In this paper, a method for the removal of noisy lines and cracks corrupted by different noise types is explored, using a cascade of filtering cycles based on the principle of symmetry among neighboring pixels. Each filtering cycle includes a filter in two perpendicular directions, one horizontal and the other vertical. Any pixel, to be deemed original, should have a number of symmetric pixels within its neighboring pixels greater than the number specified by the condition set for each direction in all the filters. Since the conditions of each filter increase gradually from one cycle to the next, it becomes more difficult for a noisy pixel to satisfy the filter conditions in each filtering cycle, while an original pixel can easily satisfy the conditions in all the filtering cycles. The reason is that a noisy pixel has a random value and therefore faces difficulty in finding a sufficient number of symmetric pixels in each direction, while an original one has a value correlated with the values of its neighboring pixels. Extensive simulation experiments prove that the proposed method efficiently detects and restores different noisy lines and cracks of different shape and thickness. Also, it retains the image details and outperforms other well-known algorithms, both objectively and subjectively. More specifically, the proposed algorithm achieves restoration performance better than the other known methods by ≥0.81dB in all simulation experiments.

中文翻译：

---

用于去除图像中的线条和裂缝的双向滤波器

在本文中，基于相邻像素之间的对称性原理，使用级联滤波循环，探索了一种去除由不同噪声类型破坏的噪声线和裂缝的方法。每个过滤周期包括两个垂直方向的过滤器，一个水平方向，另一个垂直方向。任何被视为原始像素的像素在其相邻像素内的对称像素数量应大于为所有滤波器中每个方向设置的条件指定的数量。由于每个过滤器的条件从一个循环到下一个循环逐渐增加，一个有噪声的像素在每个过滤循环中都更难满足过滤条件，而原始像素可以很容易地满足所有过滤循环的条件。原因是噪声像素具有随机值，因此难以在每个方向上找到足够数量的对称像素，而原始像素的值与其相邻像素的值相关。大量的仿真实验证明，所提出的方法有效地检测和恢复了不同形状和厚度的不同噪声线和裂缝。此外，它保留了图像细节并在客观和主观上都优于其他众所周知的算法。更具体地说，所提出的算法在所有模拟实验中都比其他已知方法实现了 ≥0.81dB 的恢复性能。大量的仿真实验证明，所提出的方法有效地检测和恢复了不同形状和厚度的不同噪声线和裂缝。此外，它保留了图像细节并在客观和主观上都优于其他众所周知的算法。更具体地说，所提出的算法在所有模拟实验中都比其他已知方法实现了 ≥0.81dB 的恢复性能。大量的仿真实验证明，所提出的方法有效地检测和恢复了不同形状和厚度的不同噪声线和裂缝。此外，它保留了图像细节并在客观和主观上都优于其他众所周知的算法。更具体地说，所提出的算法在所有模拟实验中都比其他已知方法实现了 ≥0.81dB 的恢复性能。