面向法向域网格建模的非线性引导滤波

Normal Domain Mesh Modeling Using Non-Linear Guided Filtering

网格建模是数字几何处理领域的基础性研究问题.为了提高网格建模的简便性和鲁棒性,首先提出了一种非线性的引导滤波算法.滤波过程在法向域进行,滤波后的法向是引导网格法向的局部二次变换;然后,应用上述算法研究了建模方面的2个重要问题:网格去噪和网格平滑,其中的难点在于如何构造合适的引导网格.针对去噪问题,每次迭代时利用双边法向滤波得到引导网格;针对平滑问题,引导网格以高斯滤波结果作为初始值,进而结合原始网格不断进行更新;最后,在形状复杂或特征丰富的网格模型上进行了去噪、平滑等实验,结果表明,该算法简单实用、鲁棒,去噪时能够有效地去除强噪声,保持模型的几何特征;平滑时能够提取出中小尺度的特征,保留大尺度的特征.

It is a basic research problem to model 3D mesh in the field of digital geometry processing. To improve the simplicity and robustness of mesh modeling, we first propose a non-linear guided filtering method, which is performed in normal domain. The filtered normal is a quadratic transformation of guidance mesh’s normal. Then, the above method is applied to deal with mesh denoising and mesh smoothing. The main problem is the construction of guidance mesh. For mesh denoising, we get guidance mesh by bilateral normal filtering at each iteration. For mesh smoothing, we use the result of Gaussian filtering as the initial guidance mesh, and then iteratively update it with the original mesh. Finally, we perform denoising and smoothing on mesh models with complex shape or rich features. Experimental results show that the proposed algorithm is simple, effective, and robust. Specifically, the denoising method can effectively remove strong noises and retain geometric features, and the smoothing method can extract features of small and medium scales and maintain features of large scales.