Niethammer Marc, Huang Yang, Vialard François-Xavier
UNC Chapel Hill, USA.
Med Image Comput Comput Assist Interv. 2011;14(Pt 2):655-62. doi: 10.1007/978-3-642-23629-7_80.
Registration of image-time series has so far been accomplished (i) by concatenating registrations between image pairs, (ii) by solving a joint estimation problem resulting in piecewise geodesic paths between image pairs, (iii) by kernel based local averaging or (iv) by augmenting the joint estimation with additional temporal irregularity penalties. Here, we propose a generative model extending least squares linear regression to the space of images by using a second-order dynamic formulation for image registration. Unlike previous approaches, the formulation allows for a compact representation of an approximation to the full spatio-temporal trajectory through its initial values. The method also opens up possibilities to design image-based approximation algorithms. The resulting optimization problem is solved using an adjoint method.
到目前为止，图像时间序列的配准已经通过以下方式完成：（i）通过拼接图像对之间的配准；（ii）通过解决一个联合估计问题，该问题会产生图像对之间的分段测地线路径；（iii）通过基于核的局部平均；或者（iv）通过用额外的时间不规则性惩罚来增强联合估计。在此，我们提出一种生成模型，通过使用用于图像配准的二阶动态公式，将最小二乘线性回归扩展到图像空间。与先前的方法不同，该公式允许通过其初始值对完整时空轨迹的近似进行紧凑表示。该方法还为设计基于图像的近似算法开辟了可能性。使用伴随方法解决由此产生的优化问题。
