Allen-Cahn水平集的提花织物图像去噪研究

将相变理论中的Allen-Cahn方程用于提花织物图像去噪,提出一种基于该方程的水平集去噪算法(APNACM).算法利用非局部Allen-Cahn方程在平均曲率流中的面积保留特性,在去噪过程中较好地保留了织物纹线的形状.采用水平集对Allen-Cahn方程进行数值演化,有效提高了算法对复杂纹线拓扑形变的自适应能力.为减小对水平集进行有限差分计算的开销,采用改进快速行进算法(FMM)确定适宜的相邻水平集扩张速度.实验结果表明,该算法能够对提花织物图像进行快速去噪,且去噪效果很好.

Research on jacquard fabrics image denoising using Allen-Cahn level set model

Allen-Cahn equation in phase transition theory was introduced to remove noise from jacquard images. A novel denoising method based on the equation, namely area-preserving nonlocal Allen-Cahn method (APNACM), was proposed in a level set framework. For nonlocal Allen-Cahn equation generates an area-preserving motion by mean curvature flow, it can perfectly preserve the shapes of fabric texture while in the denoising process. Then, a level set formulation was used to evolve the Allen-Cahn equation, which effectively improved the adaptive capability of the topological changes arising from complex texture curves. Finally, in order to decrease the computing expenses of level set formulation by finite difference method, an extension of the classical fast marching method (FMM) was applied to build appropriate extension velocity for the neighboring level set. Experimental results show that the APNACM algorithm is fast and effective, and can be used as a powerful denoising tool for jacquard fabrics image.