• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.267-284
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• 2014

The multiresolution analysis for Legendre multiwavelets are given, anti-derivatives of Legendre multiwavelets are used for the numerical solution of differential equations, a special form of multilevel augmentation method algorithm is proposed to solve the disrete linear system efficiently, convergence rate of the Galerkin methods is given and numerical examples are presented.

• Proceedings of the Korea Information Processing Society Conference
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• 2019.05a
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• pp.482-484
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• 2019

Learning and analyzing 3D point clouds with deep networks is challenging due to the limited and irregularity of the data. In this paper, we present a data-driven point cloud augmentation technique. The key idea is to learn multilevel features per point and to reconstruct to a similar point set. Our network is applied to a projection loss function that encourages the predicted points to remain on the geometric shapes with a particular target. We conduct various experiments using ShapeNet part data to evaluate our method and demonstrate its possibility. Results show that our generated points have a similar shape and are located closer to the object.