CN103908346A - High-precision automatic neuronavigation space registration method - Google Patents

Abstract

Translated fromChinese

本发明属医学图像处理及应用领域，涉及一种高精度自动神经导航空间配准方法。本发明方法中采用基于高斯混合模型的全局优化点集配准方法，将基于激光扫描仪获得的点云与CT获得的点云得到两个点云之间的坐标变换实现初步配准；然后采用无序点自动配准的方法，将初步配准的结果与神经导航中通过CT重建出来的病人空间再次进行配准。使用结果表明，本发明所述的方法实施简单，精度可靠，便于临床应用，可集成在现有导航系统中，从而大幅度提高导航系统精度。The invention belongs to the field of medical image processing and application, and relates to a high-precision automatic neuronavigation space registration method. In the method of the present invention, the global optimization point set registration method based on the Gaussian mixture model is adopted, and the point cloud obtained based on the laser scanner and the point cloud obtained by CT are obtained by coordinate transformation between the two point clouds to realize preliminary registration; The method of sequence point automatic registration, the result of preliminary registration is registered again with the patient space reconstructed by CT in neuronavigation. The result of use shows that the method of the invention is easy to implement, has reliable accuracy, is convenient for clinical application, and can be integrated in the existing navigation system, thereby greatly improving the accuracy of the navigation system.

Description

Translated fromChinese

一种高精度自动神经导航空间配准方法A high-precision automatic neuronavigation spatial registration method

技术领域technical field

本发明属医学图像处理及应用领域，涉及一种神经导航空间配准方法；尤其是一种高精度自动神经导航空间配准方法。该方法能使手术导航在临床应用中更精确、实用和方便。The invention belongs to the field of medical image processing and application, and relates to a neuronavigation space registration method; in particular, a high-precision automatic neuronavigation space registration method. This method can make surgical navigation more accurate, practical and convenient in clinical application.

背景技术Background technique

神经导航系统作为一种医学辅助定位设备，能够为医生提供实时的术中信息，有效弥补了传统神经外科手术方式的不足，提高了手术质量。从临床应用情况可以看出，神经导航系统的核心功能是使用图像来对手术器械进行定位和引导，因此，手术真实场景与图像引导空间的定位和配准精度将直接影响神经导航系统的性能。As a medical auxiliary positioning device, the neuronavigation system can provide doctors with real-time intraoperative information, effectively make up for the shortcomings of traditional neurosurgery methods, and improve the quality of surgery. It can be seen from the clinical application that the core function of the neuronavigation system is to use images to locate and guide surgical instruments. Therefore, the positioning and registration accuracy of the real surgical scene and the image-guided space will directly affect the performance of the neuronavigation system.

目前，神经导航系统中使用的空间配准方法主要基于点匹配和面匹配；所述点匹配方法使用较多，但其存在一些固有缺陷，如：需要专门为导航进行一次影像扫描；粘贴在头皮表面的人工标记物容易发生移位，从而引起较大的空间配准误差；标记点识别过程消耗时间较长。为了解决上述点匹配方法存在的问题，基于面匹配的空间配准方法得到关注。所述面配准使用病人固有特征进行空间配准，可以直接使用已有的图像进行导航，克服了点配准存在的缺陷，同时，因为使用了更多的信息进行空间配准，可以达到更高的配准精度。使用基于面匹配的空间配准方法时，医生首先在图像空间提取一个代表病人面部轮廓的表面点云，然后在病人空间使用激光扫描仪获取相同表面的另一点云，然后基于两个点云之间的相关性得到两个空间之间的坐标变换。At present, the spatial registration methods used in neuronavigation systems are mainly based on point matching and surface matching; the point matching method is widely used, but it has some inherent defects, such as: it needs to scan an image specially for navigation; The artificial markers on the surface are prone to shift, resulting in large spatial registration errors; the process of marker recognition takes a long time. In order to solve the problems existing in the above-mentioned point matching methods, spatial registration methods based on surface matching have attracted attention. The surface registration uses the inherent characteristics of the patient for spatial registration, and can directly use existing images for navigation, which overcomes the defects of point registration. At the same time, because more information is used for spatial registration, it can achieve more High registration accuracy. When using the spatial registration method based on face matching, the doctor first extracts a surface point cloud representing the patient's facial contour in the image space, and then uses a laser scanner to obtain another point cloud of the same surface in the patient space, and then based on the two point clouds The correlation between the coordinate transformations between the two spaces is obtained.

