Seiler Christof, Pennec Xavier, Reyes Mauricio
Institute for Surgical Technology and Biomechanics, University of Bern, Switzerland.
Med Image Comput Comput Assist Interv. 2012;15(Pt 2):130-7. doi: 10.1007/978-3-642-33418-4_17.
Locally affine (polyaffine) image registration methods capture intersubject non-linear deformations with a low number of parameters, while providing an intuitive interpretation for clinicians. Considering the mandible bone, anatomical shape differences can be found at different scales, e.g. left or right side, teeth, etc. Classically, sequential coarse to fine registration are used to handle multiscale deformations, instead we propose a simultaneous optimization of all scales. To avoid local minima we incorporate a prior on the polyaffine transformations. This kind of groupwise registration approach is natural in a polyaffine context, if we assume one configuration of regions that describes an entire group of images, with varying transformations for each region. In this paper, we reformulate polyaffine deformations in a generative statistical model, which enables us to incorporate deformation statistics as a prior in a Bayesian setting. We find optimal transformations by optimizing the maximum a posteriori probability. We assume that the polyaffine transformations follow a normal distribution with mean and concentration matrix. Parameters of the prior are estimated from an initial coarse to fine registration. Knowing the region structure, we develop a blockwise pseudoinverse to obtain the concentration matrix. To our knowledge, we are the first to introduce simultaneous multiscale optimization through groupwise polyaffine registration. We show results on 42 mandible CT images.
局部仿射（多仿射）图像配准方法用较少的参数捕捉个体间的非线性变形，同时为临床医生提供直观的解释。考虑下颌骨，在不同尺度上可以发现解剖形状差异，例如左侧或右侧、牙齿等。传统上，采用从粗到精的顺序配准来处理多尺度变形，相反，我们提出对所有尺度进行同时优化。为了避免局部最小值，我们在多仿射变换中引入先验。如果我们假设一种区域配置描述了整个图像组，并且每个区域有不同的变换，那么这种分组配准方法在多仿射背景下是自然的。在本文中，我们在生成统计模型中重新表述多仿射变形，这使我们能够在贝叶斯设置中将变形统计作为先验纳入。我们通过优化最大后验概率找到最优变换。我们假设多仿射变换服从具有均值和浓度矩阵的正态分布。先验的参数从初始的从粗到精配准中估计。知道区域结构后，我们开发了一种分块伪逆来获得浓度矩阵。据我们所知，我们是第一个通过分组多仿射配准引入同时多尺度优化的。我们展示了在42张下颌骨CT图像上的结果。
