Massachusetts Institute of Technology, and Department of Neurology, Harvard Medical School, Cambridge, MA 02139, USA.
IEEE Trans Pattern Anal Mach Intell. 2013 May;35(5):1221-33. doi: 10.1109/TPAMI.2012.196.
We address the alignment of a group of images with simultaneous registration. Therefore, we provide further insights into a recently introduced framework for multivariate similarity measures, referred to as accumulated pair-wise estimates (APE), and derive efficient optimization methods for it. More specifically, we show a strict mathematical deduction of APE from a maximum-likelihood framework and establish a connection to the congealing framework. This is only possible after an extension of the congealing framework with neighborhood information. Moreover, we address the increased computational complexity of simultaneous registration by deriving efficient gradient-based optimization strategies for APE: Gauss-Newton and the efficient second-order minimization (ESM). We present next to SSD the usage of intrinsically nonsquared similarity measures in this least squares optimization framework. The fundamental assumption of ESM, the approximation of the perfectly aligned moving image through the fixed image, limits its application to monomodal registration. We therefore incorporate recently proposed structural representations of images which allow us to perform multimodal registration with ESM. Finally, we evaluate the performance of the optimization strategies with respect to the similarity measures, leading to very good results for ESM. The extension to multimodal registration is in this context very interesting because it offers further possibilities for evaluations, due to publicly available datasets with ground-truth alignment.
我们解决了一组图像的对齐问题，同时进行了配准。因此，我们对最近引入的多元相似性度量框架进行了进一步的研究，称为累积成对估计（APE），并为其推导了有效的优化方法。更具体地说，我们从最大似然框架中严格推导出 APE，并建立了与凝结框架的联系。这只有在扩展凝结框架并加入邻域信息后才能实现。此外，我们通过为 APE 推导有效的基于梯度的优化策略来解决同时配准的计算复杂度问题：高斯牛顿和高效二阶最小化（ESM）。我们在这个最小二乘优化框架中展示了固有非平方相似性度量的 SSD 用法。ESM 的基本假设是通过固定图像来近似完全对齐的移动图像，这限制了它在单模态配准中的应用。因此，我们结合了最近提出的图像结构表示，允许我们使用 ESM 进行多模态配准。最后，我们根据相似性度量评估了优化策略的性能，ESM 取得了非常好的结果。这种对多模态配准的扩展在这种情况下非常有趣，因为它提供了更多的评估可能性，因为有带有真实对齐的公共可用数据集。