所述的点云之间的相关性，总体上可分为单点与单点的一一对应，单点与多点间的相关性，多点与多点间相关性即模糊相关性三个方面；其中，基于单点与单点一一对应进行点云配准的主流方法是迭代最近点(ICP：Iterative Closest Point)算法及其各种改进算法；该类方法直观、简单且具有较高的匹配精度，但存在对初始位置敏感等缺陷。所述单点与多点间的相关性，也就是点与点间的对应关系通过一定的权值来表示，即模型点集中的每一个点与场景点集中所有点的加权组合相对应。然而，在临床应用中，单点间的一一对应和点与多点之间的相关性往往较难确定；为了解决上述问题，无需建立明确的点之间相关性，即基于模糊相关性的点集配准方法被提出。该类方法主要基于统计和测度理论，使用概率密度分布描述点集空间；然而，点集配准各类方法中存在的一个比较共性的问题——收敛到局部最优解而非全局最优解依然存在。The correlation between the point clouds can be generally divided into one-to-one correspondence between single points and single points, correlation between single points and multiple points, and correlation between multiple points and multiple points, that is, fuzzy correlation. Among them, the mainstream method for point cloud registration based on the one-to-one correspondence between single points and single points is the iterative closest point (ICP: Iterative Closest Point) algorithm and its various improved algorithms; this type of method is intuitive, simple and has high Matching accuracy, but there are defects such as sensitivity to the initial position. The correlation between a single point and multiple points, that is, the corresponding relationship between points is represented by a certain weight, that is, each point in the model point set corresponds to the weighted combination of all points in the scene point set. However, in clinical applications, the one-to-one correspondence between single points and the correlation between points and multiple points are often difficult to determine; in order to solve the above problems, there is no need to establish a clear correlation between points, that is, based on fuzzy A point set registration method is proposed. This type of method is mainly based on statistics and measurement theory, and uses probability density distribution to describe the point set space; however, there is a common problem in various methods of point set registration—converging to a local optimal solution rather than a global optimal solution is still exist.

因此，目前需要一种自动神经导航空间配准方法；该方法能使手术导航在临床应用中更精确、实用和方便。Therefore, there is a need for an automatic neuronavigation spatial registration method; this method can make surgical navigation more accurate, practical and convenient in clinical applications.

与本发明有关的参考文献有：References relevant to the present invention are:

1 G.Eggers，J.Muhling and R.Marmulla，Image-to-patient registration techniques in headsurgery，Int.J.Oral.Max.Surg.，2006，35：1081-10951 G. Eggers, J. Muhling and R. Marmulla, Image-to-patient registration techniques in head surgery, Int. J. Oral. Max. Surg., 2006, 35: 1081-1095

2 P.J.Besl and N.D.McKay，A method for registration of 3-D shapes，IEEE Transactions onPattern Analysis and Machine Intelligence，1992，14(2)：239-256。2 P.J.Besl and N.D.McKay, A method for registration of 3-D shapes, IEEE Transactions on Pattern Analysis and Machine Intelligence, 1992, 14(2): 239-256.

发明内容Contents of the invention

本发明的目的在于提供一种自动神经导航空间配准方法；尤其是一种高精度自动神经导航空间配准方法。该方法能使手术导航在临床应用中更精确、实用和方便。The purpose of the present invention is to provide an automatic neuronavigation space registration method; especially a high-precision automatic neuronavigation space registration method. This method can make surgical navigation more accurate, practical and convenient in clinical application.

