Non-rigid registration, which deforms a source shape in a non-rigid way to align with a target shape, is a classical problem in computer vision. Such problems can be challenging because of imperfect data (noise, outliers and partial overlap) and high degrees of freedom. Existing methods typically adopt the $\ell_{p}$ type robust norm to measure the alignment error and regularize the smoothness of deformation, and use a proximal algorithm to solve the resulting non-smooth optimization problem. However, the slow convergence of such algorithms limits their wide applications. In this paper, we propose a formulation for robust non-rigid registration based on a globally smooth robust norm for alignment and regularization, which can effectively handle outliers and partial overlaps. The problem is solved using the majorization-minimization algorithm, which reduces each iteration to a convex quadratic problem with a closed-form solution. We further apply Anderson acceleration to speed up the convergence of the solver, enabling the solver to run efficiently on devices with limited compute capability. Extensive experiments demonstrate the effectiveness of our method for non-rigid alignment between two shapes with outliers and partial overlaps, with quantitative evaluation showing that it outperforms state-of-the-art methods in terms of registration accuracy and computational speed. The source code is available at https://github.com/yaoyx689/AMM_NRR.
翻译:以非硬化的方式将源形状变形,使其与目标形状相一致的非硬化登记,是计算机视觉的一个古老问题。由于数据不完善(噪音、外部线和部分重叠)和高度自由,这些问题可能具有挑战性。现有方法通常采用$@ ⁇ p}($ell ⁇ p})型强性规范,以测量校正误差,规范变形的平滑性,并使用一种原始算法来解决由此产生的非软优化问题。然而,这种算法的缓慢趋同限制了其广泛的应用。在本文中,我们提出一种基于全球平稳稳健的校正和规范化规范的强非硬化登记方法,可以有效地处理校正和部分重叠。问题正在通过主要化-最小化算法来解决,将每种偏差都降低为连接度的二次二次二次二次曲线,采用封闭式解决方案。我们进一步应用安德森加速来加快解析器的趋同速度,使解算器能够以有限的折算能力有效地运行设备。我们的广泛实验展示了非硬化的Nridid登记方法的有效性,在两种形式上显示非精确度-imalalal-alalalalal-tractionslational