College of Computer Science and Technology, Qingdao University, Qingdao, Shandong, China.
School of Electrical Engineering, Computing and Mathematical Sciences, Curtin University, Perth, WA, Australia.
PLoS One. 2022 Mar 15;17(3):e0261195. doi: 10.1371/journal.pone.0261195. eCollection 2022.
The Euler's elastica energy regularizer has been widely used in image processing and computer vision tasks. However, finding a fast and simple solver for the term remains challenging. In this paper, we propose a new dual method to simplify the solution. Classical fast solutions transform the complex optimization problem into simpler subproblems, but introduce many parameters and split operators in the process. Hence, we propose a new dual algorithm to maintain the constraint exactly, while using only one dual parameter to transform the problem into its alternate optimization form. The proposed dual method can be easily applied to level-set-based segmentation models that contain the Euler's elastic term. Lastly, we demonstrate the performance of the proposed method on both synthetic and real images in tasks image processing tasks, i.e. denoising, inpainting, and segmentation, as well as compare to the Augmented Lagrangian method (ALM) on the aforementioned tasks.
欧拉弹性体能量正则化项在图像处理和计算机视觉任务中得到了广泛的应用。然而，找到一个快速而简单的方法来求解这个项仍然具有挑战性。在本文中，我们提出了一种新的对偶方法来简化求解过程。经典的快速求解方法将复杂的优化问题转化为更简单的子问题，但在这个过程中引入了许多参数和分裂算子。因此，我们提出了一种新的对偶算法，以保持约束的精确性，同时只使用一个对偶参数将问题转化为其交替优化形式。所提出的对偶方法可以很容易地应用于基于水平集的分割模型，这些模型包含欧拉弹性项。最后，我们在图像处理任务（如去噪、修复和分割）中展示了所提出的方法在合成和真实图像上的性能，并与上述任务中的增广拉格朗日方法（ALM）进行了比较。