本发明采用基于高斯混合模型的全局优化点集配准方法，并结合无序点自动匹配方法进一步提高配准精度，即：通过空间定位仪使手术真实场景与图像引导空间处于同一空间，并使用激光扫描仪获取病人头部表面的点云；然后基于激光扫描仪获得的点云与CT获得的点云之间相关性得到两个点云之间的坐标变换实现初步配准；在神经导航过程中，使用无序点自动配准方法将初步配准的结果进行再次匹配，提高配准精度。The present invention adopts the global optimization point set registration method based on the Gaussian mixture model, and combines the disordered point automatic matching method to further improve the registration accuracy, that is, the real scene of the operation and the image guidance space are in the same space through the space locator, and the laser is used to The scanner obtains the point cloud of the patient's head surface; then based on the correlation between the point cloud obtained by the laser scanner and the point cloud obtained by CT, the coordinate transformation between the two point clouds is obtained to achieve preliminary registration; in the neuronavigation process , using the random point automatic registration method to match the results of the preliminary registration again to improve the registration accuracy.

本发明所述的方法中，首先采用基于高斯混合模型的全局优化点集配准方法，将基于激光扫描仪获得的点云与CT获得的点云得到两个点云之间的坐标变换实现初步配准，然后采用无序点自动配准的方法，将初步配准的结果与神经导航中通过CT重建出来的病人空间再次进行配准；In the method of the present invention, first adopt the global optimization point set registration method based on the Gaussian mixture model, and obtain the coordinate transformation between the two point clouds based on the point cloud obtained by the laser scanner and the point cloud obtained by CT to realize the preliminary registration. Then use the method of automatic registration of disordered points to re-register the results of the initial registration and the patient space reconstructed by CT in neuronavigation;

其中，in,

所述采用基于高斯混合模型的全局优化点集配准方法，将基于激光扫描仪获得的点云与CT获得的点云得到两个点云之间的坐标变换实现初步配准，是用激光扫描仪获得的点云和CT获得的点云采用基于高斯混合模型的全局优化点集配准方法实现配准；Said adopting the global optimization point set registration method based on Gaussian mixture model, the coordinate transformation between the point cloud obtained based on the laser scanner and the point cloud obtained by CT to obtain the preliminary registration between the two point clouds is to use the laser scanner The obtained point cloud and the point cloud obtained by CT are registered using the global optimization point set registration method based on the Gaussian mixture model;

所述采用无序点自动配准的方法，将初步配准的结果与神经导航中通过CT重建出来的病人空间再次进行配准，是将初步配准结果与神经导航中通过CT重建出来的病人空间采用无序点自动配准的方法再次进行配准。The method of automatic registration of disordered points is used to register the results of preliminary registration with the patient space reconstructed by CT in neuronavigation. The space is re-registered using the method of automatic registration of unordered points.

具体而言，本发明的自动神经导航空间配准方法，其特征在于，包括以下步骤：Specifically, the automatic neural navigation spatial registration method of the present invention is characterized in that it includes the following steps:

(1)基于高斯混合模型的全局优化点集配准方法(1) Global optimization point set registration method based on Gaussian mixture model

传统的点集配准方法通常将点集中各点的位置视作独立特征，点集的整体特征往往被忽略，而该方法将进行配准的点集看作一个整体，将点集内点与点在整体空间和子空间的相关性作为点集的特征，实施配准，从而最终实现了基于全局优化的点集配准；本发明提出的方法引入了点与点间的相关性，不仅解决了局部收敛的缺陷，同时还提高了配准的精度；The traditional point set registration method usually regards the position of each point in the point set as an independent feature, and the overall feature of the point set is often ignored. However, this method regards the point set for registration as a whole, and the points in the point set and the point The correlation in the overall space and the subspace is used as the feature of the point set to perform registration, thereby finally realizing the point set registration based on global optimization; the method proposed by the invention introduces the correlation between points and not only solves the problem of local convergence defects, while also improving the accuracy of registration;

通常，高斯混合模型的概率密度函数可表示为：In general, the probability density function of a Gaussian mixture model can be expressed as:

