in mesh denoising, normal map embossing, mesh inpainting and mesh segmentation.
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    Stable and Efficient Differential Estimators on Oriented Point Clouds
    (The Eurographics Association and John Wiley & Sons Ltd., 2021) Lejemble, Thibault; Coeurjolly, David; Barthe, Loïc; Mellado, Nicolas; Digne, Julie and Crane, Keenan
    Point clouds are now ubiquitous in computer graphics and computer vision. Differential properties of the point-sampled surface, such as principal curvatures, are important to estimate in order to locally characterize the scanned shape. To approximate the surface from unstructured points equipped with normal vectors, we rely on the Algebraic Point Set Surfaces (APSS) [GG07] for which we provide convergence and stability proofs for the mean curvature estimator. Using an integral invariant viewpoint, this first contribution links the algebraic sphere regression involved in the APSS algorithm to several surface derivatives of different orders. As a second contribution, we propose an analytic method to compute the shape operator and its principal curvatures from the fitted algebraic sphere. We compare our method to the state-of-the-art with several convergence and robustness tests performed on a synthetic sampled surface. Experiments show that our curvature estimations are more accurate and stable while being faster to compute compared to previous methods. Our differential estimators are easy to implement with little memory footprint and only require a unique range neighbors query per estimation. Its highly parallelizable nature makes it appropriate for processing large acquired data, as we show in several real-world experiments.