摘要
医学图像非刚性配准是医学图像处理和分析的关键步骤，是图像对比、数据融合、目标识别和病理变化分析的必要前提。目前，医学图像非刚性配准主要应用于医学图像融合预处理、手术精确导航、疗效评估、病理跟踪、辅助医疗诊断和放射治疗规划等方面。本文主要研究医学图像非刚性配准算法，围绕配准精度、鲁棒性、拓扑保持性和计算速度等问题展开研究工作，重点研究了具有拓扑保持性的diffeomorphic Demons算法、基于特征点配准的t分布混合模型、基于特征点与灰度的混合配准算法和基于GPU的二级并行加速算法，其研究成果如下。
针对diffeomorphic Demons算法配准后的变形场不具备拓扑保持性的问题，使用计算机视觉中的黎曼流形，通过Sochen-Kimmel-Malladi非线性扩散方程将图像所在的欧式空间嵌入到高维黎曼空间中，将三维图像看作黎曼空间中的四维流形，把图像配准问题转换成为曲面演化问题。通过最小化Polyakov泛函并同时计算图像变形场和灰度偏移以校正因灰度变化引起的图像拓扑改变。使用分割结果作为先验知识，标记图像中拓扑变化的区域以约束变形场能量分部，强化浮动图像的拓扑保持性。
针对高斯混合模型抗外点干扰能力弱的问题，将高斯混合模型推广为t分布混合模型，提出了基于t分布混合模型的特征点非刚性配准算法。使用EM算法最小化非刚性配准参数的条件期望获得其闭合解。t分布混合模型通过计算浮动点的权重，减小了外点对配准结果的影响；计算浮动点的自由度，自适应地改变其概率密度分布，提高了算法的鲁棒性，并避免了噪声水平估计误差影响配准结果。使用含局部空间约束性质的Dirichlet分布作为t分布混合模型的浮动点先验权重，增加其空间约束性质，提高特征点配准的准确性和抗干扰能力。在t分布混合模型中加入点集位移的正则项，使邻近点具有运动一致性。根据特征点刚性配准、仿射配准和非刚性配准的约束性质，将t分布混合模型的非刚性配准算法进一步推广到刚性配准算法和仿射配准算法。
针对非刚性配准时易出现变形场混叠的问题，提出了基于特征点和灰度的混合配准算法。首先使用特征点配准的位移向量场和改进的距离函数预校正diffeomorphic Demons算法的变形场，然后使用含改进正则项的diffeomorphicDemons算法继续精确配准图像并配准图像过校正区域。含改进正则项的diffeomorphic Demons算法根据像素到目标区域的距离自适应地改变更新步长。当像素在目标区域附近时，更新步长较小，可精确精确配准图像；像素在图像边缘时，更新步长较大，可配准过校正的像素并加快收敛速度。
针对基于归一化互信息测度的B样条非刚性配准算法计算量大、配准缓慢的问题，提出了基于B样条的二层并行算法。对归一化互信息使用数据并行算法；对梯度下降流使用任务并行算法，并将数据并行算法嵌入到任务并行算法中。为进一步减少计算量，提出了基于图像多层次局部熵的控制点分布优化算法，使活动控制点仅分布于待配准的目标之上；使用B样条系数的快速算法；使用Greedy算法均衡因控制点分布优化造成的线程块计算量不平衡的问题。
Medical image registration is a key component in medical image processing andanalysis, including image comparison, image fusion and image variation analysis andtarget recognition. Medical image registration is now applied in image fusion, surgicalnavigation, response evaluation, pathological tracking, auxiliary medical diagnosisand radiotherapy planning. In this dissertation, we concentrate on the non-rigidregistration algorithm based on image intensity, feature points and mixture algorithmto improve the veracity, accuracy and topological homeomorphism. GPU is used toaccelerate the non-rigid registration. The major contributions of this dissertation are asfollows.
A diffeomorphic Demons algorithm with topological homeomorphism based onRiemannian manifold is proposed due to the traditional diffeomorphic Demonsalgorithm lacking of topological homeomorphism. A three dimensional medicalimages is treated as a four dimensional manifold in four dimensional Riemannianspace by Sochen-Kimmel-Malladi Nonlinear diffusion equation. So, the three imageregistration is transformed to a four dimensional curve evolution. In order to correctthe topology change caused by intensity offset, the deformation field and the intensityoffset are computed at the same time by minimizing the Polyakov functional. Asegmentation result is used as the prior knowledge to constraint the deformation fieldenergy and strengthens the topological homeomorphism
A robust non-rigid registration approach based on the Students’t-distributionmixture model is proposed due to the Gaussian mixture model being vulnerable by theoutliers and the data with longer than normal tails. The Gaussian mixture model is a special case of the Students’t-distribution mixture model in theory. The parameter setof the Students’t-distribution mixture model is solved by EM algorithm. The weight ofeach float point is calculated in EM algorithm instead of a constant in order to reducethe impact of outliers. The degree of freedom of each point in theStudents’t-distribution mixture model is calculated to change the probability densitydistribution to avoid estimating the noise level of data sets in the Gaussian mixturemodel that may bring the additional error. We impose the local spatial constraints byadding the Dirichlet distribution and enhance the accuracy and anti-jammingcapability of the Students’t-distribution mixture models. The points have a feature ofcoherent point drift by adding regularization into the expectation function. Moreover,we extend the algorithm to rigid registration and affine registration.
In order to solve the problem of the aliasing transformation field in medicalimages registration, a hybrid non-rigid registration algorithm including feature pointsand intensity is proposed in this dissertation. A double-layer correction approach isused to revise the aliasing transformation field produced by the diffeomorphicDemons algorithm. Firstly, the displacement vectors produced by feature pointregistration are used to pre-correct the field. Secondly, the diffeomorphic Demonsalgorithm with an improved regularization is used to align the corrected image. Theupdate step length is selected adaptively according to the distances between the pixelsand the interval region. The improved diffeomorphic Demons algorithm not onlyimproves the accurate in the target regions but also improves the veracity in theovercorrection regions.
The non-rigid registration is slow due to a large number of control points, theiterative strategy and the normalized mutual information (NMI). A parallel algorithmcombining a B-spline coefficient optimization algorithm is proposed to accelerateregistration. In this algorithm, the data parallel algorithm computes NMI and the taskparallel algorithm, which the data parallel algorithm is embedded in, computes thegradient descent flow. Control points are restrained on the targets by computing imagelocal entropy to reduce computation. A thread balance algorithm based on Greedy isused to solve the computation imbalance problem caused by the uneven distribution of control points.
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