$\mathrm{<span><span>f</span>f</span>}<span><span>(</span>(</span>\mathrm{<span><span>X</span>x</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>i</span>i</span>}}\mathrm{<span><span>\&phi;</span>\&phi;</span>}<span><span>(</span>(</span>\mathrm{<span><span>X</span>x</span>}<span><span>|</span>|</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>$

其中，$\mathrm{\&phi;}\left(X\right|{\mathrm{\&mu;}}_i,{\mathrm{\&Sigma;}}_i)=\frac{\exp [-\frac{1}{2}{(X-{\mathrm{\&mu;}}_i)}^T{\mathrm{\&Sigma;}}_i^{-1}(X-{\mathrm{\&mu;}}_i)]}{\sqrt{{\left(2\mathrm{\&pi;}\right)}^d\left|\det \left({\mathrm{\&Sigma;}}_i\right)\right|}}---\left(2\right)$in,$\mathrm{\&phi;}\left(x\right|{\mathrm{\&mu;}}_i,{\mathrm{\&Sigma;}}_i)=\frac{\exp [-\frac{1}{2}{(x-{\mathrm{\&mu;}}_i)}^T{\mathrm{\&Sigma;}}_i^{-1}(x-{\mathrm{\&mu;}}_i)]}{\sqrt{{\left(2\mathrm{\&pi;}\right)}^d\left|\det \left({\mathrm{\&Sigma;}}_i\right)\right|}}---\left(2\right)$

根据高斯混合模型的定义，本发明定义了点集所表示的数据空间中点与点之间的相关性，可表示为：According to the definition of the Gaussian mixture model, the present invention defines the correlation between points and points in the data space represented by the point set, which can be expressed as:

$\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>i</span>i</span>}}\mathrm{<span><span>\&phi;</span>\&phi;</span>}<span><span>(</span>(</span>\mathrm{<span><span>X</span>x</span>}<span><span>|</span>|</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span>\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>j</span>j</span>}}\mathrm{<span><span>\&phi;</span>\&phi;</span>}<span><span>(</span>(</span>\mathrm{<span><span>X</span>x</span>}<span><span>|</span>|</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>j</span>j</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>j</span>j</span>}}<span><span>)</span>)</span>$

$<span><span>(</span>(</span>\mathrm{<span><span>3</span>3</span>}<span><span>)</span>)</span>$

$<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>i</span>i</span>}}{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>j</span>j</span>}}\mathrm{<span><span>\&phi;</span>\&phi;</span>}<span><span>(</span>(</span>\mathrm{<span><span>X</span>x</span>}<span><span>|</span>|</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span>\mathrm{<span><span>\&phi;</span>\&phi;</span>}<span><span>(</span>(</span>\mathrm{<span><span>X</span>x</span>}<span><span>|</span>|</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>j</span>j</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>j</span>j</span>}}<span><span>)</span>)</span>$

从而，对于点集P所表示的整个数据空间中所有点相关性总和，即该数据空间的全局特征可表示为：Therefore, for the sum of all point correlations in the entire data space represented by the point set P, that is, the global characteristics of the data space can be expressed as:

$\mathrm{<span><span>gmm</span>gmm</span>}<span><span>\_</span>\_</span>\mathrm{<span><span>correlation</span>correlation</span>}<span><span>(</span>(</span>\mathrm{<span><span>P</span>P</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>i</span>i</span>}}{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>j</span>j</span>}}<span><span>\&Integral;</span>\&Integral;</span>\mathrm{<span><span>\&phi;</span>\&phi;</span>}<span><span>(</span>(</span>\mathrm{<span><span>X</span>x</span>}<span><span>|</span>|</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span>\mathrm{<span><span>\&phi;</span>\&phi;</span>}<span><span>(</span>(</span>\mathrm{<span><span>X</span>x</span>}<span><span>|</span>|</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>j</span>j</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>j</span>j</span>}}<span><span>)</span>)</span>\mathrm{<span><span>dX</span>wxya</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4</span>4</span>}<span><span>)</span>)</span>$

