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首页> 外文期刊>Journal of Computational Physics >Wavelet frame based surface reconstruction from unorganized points
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Wavelet frame based surface reconstruction from unorganized points

机译：基于无组织点的小波框架曲面重构

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摘要

Applications of wavelet frames to image restoration problems (e.g. image deblurring and inpainting) have been successful due to their redundancy and capability of sparsely approximating piecewise smooth functions like images (see e.g. [13,14,8]). However, wavelet frames have not yet been used for surface reconstruction problems. Recently in [6], connections between one of the wavelet frame based image restoration model [8,28,48] and variational models (e.g. the ROF model [45]) were rigorously established. Such connections not only grant new insights to wavelet frame based image restorations, it also case a geometric explanation to wavelet frame based approaches. This leads us to a wavelet frame based model, as well as a fast algorithm, to reconstruct implicit surfaces from unorganized point sets in R3. We will demonstrate the effectiveness of the proposed model using several commonly used examples.
机译：小波帧在图像恢复问题（例如图像去模糊和修复）上的应用已经成功，这是因为它们具有冗余性并且能够像图像一样稀疏地逼近分段平滑函数（请参见[13,14,8]）。但是，小波框架尚未用于表面重建问题。最近在[6]中，严格建立了基于小波帧的图像恢复模型[8,28,48]和变化模型（例如ROF模型[45]）之间的连接。这样的联系不仅为基于小波帧的图像恢复提供了新的见解，而且还为基于小波帧的方法提供了几何解释。这使我们得到了基于小波框架的模型以及一种快速算法，可以从R3中的无组织点集中重建隐含曲面。我们将使用几个常用示例来证明所提出模型的有效性。

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