Beltrami流及其在图像去噪中的应用

偏微分方程是图像处理主要的方法之一,一般通过其对应的变分模型给出方程的意义,并依此设计优化原偏微分方程以取得最佳的处理效果。针对图像去噪问题,基于经典的Beltrami几何流方法提出了图像流形上一种新的度量张量模型,具有该度量模型的Beltrami流具有清晰的几何意义,并依此提出了该度量模型中参数的优化选择方法。同时,该模型为经典的偏微分方程去噪方法提供了统一框架,且参数的优化选择使得Beltrami流在平滑噪声与边缘保持方面取得了良好的平衡。实验表明该方法提高了图像去噪效果,尤其是对于边缘丰富的图像效果更加明显。

Beltrami flow and its application in image denoising

Partial differential equation (PDE) is one of the main methods for image processing and its significance is usually shown by the corresponding variable model, according to which the PDE can be optimized further to reach ideal results. Based on the classic Beltrami flow for image processing, a new metric tensor model on the image manifold is proposed for image denoising. The Beltrami flow with this metric tensor has clear geometrical significance, which induces the optimal selection method for parameters in the metric tensor. Meanwhile, this model provides a unified framework for the classic PDE based image denoising methods and the optimal selection method for its parameters makes the Beltrami flow have a better balance between smoothing the noise and preserving the edges. The experiment results show that the image denoising quality is greatly improved, especially for the images with abundant edges.