Benameur Said, Mignotte Max, Destrempes François, De Guise Jacques A
Laboratoire de recherche en imagerie et orthopédie, University of Montréal Hospital Research Centre, Montréal, QC H2L 2W5, Canada.
IEEE Trans Biomed Eng. 2005 Oct;52(10):1713-28. doi: 10.1109/TBME.2005.855717.
In this paper, we present an original method for the three-dimensional (3-D) reconstruction of the scoliotic rib cage from a planar and a conventional pair of calibrated radiographic images (postero-anterior with normal incidence and lateral). To this end, we first present a robust method for estimating the model parameters in a mixture of probabilistic principal component analyzers (PPCA). This method is based on the stochastic expectation maximization (SEM) algorithm. Parameters of this mixture model are used to constrain the 3-D biplanar reconstruction problem of scoliotic rib cage. More precisely, the proposed PPCA mixture model is exploited for dimensionality reduction and to obtain a set of probabilistic prior models associated with each detected class of pathological deformations observed on a representative training scoliotic rib cage population. By using an appropriate likelihood, for each considered class-conditional prior model, the proposed 3-D reconstruction is stated as an energy function minimization problem, which is solved with an exploration/selection algorithm. The optimal 3-D reconstruction then corresponds to the class of deformation and parameters leading to the minimal energy. This 3-D method of reconstruction has been successfully tested and validated on a database of 20 pairs of biplanar radiographic images of scoliotic patients, yielding very promising results. As an alternative to computed tomography-scan 3-D reconstruction this scheme has the advantage of low radiation for the patient, and may also be used for diagnosis and evaluation of deformity of a scoliotic rib cage. The proposed method remains sufficiently general to be applied to other reconstruction problems for which a database of objects to be reconstructed is available (with two or more radiographic views).
在本文中，我们提出了一种从平面和常规的一对校准的X射线图像（正位垂直入射和侧位）对脊柱侧弯胸廓进行三维（3-D）重建的原创方法。为此，我们首先提出了一种在概率主成分分析器（PPCA）混合模型中估计模型参数的稳健方法。该方法基于随机期望最大化（SEM）算法。此混合模型的参数用于约束脊柱侧弯胸廓的三维双平面重建问题。更确切地说，所提出的PPCA混合模型用于降维和获得与在代表性的脊柱侧弯胸廓训练群体上观察到的每个检测到的病理变形类别相关的一组概率先验模型。通过使用适当的似然性，对于每个考虑的类条件先验模型，将所提出的三维重建表述为能量函数最小化问题，该问题通过探索/选择算法求解。然后，最优的三维重建对应于导致能量最小的变形类别和参数。这种三维重建方法已在20对脊柱侧弯患者的双平面X射线图像数据库上成功进行了测试和验证，取得了非常有前景的结果。作为计算机断层扫描三维重建的替代方法，该方案具有对患者辐射低的优点，并且还可用于脊柱侧弯胸廓畸形的诊断和评估。所提出的方法足够通用，可应用于其他有可用待重建对象数据库（有两个或更多X射线视图）的重建问题。