对于3维点集P表示的3维数据空间经过投影变换，可形成3个1维数据空间；每个1维数据空间可使用混合高斯模型进行表示，其表示形式与(4)一致；For the 3-dimensional data space represented by the 3-dimensional point set P, three 1-dimensional data spaces can be formed through projection transformation; each 1-dimensional data space can be represented by a mixed Gaussian model, and its representation form is consistent with (4);

假设，需要进行配准的两个点集，分别是同一数据空间不同的采样结果，因此它们代表了同一的数据空间，其相应的投影变换形成的子空间也是一致的，对应子空间的点与点之间相关性总和也可认为是接近相等的；基于上述思想，刚体点集配准问题可以转变为最小化式(6)所表示的目标函数，M_l和S_l分别表示两个点集代表的对应子空间。Assume that the two point sets that need to be registered are different sampling results of the same data space, so they represent the same data space, and the subspace formed by the corresponding projection transformation is also consistent, and the points corresponding to the subspace are consistent with The sum of the correlations between points can also be considered to be nearly equal; based on the above ideas, the registration problem of rigid body point sets can be transformed into the objective function represented by the minimization formula (6), and M_l and S_l represent two point sets representing the corresponding subspace of .

dRMS_l＝(gmm_correlation(M_l)-gmm_correlation(S_l))²   (6)dRMS_l ＝(gmm_correlation(M_l )-gmm_correlation(S_l ))² (6)

在进行点集配准的过程中，假设表示整个数据空间的高斯混合模型各个混合分量是均匀分布的，即式(4)中的同时，各个混合分量的协方差矩阵是一致的，即式(4)中的∑_i＝∑_j；In the process of point set registration, it is assumed that each mixed component of the Gaussian mixture model representing the entire data space is uniformly distributed, that is, in formula (4) At the same time, the covariance matrix of each mixed component is consistent, that is, ∑_i = ∑_j in formula (4);

(2)无序点自动匹配方法(2) Unordered point automatic matching method

将待匹配的点集按照点与点之间的距离关系映射到新的点集空间，然后根据距离阈值与目标点集通过剪枝的方法获得最终的匹配关系；该方法大大提高了导航配准精度和效率；Map the point set to be matched to a new point set space according to the distance relationship between points and points, and then obtain the final matching relationship by pruning according to the distance threshold and the target point set; this method greatly improves navigation registration. precision and efficiency;

其包括步骤为：It includes the steps of:

①获取手术真实场景中标记点做为目标点集，获取步骤(1)中初步配准结果中的特征点做为待匹配点集；① Obtain the marked points in the real surgical scene as the target point set, and obtain the feature points in the preliminary registration result in step (1) as the point set to be matched;

②从待匹配点集中取出四个点，对其中每一个点获得与其他三个点之间的距离关系并按照一定的顺序进行排列，形成一个新的点的空间描述；② Take four points from the set of points to be matched, and obtain the distance relationship between each point and the other three points and arrange them in a certain order to form a new spatial description of points;

③对四个点的新的空间描述做如下处理：每两个点对应元素之间做差值并取绝对值然后求和；取所有和值中的最小值；③The new spatial description of the four points is processed as follows: make a difference between the corresponding elements of each two points and take the absolute value and then sum; take the minimum value of all sums;

④对待匹配点集中所有的四个点的组合重复上述步骤②和步骤③中的操作，获得步骤③中所有最小值中的最大值对应的四个点的组合；④Repeat the operations in the above steps ② and ③ for the combination of all four points in the matching point set to obtain the combination of four points corresponding to the maximum value among all the minimum values in step ③;

⑤对目标点集做四个点的排列，每一组排列分别与上述步骤④中获得的四个点的组合做剪枝，逐步排除不符合阈值判定的目标点集的排列；⑤ Arrangement of four points on the target point set, and each group of arrangement is pruned with the combination of the four points obtained in the above step ④, and gradually excludes the arrangement of the target point set that does not meet the threshold judgment;

⑥最后获得与待匹配点集相对应的目标点集的一组排列。⑥Finally, a set of arrangement of the target point set corresponding to the point set to be matched is obtained.

