36-Issue 1

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https://diglib.eg.org/handle/10.2312/2631200

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Browsing 36-Issue 1 by Subject "digital geometry processing"

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    Accurate and Efficient Computation of Laplacian Spectral Distances and Kernels
    (© 2017 The Eurographics Association and John Wiley & Sons Ltd., 2017) Patané, Giuseppe; Chen, Min and Zhang, Hao (Richard)
    This paper introduces the Laplacian spectral distances, as a function that resembles the usual distance map, but exhibits properties (e.g. smoothness, locality, invariance to shape transformations) that make them useful to processing and analysing geometric data. Spectral distances are easily defined through a filtering of the Laplacian eigenpairs and reduce to the heat diffusion, wave, biharmonic and commute‐time distances for specific filters. In particular, the smoothness of the spectral distances and the encoding of local and global shape properties depend on the convergence of the filtered eigenvalues to zero. Instead of applying a truncated spectral approximation or prolongation operators, we propose a computation of Laplacian distances and kernels through the solution of sparse linear systems. Our approach is free of user‐defined parameters, overcomes the evaluation of the Laplacian spectrum and guarantees a higher approximation accuracy than previous work.
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    Towards Globally Optimal Normal Orientations for Large Point Clouds
    (© 2017 The Eurographics Association and John Wiley & Sons Ltd., 2017) Schertler, Nico; Savchynskyy, Bogdan; Gumhold, Stefan; Chen, Min and Zhang, Hao (Richard)
    Various processing algorithms on point set surfaces rely on consistently oriented normals (e.g. Poisson surface reconstruction). While several approaches exist for the calculation of normal directions, in most cases, their orientation has to be determined in a subsequent step. This paper generalizes propagation‐based approaches by reformulating the task as a graph‐based energy minimization problem. By applying global solvers, we can achieve more consistent orientations than simple greedy optimizations. Furthermore, we present a streaming‐based framework for orienting large point clouds. This framework orients patches locally and generates a globally consistent patch orientation on a reduced neighbour graph, which achieves similar quality to orienting the full graph.Various processing algorithms on point set surfaces rely on consistently oriented normals (e.g. Poisson surface reconstruction).While several approaches exist for the calculation of normal directions, in most cases, their orientation has to be determined in a subsequent step. This paper generalizes propagation‐based approaches by reformulating the task as a graph‐based energy minimization problem and presents a streaming‐based out‐of‐core implementation.