34-Issue 5

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https://diglib.eg.org/handle/10.2312/12669

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Browsing 34-Issue 5 by Subject "Hierarchy and geometric transformations"

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    Sparse Non-rigid Registration of 3D Shapes
    (The Eurographics Association and John Wiley & Sons Ltd., 2015) Yang, Jingyu; Li, Ke; Li, Kun; Lai, Yu-Kun; Mirela Ben-Chen and Ligang Liu
    Non-rigid registration of 3D shapes is an essential task of increasing importance as commodity depth sensors become more widely available for scanning dynamic scenes. Non-rigid registration is much more challenging than rigid registration as it estimates a set of local transformations instead of a single global transformation, and hence is prone to the overfitting issue due to underdetermination. The common wisdom in previous methods is to impose an l2-norm regularization on the local transformation differences. However, the l2-norm regularization tends to bias the solution towards outliers and noise with heavy-tailed distribution, which is verified by the poor goodnessof- fit of the Gaussian distribution over transformation differences. On the contrary, Laplacian distribution fits well with the transformation differences, suggesting the use of a sparsity prior. We propose a sparse non-rigid registration (SNR) method with an l1-norm regularized model for transformation estimation, which is effectively solved by an alternate direction method (ADM) under the augmented Lagrangian framework. We also devise a multi-resolution scheme for robust and progressive registration. Results on both public datasets and our scanned datasets show the superiority of our method, particularly in handling large-scale deformations as well as outliers and noise.
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    Unconditionally Stable Shock Filters for Image and Geometry Processing
    (The Eurographics Association and John Wiley & Sons Ltd., 2015) Prada, Fabian; Kazhdan, Misha; Mirela Ben-Chen and Ligang Liu
    This work revisits the Shock Filters of Osher and Rudin [OR90] and shows how the proposed filtering process can be interpreted as the advection of image values along flow-lines. Using this interpretation, we obtain an efficient implementation that only requires tracing flow-lines and re-sampling the image. We show that the approach is stable, allowing the use of arbitrarily large time steps without requiring a linear solve. Furthermore, we demonstrate the robustness of the approach by extending it to the processing of signals on meshes in 3D.