Wang Yuanxiang, Salehian Hesamoddin, Cheng Guang, Vemuri Baba C
Department of ECE, University of Florida, Gainesville, FL.
Department of CISE, University of Florida, Gainesville, FL.
Conf Comput Vis Pattern Recognit Workshops. 2014 Jun;2014:3051-3056. doi: 10.1109/CVPR.2014.390.
Tractography refers to the process of tracing out the nerve fiber bundles from diffusion Magnetic Resonance Images (dMRI) data acquired either in vivo or ex-vivo. Tractography is a mature research topic within the field of diffusion MRI analysis, nevertheless, several new methods are being proposed on a regular basis thereby justifying the need, as the problem is not fully solved. Tractography is usually applied to the model (used to represent the diffusion MR signal or a derived quantity) reconstructed from the acquired data. Separating shape and orientation of these models was previously shown to approximately preserve diffusion anisotropy (a useful bio-marker) in the ubiquitous problem of interpolation. However, no further intrinsic geometric properties of this framework were exploited to date in literature. In this paper, we propose a new intrinsic recursive filter on the product manifold of shape and orientation. The recursive filter, dubbed IUKFPro, is a generalization of the unscented Kalman filter (UKF) to this product manifold. The salient contributions of this work are: (1) A new intrinsic UKF for the product manifold of shape and orientation. (2) Derivation of the Riemannian geometry of the product manifold. (3) IUKFPro is tested on synthetic and real data sets from various tractography challenge competitions. From the experimental results, it is evident that IUKFPro performs better than several competing schemes in literature with regards to some of the error measures used in the competitions and is competitive with respect to others.
纤维束成像指的是从在体或离体获取的扩散磁共振成像（dMRI）数据中追踪神经纤维束的过程。纤维束成像是扩散磁共振成像分析领域中一个成熟的研究课题，然而，仍不断有新方法被提出，这表明尽管该问题尚未完全解决，但仍有研究的必要。纤维束成像通常应用于从采集数据重建的模型（用于表示扩散磁共振信号或一个派生量）。先前研究表明，在普遍存在的插值问题中，分离这些模型的形状和方向能近似保留扩散各向异性（一种有用的生物标志物）。然而，迄今为止，文献中尚未利用该框架的其他内在几何特性。在本文中，我们在形状和方向的乘积流形上提出了一种新的内在递归滤波器。这种递归滤波器被称为IUKFPro，它是无迹卡尔曼滤波器（UKF）在此乘积流形上的推广。这项工作的突出贡献包括：（1）为形状和方向的乘积流形设计了一种新的内在UKF。（2）推导了乘积流形的黎曼几何。（3）IUKFPro在来自各种纤维束成像挑战赛的合成数据集和真实数据集上进行了测试。从实验结果来看，很明显，就比赛中使用的一些误差度量而言，IUKFPro的表现优于文献中的几种竞争方案，并且在其他方面也具有竞争力。