本发明的自动神经导航空间配准方法与现有技术相比，具有以下优点：Compared with the prior art, the automatic neuronavigation spatial registration method of the present invention has the following advantages:

(1)解决了基于点匹配的的空间配准弊端；(1) Solve the disadvantages of spatial registration based on point matching;

(2)本方法为一种全自动的图像病人空间配准方法，减少了医生的工作量；(2) The method is a fully automatic image patient spatial registration method, which reduces the workload of doctors;

(3)本方法为一种全局优化的点集配准方法，降低了初始位置对点集配准方法的影响；(3) This method is a globally optimized point set registration method, which reduces the impact of the initial position on the point set registration method;

(4)提高了配准效率和精度，减小了配准误差。(4) The registration efficiency and precision are improved, and the registration error is reduced.

本发明所述的方法实施简单，精度可靠，便于临床应用，可集成在现有导航系统中，从而大幅度提高导航系统精度。The method of the invention is simple to implement, reliable in accuracy, convenient for clinical application, and can be integrated in the existing navigation system, thereby greatly improving the accuracy of the navigation system.

具体实施方式Detailed ways

实施例1Example 1

本发明的自动神经导航空间配准方法，包括以下步骤：The automatic neuronavigation space registration method of the present invention comprises the following steps:

(1)基于高斯混合模型的全局优化点集配准方法(1) Global optimization point set registration method based on Gaussian mixture model

将进行配准的点集看作一个整体，将点集内点与点在整体空间和子空间的相关性作为点集的特征，实施配准，从而最终实现了基于全局优化的点集配准；本发明提出的方法引入了点与点间的相关性，不仅解决了局部收敛的缺陷，同时还提高了配准的精度；The point set for registration is regarded as a whole, and the correlation between the points in the point set and the points in the overall space and subspace is used as the feature of the point set to perform registration, thus finally realizing the point set registration based on global optimization; this paper The method proposed by the invention introduces the correlation between points, which not only solves the defect of local convergence, but also improves the accuracy of registration;

通常，高斯混合模型的概率密度函数可表示为：In general, the probability density function of a Gaussian mixture model can be expressed as:

$\mathrm{<span><span>f</span>f</span>}<span><span>(</span>(</span>\mathrm{<span><span>X</span>x</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>i</span>i</span>}}\mathrm{<span><span>\&phi;</span>\&phi;</span>}<span><span>(</span>(</span>\mathrm{<span><span>X</span>x</span>}<span><span>|</span>|</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>$

其中，$\mathrm{\&phi;}\left(X\right|{\mathrm{\&mu;}}_i,{\mathrm{\&Sigma;}}_i)=\frac{\exp [-\frac{1}{2}{(X-{\mathrm{\&mu;}}_i)}^T{\mathrm{\&Sigma;}}_i^{-1}(X-{\mathrm{\&mu;}}_i)]}{\sqrt{{\left(2\mathrm{\&pi;}\right)}^d\left|\det \left({\mathrm{\&Sigma;}}_i\right)\right|}}---\left(2\right)$in,$\mathrm{\&phi;}\left(x\right|{\mathrm{\&mu;}}_i,{\mathrm{\&Sigma;}}_i)=\frac{\exp [-\frac{1}{2}{(x-{\mathrm{\&mu;}}_i)}^T{\mathrm{\&Sigma;}}_i^{-1}(x-{\mathrm{\&mu;}}_i)]}{\sqrt{{\left(2\mathrm{\&pi;}\right)}^d\left|\det \left({\mathrm{\&Sigma;}}_i\right)\right|}}---\left(2\right)$

根据高斯混合模型的定义，本发明定义了点集所表示的数据空间中点与点之间的相关性，可表示为：According to the definition of the Gaussian mixture model, the present invention defines the correlation between points and points in the data space represented by the point set, which can be expressed as:

