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收稿：2018-12-14，
修回：2019-3-12，
纸质出版：2019-08-16
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目的
2
在去噪的过程中保持网格模型的特征结构是网格去噪领域研究的热点问题。为了能够在去噪中保持模型特征，本文提出一种基于变分形状近似（VSA）分割算法的保特征网格去噪算法。
方法
2
引入变分形状近似分割算法分析并提取噪声网格模型的几何特征，分3步进行去噪。第1步使用变分形状近似算法对网格进行分割，对模型进行分块降噪预处理。第2步通过分析变分形状近似算法提取分割边界中的特征信息，将网格划分为特征区域与非特征区域。对两个区域用不同的滤波器联合滤波面法向量。第3步根据滤波后的面法向量，使用非迭代的网格顶点更新方法更新顶点位置。
结果
2
相较于现有全局去噪方法，本文方法可以很好地保持网格模型的特征，引入的降噪预处理对于非均匀网格的拓扑结构保持有着很好的效果。通过对含有不同程度高斯噪声的网格模型进行实验表明，本文算法无论在直观上还是定量分析的结果都相较于对比的方法有着更好的去噪效果，实验中与对比算法相比去噪效果提升15%。结论与现有的网格去噪算法对比，实验结果表明本文算法在中等高斯噪声下更加鲁棒，对常见模型有着比较好的去噪效果，能更好地处理不均匀采样的网格模型，恢复模型原有的特征信息和拓扑结构。
结论
2
与现有的网格去噪算法对比，实验结果表明本文算法在中等高斯噪声下更加鲁棒，对常见模型有着比较好的去噪效果，能更好地处理不均匀采样的网格模型，恢复模型原有的特征信息和拓扑结构。
Objective
2
With the rapid development of 3D scanner and growing requirements for 3D models in various applications
interest in developing high-quality 3D models is increasing. The unavoidable noise not only damages the quality of 3D models but also affects their appearance. The earliest mesh denoising algorithm is implemented by adjusting the positions of vertices; this process is called the one-step denoising method. Then
the two-step denoising framework that first filters the normal vector of the patch and then updates the vertex position according to the patch normal vector is proposed to improve the denoising effects. Both methods have their own advantages. More algorithms are being proposed as the denoising process matures. However
removing noise while preserving the structural features of the model remains a challenging problem that needs to be solved. Feature preserving methods for mesh denoising have recently become a hot topic in this research field. This paper proposes a three-step denoising framework to retain the feature information of 3D models in the process of denoising
which adds a preprocessing operation to better preserve the features of the mesh and maintain the mesh topology.
Method
2
The proposed method adds a preprocessing stage before the traditional denoising method and introduces the variational shape approximation (VSA) segmentation algorithm to extract the feature information of the model. On the basis of the combined filters
different features can be processed separately for mesh denoising. The VSA method is a mesh segmentation solution for 3D models
which can extract sharp features from the given meshes. This method performs better in extracting the structural features from the meshes with different noise. The VSA segmentation result also enables the mesh to reduce noise
and it can perform a noise-reducing operation on the entire model without losing the feature information. Specifically
each of the divided regions is locally reduced in noise and finally combined into a grid to obtain an initial low-level noise mesh input. The proposed method uses three major steps to denoise a given mesh. First
the VSA method is used to divide the mesh into several segments. For each segment
local Laplacian smoothing is introduced for the preprocessing of the mesh. Second
on the basis of the difference between the normal of two adjacent surfaces
a predefined feature pattern is used to match the boundaries of the partitions
and the feature boundaries are expanded to divide the model into feature and non-feature regions. In the non-feature region
the center plane normal is filtered by the weighted average neighborhood inner normal vector. For the feature region
the weighted one neighborhood uniform surface normal vector is used to filter the central plane normal. Third
on the basis of the filtered surface normal
the position of the vertex is updated in a non-iterative manner.
Result
2
The proposed method uses extracted information from noisy meshes to classify different feature segments. The feature information is extracted from the segmentation results based on the VSA method
which gives better results than other existing methods. In the case of moderate Gaussian noise
the results of our method are superior to the results of other methods in the models with sharp features. This method can maintain the characteristics of the model effectively
and the introduced noise reduction preprocessing has a good effect on the preservation of the topology of the nonuniform mesh. This method also has a good effect on other kinds of models
generating good denoising results in the experiment. Consistent with experimental observations obtained by calculating the average angle error of the original and the denoising models
the proposed method has a better denoising effect in visual and numerical aspects than the other method. In the experimental test
the denoising effect is improved by more than 15% compared with the other method.
Conclusion
2
The proposed method can better maintain the characteristics of the model with sharp features than the other methods and has advantages in producing an overall denoising effect. For non-uniformly sampled meshes
this method has a better denoising effect while maintaining the original topology of the mesh. The proposed method obtains robust results for meshes with middle-level noise and can preserve the original feature information of the given meshes.
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