【摘要】：隨著醫(yī)學成像技術的發(fā)展,越來越多的臨床應用要求對來自不同主體,不同時期或不同成像設備的醫(yī)學圖像進行比較和分析。醫(yī)學圖像配準是醫(yī)學圖像分析和計算解剖的一個關鍵步驟,被廣泛應用在疾病診斷、手術導航、人腦圖譜和各種醫(yī)學評價等方面。然而,醫(yī)學圖像的多樣性、復雜性和非連續(xù)性等特征使得醫(yī)學圖像配準技術具有很大的挑戰(zhàn)性。醫(yī)學圖像數(shù)據(jù)(如擴散張量圖像)通常都是非線性結構,存在于非線性的流形上。已有的配準技術,無論單模態(tài)還是多模態(tài),剛體還是非剛體,基于參數(shù)還是非參數(shù),要么忽略流形的非線性幾何,直接在線性的歐式空間下進行研究,要么對非線性數(shù)據(jù)結構所包含的豐富的空間信息考慮不夠。然而這些信息對空間變換下圖像拓撲結構的保持具有重要意義。本文較系統(tǒng)地對幾種醫(yī)學成像技術進行了研究,尤其是磁共振成像技術和擴散張量成像技術。以拓撲學、微分幾何和幾何代數(shù)作為空間分析的數(shù)學工具,對醫(yī)學數(shù)據(jù)的特征拓撲結構以及數(shù)據(jù)間的空間關系進行深入探討,圍繞配準算法的魯棒性,精度和拓撲保持性對非線性醫(yī)學成像數(shù)據(jù)的高維空間分布關系進行研究。本文的主要貢獻如下。(1)傳統(tǒng)的非參數(shù)微分同胚配準算法只是基于像素灰度恒定的假設,忽略了高維空間變換中數(shù)據(jù)流形的非線性結構的豐富性和拓撲性對保持合理物理結構的影響。本文在微分同胚Demons算法的基礎上,提出了一種局部自適應拓撲保持的MR圖像配準。為了獲得更豐富的空間信息和幾何結構,首先構造正定對稱矩陣,并在一定條件下形成高維非線性的李群流形,然后利用流形學習方法進行自適應的鄰域選擇,從而更精確地逼近流形的線性切空間,保持流形的非線性結構,使圖像特征空間的拓撲結構在非線性的微分同胚變換中更好地保持物理合理性。(2)針對傳統(tǒng)的DT圖像中張量的重定向策略只適合于剛體配準或因迭代產(chǎn)生的計算代價,本文把張量集轉(zhuǎn)換成一種點集的規(guī)范式,提出一種規(guī)范式下的DT圖像仿射配準。在這種規(guī)范式下,仿射變換下兩個張量集之間的配準就可以轉(zhuǎn)換為旋轉(zhuǎn)變換下規(guī)范式之間的配準,但仍然保持了仿射變換中的非剛體形變分量對重定向的影響,使得形變在解剖結構上更合理。傳統(tǒng)的基于重定向的DT圖像仿射配準算法只提取剛體旋轉(zhuǎn)部分進行空間變化,忽略平移,縮放和切變等形變分量對仿射變換的影響。所以比較傳統(tǒng)方法,本文算法用于仿射變換能獲得更好地精度。進一步,為了改善由于重定向引起的計算代價,使優(yōu)化過程更有效率,利用旋轉(zhuǎn)變換群---李群SO(3)描述彌散張量的特殊數(shù)學結構,用單位四元數(shù)旋轉(zhuǎn)替代三維旋轉(zhuǎn)矩陣,從絕對定向中找到最優(yōu)閉式解,能大大減少計算代價。(3)針對傳統(tǒng)多模態(tài)配準方法忽視圖像的空間結構和像素間的空間關系和假定灰度全局一致,提出一種基于學習理論的多模態(tài)圖像配準算法。本文利用自回歸線性動態(tài)模型描述圖像的局部高維非線性空間結構,這使得特征空間包含了更多空間信息。然后通過參數(shù)化動態(tài)模型構造出具有李群結構的群元素,并形成黎曼流形,接下來把黎曼流形嵌入到更高維的再生核希爾伯特空間,再在核空間引入核函數(shù)尋找最優(yōu)的相似性測度,這種核技巧可以把非線性數(shù)據(jù)映射到一個隱式的高維中進行處理。算法不僅對剛體配準,而且對仿射配準也適用。
[Abstract]:With the development of medical imaging technology, more and more clinical applications require the comparison and analysis of medical images from different subjects, different periods or different imaging equipments. However, the diversity, complexity and discontinuity of medical images make medical image registration challenging. Medical image data (such as diffusion tensor images) are usually nonlinear structures and exist on nonlinear manifolds. Rigid or non-rigid, based on parameters or non-parameters, or ignoring the nonlinear geometry of manifolds, directly study in linear Euclidean space, or the rich spatial information contained in the non-linear data structure is not considered enough. Several medical imaging techniques, especially magnetic resonance imaging and diffusion tensor imaging, are systematically studied. Topology, differential geometry and geometric algebra are used as mathematical tools for spatial analysis. The characteristic topological structure of medical data and the spatial relationship between medical data are discussed in detail. The robustness of registration algorithm is focused on. The main contributions of this paper are as follows. (1) The traditional non-parametric differential homeomorphism registration algorithm is based on the assumption that the pixel gray level is constant, ignoring the richness and topological pairs of the nonlinear structure of the data manifold in the high-dimensional space transformation. Based on the differential homeomorphism Demons algorithm, a locally adaptive topology preserving MR image registration algorithm is proposed in this paper. In order to obtain more spatial information and geometric structure, a positive definite symmetric matrix is constructed, and a high-dimensional nonlinear Lie group manifold is formed under certain conditions, and then a manifold is used. Adaptive neighborhood selection is used to approximate the linear tangent space of the manifold more accurately and keep the nonlinear structure of the manifold, so that the topological structure of the image feature space can keep the physical rationality better in the nonlinear differential homeomorphism transformation. (2) The traditional DT image tensor redirection strategy is only suitable for rigid bodies. In this paper, tensor set is transformed into a normal form of point set, and a new affine registration method for DT images is proposed. In this form, the registration between two tensor sets under affine transformation can be transformed into the registration between the normalizations under rotational transformation, but the affine transformation is still preserved. The influence of non-rigid deformation components on redirection makes the deformation more reasonable in anatomical structure. The traditional affine registration algorithm based on redirection only extracts the rotational part of rigid body for spatial change, ignoring the effects of translation, scaling and shear on affine transformation. Further, in order to improve the computational cost caused by redirection and make the optimization process more efficient, the special mathematical structure of the dispersion tensor is described by the rotational transformation group-Lie group SO(3). The unit quaternion rotation is used instead of the three-dimensional rotation matrix to find the optimal closed-form solution from the absolute orientation, which can be greatly reduced. (3) Aiming at the neglect of spatial structure and spatial relationship between pixels and the assumption that gray level is globally consistent in traditional multi-modal registration methods, a multi-modal image registration algorithm based on learning theory is proposed. Spaces contain more spatial information. Then, group elements with Lie group structure are constructed by parameterized dynamic model, and Riemannian manifolds are formed. Next, Riemannian manifolds are embedded into higher dimensional reproducing kernel Hilbert space, and kernel functions are introduced into kernel space to find the optimal similarity measure. The algorithm is not only suitable for rigid registration, but also for affine registration.
【學位授予單位】：電子科技大學
【學位級別】：博士
【學位授予年份】：2017
【分類號】：TP391.41

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本文編號：2178575