$\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>i</span>i</span>}}\mathrm{<span><span>\&phi;</span>\&phi;</span>}<span><span>(</span>(</span>\mathrm{<span><span>X</span>x</span>}<span><span>|</span>|</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span>\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>j</span>j</span>}}\mathrm{<span><span>\&phi;</span>\&phi;</span>}<span><span>(</span>(</span>\mathrm{<span><span>X</span>x</span>}<span><span>|</span>|</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>j</span>j</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>j</span>j</span>}}<span><span>)</span>)</span>$

$<span><span>(</span>(</span>\mathrm{<span><span>3</span>3</span>}<span><span>)</span>)</span>$

$<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>i</span>i</span>}}{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>j</span>j</span>}}\mathrm{<span><span>\&phi;</span>\&phi;</span>}<span><span>(</span>(</span>\mathrm{<span><span>X</span>x</span>}<span><span>|</span>|</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span>\mathrm{<span><span>\&phi;</span>\&phi;</span>}<span><span>(</span>(</span>\mathrm{<span><span>X</span>x</span>}<span><span>|</span>|</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>j</span>j</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>j</span>j</span>}}<span><span>)</span>)</span>$

从而，对于点集P所表示的整个数据空间中所有点相关性总和，即该数据空间的全局特征可表示为：Therefore, for the sum of all point correlations in the entire data space represented by the point set P, that is, the global characteristics of the data space can be expressed as:

$\mathrm{<span><span>gmm</span>gmm</span>}<span><span>\_</span>\_</span>\mathrm{<span><span>correlation</span>correlation</span>}<span><span>(</span>(</span>\mathrm{<span><span>P</span>P</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>i</span>i</span>}}{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>j</span>j</span>}}<span><span>\&Integral;</span>\&Integral;</span>\mathrm{<span><span>\&phi;</span>\&phi;</span>}<span><span>(</span>(</span>\mathrm{<span><span>X</span>x</span>}<span><span>|</span>|</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span>\mathrm{<span><span>\&phi;</span>\&phi;</span>}<span><span>(</span>(</span>\mathrm{<span><span>X</span>x</span>}<span><span>|</span>|</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>j</span>j</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>j</span>j</span>}}<span><span>)</span>)</span>\mathrm{<span><span>dX</span>wxya</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4</span>4</span>}<span><span>)</span>)</span>$

对于3维点集P表示的3维数据空间经过投影变换，可形成3个1维数据空间；每个1维数据空间可使用混合高斯模型进行表示，其表示形式与(4)一致；For the 3-dimensional data space represented by the 3-dimensional point set P, three 1-dimensional data spaces can be formed through projection transformation; each 1-dimensional data space can be represented by a mixed Gaussian model, and its representation form is consistent with (4);

假设，需要进行配准的两个点集，分别是同一数据空间不同的采样结果，因此它们代表了同一的数据空间，其相应的投影变换形成的子空间也是一致的，对应子空间的点与点之间相关性总和也可认为是接近相等的；基于上述思想，刚体点集配准问题可以转变为最小化式(6)所表示的目标函数，M_l和S_l分别表示两个点集代表的对应子空间。Assume that the two point sets that need to be registered are different sampling results of the same data space, so they represent the same data space, and the subspace formed by the corresponding projection transformation is also consistent, and the points corresponding to the subspace are consistent with The sum of the correlations between points can also be considered to be nearly equal; based on the above ideas, the registration problem of rigid body point sets can be transformed into the objective function represented by the minimization formula (6), and M_l and S_l represent two point sets representing the corresponding subspace of .

dRMS_l＝(gmm_correlation(M_l)-gmm_correlation(S_l))²     (6)dRMS_l ＝(gmm_correlation(M_l )-gmm_correlation(S_l ))² (6)

在进行点集配准的过程中，假设表示整个数据空间的高斯混合模型各个混合分量是均匀分布的，即式(4)中的同时，各个混合分量的协方差矩阵是一致的，即式(4)中的∑_i＝∑_j；In the process of point set registration, it is assumed that each mixed component of the Gaussian mixture model representing the entire data space is uniformly distributed, that is, in formula (4) At the same time, the covariance matrix of each mixed component is consistent, that is, ∑_i = ∑_j in formula (4);

