A finite element-based image segmentation strategy enhanced by an anisotropic mesh adaptation procedure is presented. The methodology relies on a split Bregman algorithm for the minimisation of a region-based energy functional and on an anisotropic recovery-based error estimate to drive mesh adaptation. More precisely, a Bayesian energy functional is considered to account for image spatial information, ensuring that the methodology is able to identify inhomogeneous spatial patterns in complex images. In addition, the anisotropic mesh adaptation guarantees a sharp detection of the interface between background and foreground of the image, with a reduced number of degrees of freedom. The resulting split-adapt Bregman algorithm is tested on a set of real images showing the accuracy and robustness of the method, even in the presence of Gaussian, salt and pepper and speckle noise.

提出了一种通过各向异性网格自适应程序增强的基于有限元的图像分割策略。该方法依靠分裂 Bregman 算法来最小化基于区域的能量泛函和基于各向异性恢复的误差估计来驱动网格自适应。更准确地说，贝叶斯能量泛函被认为可以解释图像空间信息，确保该方法能够识别复杂图像中的不均匀空间模式。此外，各向异性网格自适应保证了图像背景和前景之间界面的清晰检测，同时减少了自由度的数量。生成的拆分自适应 Bregman 算法在一组真实图像上进行了测试，显示了该方法的准确性和鲁棒性，即使在高斯存在的情况下，