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Left ventricle segmentation in MRI via convex relaxed distribution matching

机译：通过凸松弛分布匹配MRI的左心室分割

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A fundamental step in the diagnosis of cardiovascular diseases, automatic left ventricle (LV) segmentation in cardiac magnetic resonance images (MRIs) is still acknowledged to be a difficult problem. Most of the existing algorithms require either extensive training or intensive user inputs. This study investigates fast detection of the left ventricle (LV) endo- and epicardium surfaces in cardiac MRI via convex relaxation and distribution matching. The algorithm requires a single subject for training and a very simple user input, which amounts to a single point (mouse click) per target region (cavity or myocardium). It seeks cavity and myocardium regions within each 3D phase by optimizing two functionals, each containing two distribution-matching constraints: (1) a distance-based shape prior and (2) an intensity prior. Based on a global measure of similarity between distributions, the shape prior is intrinsically invariant with respect to translation and rotation. We further introduce a scale variable from which we derive a fixed-point equation (FPE), thereby achieving scale-invariance with only few fast computations. The proposed algorithm relaxes the need for costly pose estimation (or registration) procedures and large training sets, and can tolerate shape deformations, unlike template (or atlas) based priors. Our formulation leads to a challenging problem, which is not directly amenable to convex-optimization techniques. For each functional, we split the problem into a sequence of sub-problems, each of which can be solved exactly and globally via a convex relaxation and the augmented Lagrangian method. Unlike related graph-cut approaches, the proposed convex-relaxation solution can be parallelized to reduce substantially the computational time for 3D domains (or higher), extends directly to high dimensions, and does not have the grid-bias problem. Our parallelized implementation on a graphics processing unit (GPU) demonstrates that the proposed algorithm requires about 3.87 s for a typical cardiac MRI volume, a speed-up of about five times compared to a standard implementation. We report a performance evaluation over 400 volumes acquired from 20 subjects, which shows that the obtained 3D surfaces correlate with independent manual delineations. We further demonstrate experimentally that (1) the performance of the algorithm is not significantly affected by the choice of the training subject and (2) the shape description we use does not change significantly from one subject to another. These results support the fact that a single subject is sufficient for training the proposed algorithm.
机译：心血管疾病诊断的基本步骤，心脏磁共振图像（MRIS）的自动左心室（LV）分割仍然被认为是难题。大多数现有算法需要广泛的培训或密集用户输入。本研究通过凸松弛和分布匹配研究了心脏MRI中的左心室（LV）内切和心外膜表面的快速检测。该算法需要单个主题进行训练和一个非常简单的用户输入，其相当于每个目标区域（腔或心肌）的单点（鼠标点击）。它通过优化两个功能来寻找每个3D相位内的腔和心肌区域，每个功能包括两个分布匹配约束：（1）之前的距离基形状和（2）的强度。基于分布之间的全球相似度的标准，形状之前的形状是关于转换和旋转的本质上不变。我们进一步介绍了一种规模变量，我们从中导出了一个定点方程（FPE），从而实现了少量快速计算的比例不变性。该算法可以放松昂贵的姿势估计（或注册）程序和大型训练集的需要，并且可以容忍与基于模板（或阿特拉斯）的前沿的形状变形。我们的配方导致了一个具有挑战性的问题，这与凸优化技术不直接均可。对于每个功能，我们将问题分解为一系列子问题，每个问题可以通过凸松弛和增强的拉格朗日方法完全和全局解决。与相关的图形切割方法不同，所提出的凸松弛溶液可以并行化以降低3D域（或更高）的基本计算时间，直接延伸到高维度，并且没有网格偏置问题。我们在图形处理单元（GPU）上的并行化实现表明，与标准实施相比，所提出的算法需要大约3.87秒，速度约为五次。我们报告了从20个科目获得的400卷上的绩效评估，这表明所获得的3D表面与独立手动描绘相关。我们进一步通过实验证明（1）算法的性能不会受到训练主题的选择的显着影响，并且（2）我们使用的形状描述不会从一个受试者那么显着变化。这些结果支持单个受试者足以培训所提出的算法。

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