Zöllei Lilla, Jenkinson Mark, Timoner Samson, Wells William
A. A. Martinos Center, MGH, USA.
Inf Process Med Imaging. 2007;20:662-74. doi: 10.1007/978-3-540-73273-0_55.
We formalize the pair-wise registration problem in a maximum a posteriori (MAP) framework that employs a multinomial model of joint intensities with parameters for which we only have a prior distribution. To obtain an MAP estimate of the aligning transformation alone, we treat the multinomial parameters as nuisance parameters, and marginalize them out. If the prior on those is uninformative, the marginalization leads to registration by minimization of joint entropy. With an informative prior, the marginalization leads to minimization of the entropy of the data pooled with pseudo observations from the prior. In addition, we show that the marginalized objective function can be optimized by the Expectation-Maximization (EM) algorithm, which yields a simple and effective iteration for solving entropy-based registration problems. Experimentally, we demonstrate the effectiveness of the resulting EM iteration for rapidly solving a challenging intra-operative registration problem.
我们在最大后验概率（MAP）框架中形式化成对配准问题，该框架采用联合强度的多项式模型，其参数我们仅有先验分布。为了单独获得对齐变换的MAP估计，我们将多项式参数视为干扰参数，并将它们边缘化。如果这些参数的先验信息不充分，边缘化会导致通过最小化联合熵进行配准。对于有信息先验，边缘化会导致最小化与来自先验的伪观测合并的数据的熵。此外，我们表明边缘化后的目标函数可以通过期望最大化（EM）算法进行优化，该算法为解决基于熵的配准问题提供了一种简单有效的迭代方法。通过实验，我们证明了所得EM迭代对于快速解决具有挑战性的术中配准问题的有效性。
