Department of Radiation Oncology, Beaumont Health Systems, Royal Oak, MI, USA.
Department of Computation and Applied Mathematics, Rice University, Houston, TX, USA.
Med Phys. 2019 May;46(5):2194-2203. doi: 10.1002/mp.13457. Epub 2019 Mar 14.
Intensity-based deformable image registration (DIR) requires minimizing an image dissimilarity metric. Imaged anatomy, such as bones and vasculature, as well as the resolution of the digital grid, can often cause discontinuities in the corresponding objective function. Consequently, the application of a gradient-based optimization algorithm requires a preprocessing image smoothing to ensure the existence of necessary image derivatives. Simple block matching (exhaustive search) methods do not require image derivative approximations, but their general effectiveness is often hindered by erroneous solutions (outliers). Block match methods are therefore often coupled with a statistical outlier detection method to improve results.
The purpose of this work is to present a spatially accurate, intensity-based DIR optimization formulation that can be solved with a straightforward gradient-free quadratic penalty algorithm and is suitable for 4D thoracic computed tomography (4DCT) registration. Additionally, a novel regularization strategy based on the well-known leave-one-out robust statistical model cross-validation method is introduced.
The proposed Quadratic Penalty DIR (QPDIR) method minimizes both an image dissimilarity term, which is separable with respect to individual voxel displacements, and a regularization term derived from the classical leave-one-out cross-validation statistical method. The resulting DIR problem lends itself to a quadratic penalty function optimization approach, where each subproblem can be solved by straightforward block coordinate descent iteration.
The spatial accuracy of the method was assessed using expert-determined landmarks on ten 4DCT datasets available on www.dir-lab.com. The QPDIR algorithm achieved average millimeter spatial errors between 0.69 (0.91) and 1.19 (1.26) on the ten test cases. On all ten 4DCT test cases, the QPDIR method produced spatial accuracies that are superior or equivalent to those produced by current state-of-the-art methods. Moreover, QPDIR achieved accuracies at the resolution of the landmark error assessment (i.e., the interobserver error) on six of the ten cases.
The QPDIR algorithm is based on a simple quadratic penalty function formulation and a regularization term inspired by leave-one-out cross validation. The formulation lends itself to a parallelizable, gradient-free, block coordinate descent numerical optimization method. Numerical results indicate that the method achieves a high spatial accuracy on 4DCT inhale/exhale phases.
基于强度的变形图像配准（DIR）需要最小化图像相似度度量。成像解剖结构，如骨骼和脉管系统，以及数字网格的分辨率，通常会导致目标函数的不连续。因此，应用基于梯度的优化算法需要对预处理图像进行平滑处理，以确保存在必要的图像导数。简单的块匹配（穷举搜索）方法不需要图像导数近似，但由于错误的解（异常值），其通常的有效性受到阻碍。因此，块匹配方法通常与统计异常值检测方法相结合，以提高结果。
本工作旨在提出一种空间精确的基于强度的 DIR 优化公式，该公式可以用直接的无梯度二次惩罚算法求解，适用于 4D 胸部 CT（4DCT）配准。此外，还引入了一种基于著名的留一法稳健统计模型交叉验证方法的新正则化策略。
所提出的二次惩罚 DIR（QPDIR）方法最小化了图像相似度项和由经典留一法交叉验证统计方法推导的正则化项。由此产生的 DIR 问题适合于二次惩罚函数优化方法，其中每个子问题都可以通过直接的块坐标下降迭代来解决。
使用可在 www.dir-lab.com 上获得的十个 4DCT 数据集上的专家确定的标志点评估了该方法的空间准确性。QPDIR 算法在十个测试案例中的平均毫米空间误差分别为 0.69（0.91）和 1.19（1.26）。在所有十个 4DCT 测试案例中，QPDIR 方法产生的空间精度均优于或等同于当前最先进的方法。此外，QPDIR 在十个案例中的六个案例中达到了标志点误差评估的分辨率（即观察者间误差）的精度。
QPDIR 算法基于简单的二次惩罚函数公式和受留一法交叉验证启发的正则化项。该公式适用于可并行化、无梯度、块坐标下降数值优化方法。数值结果表明，该方法在 4DCT 吸气/呼气阶段达到了很高的空间精度。
