Glocker Ben, Paragios Nikos, Komodakis Nikos, Tziritas Georgios, Navab Nassir
GALEN Group, Laboratoire de Mathématiques Appliquées aux Systèmes, Ecole Centrale de Paris.
Inf Process Med Imaging. 2007;20:408-20. doi: 10.1007/978-3-540-73273-0_34.
In this paper we propose a novel non-rigid volume registration based on discrete labeling and linear programming. The proposed framework reformulates registration as a minimal path extraction in a weighted graph. The space of solutions is represented using a set of a labels which are assigned to predefined displacements. The graph topology corresponds to a superimposed regular grid onto the volume. Links between neighborhood control points introduce smoothness, while links between the graph nodes and the labels (end-nodes) measure the cost induced to the objective function through the selection of a particular deformation for a given control point once projected to the entire volume domain, Higher order polynomials are used to express the volume deformation from the ones of the control points. Efficient linear programming that can guarantee the optimal solution up to (a user-defined) bound is considered to recover the optimal registration parameters. Therefore, the method is gradient free, can encode various similarity metrics (simple changes on the graph construction), can guarantee a globally sub-optimal solution and is computational tractable. Experimental validation using simulated data with known deformation, as well as manually segmented data demonstrate the extreme potentials of our approach.
在本文中，我们提出了一种基于离散标记和线性规划的新型非刚性体积配准方法。所提出的框架将配准重新表述为加权图中的最小路径提取。解空间使用一组分配给预定义位移的标签来表示。图拓扑对应于叠加在体积上的规则网格。邻域控制点之间的链接引入了平滑性，而图节点与标签（端点）之间的链接则衡量了一旦投影到整个体积域上，为给定控制点选择特定变形时目标函数所产生的代价。高阶多项式用于从控制点的变形来表达体积变形。考虑使用能保证在（用户定义的）界限内获得最优解的高效线性规划来恢复最优配准参数。因此，该方法无需梯度，能够编码各种相似性度量（在图构建上进行简单更改），能保证全局次优解且计算上易于处理。使用具有已知变形的模拟数据以及手动分割数据进行的实验验证证明了我们方法的巨大潜力。