(2)无序点自动匹配方法(2) Unordered point automatic matching method

将待匹配的点集按照点与点之间的距离关系映射到新的点集空间，然后根据距离阈值与目标点集通过剪枝的方法获得最终的匹配关系；该方法大大提高了导航配准精度和效率；Map the point set to be matched to a new point set space according to the distance relationship between points and points, and then obtain the final matching relationship by pruning according to the distance threshold and the target point set; this method greatly improves navigation registration. precision and efficiency;

其包括步骤为：It includes the steps of:

①获取手术真实场景中标记点做为目标点集，获取步骤(1)中初步配准结果中的特征点做为待匹配点集；① Obtain the marked points in the real surgical scene as the target point set, and obtain the feature points in the preliminary registration result in step (1) as the point set to be matched;

②从待匹配点集中取出四个点，对其中每一个点获得与其他三个点之间的距离关系并按照一定的顺序进行排列，形成一个新的点的空间描述；② Take four points from the set of points to be matched, and obtain the distance relationship between each point and the other three points and arrange them in a certain order to form a new spatial description of points;

③对四个点的新的空间描述做如下处理：每两个点对应元素之间做差值并取绝对值然后求和；取所有和值中的最小值；③The new spatial description of the four points is processed as follows: make a difference between the corresponding elements of each two points and take the absolute value and then sum; take the minimum value of all sums;

④对待匹配点集中所有的四个点的组合重复上述步骤②和步骤③中的操作，获得步骤③中所有最小值中的最大值对应的四个点的组合；④Repeat the operations in the above steps ② and ③ for the combination of all four points in the matching point set to obtain the combination of four points corresponding to the maximum value among all the minimum values in step ③;

⑤对目标点集做四个点的排列，每一组排列分别与上述步骤④中获得的四个点的组合做剪枝，逐步排除不符合阈值判定的目标点集的排列；⑤ Arrangement of four points on the target point set, and each group of arrangement is pruned with the combination of the four points obtained in the above step ④, and gradually excludes the arrangement of the target point set that does not meet the threshold judgment;

⑥最后获得与待匹配点集相对应的目标点集的一组排列。⑥Finally, a set of arrangement of the target point set corresponding to the point set to be matched is obtained.

上述实施例的结果表明，本发明解决了基于点匹配的的空间配准弊端；所述方法为一种全自动的图像病人空间配准方法，减少了医生的工作量；该方法还是一种全局优化的点集配准方法，降低了初始位置对点集配准方法的影响；本发明提高了配准效率和精度，减小了配准误差；此外，所述方法实施简单，精度可靠，便于临床应用，可集成在现有导航系统中，从而大幅度提高导航系统精度。The results of the above embodiments show that the present invention solves the disadvantages of spatial registration based on point matching; the method is a fully automatic image patient spatial registration method, which reduces the workload of doctors; the method is also a global The optimized point set registration method reduces the influence of the initial position on the point set registration method; the invention improves the registration efficiency and accuracy, and reduces the registration error; in addition, the method is simple to implement, reliable in accuracy, and convenient for clinical application , can be integrated in the existing navigation system, thereby greatly improving the accuracy of the navigation system.

Claims (5)

Translated fromChinese

1.一种高精度自动神经导航空间配准方法，其特征在于，包括步骤：1. A high-precision automatic neuronavigation space registration method, is characterized in that, comprises steps:(1)采用基于高斯混合模型的全局优化点集配准方法，将基于激光扫描仪获得的点云与CT获得的点云得到两个点云之间的坐标变换实现初步配准；(1) Using the global optimization point set registration method based on the Gaussian mixture model, the point cloud obtained based on the laser scanner and the point cloud obtained by CT are obtained by coordinate transformation between the two point clouds to achieve preliminary registration;(2)采用无序点自动配准的方法，将初步配准的结果与神经导航中通过CT重建出来的病人空间再次进行配准。(2) Using the method of automatic registration of unordered points, the results of preliminary registration are re-registered with the patient space reconstructed by CT in neuronavigation.2.根据权利要求1所述的方法，其特征在于，所述步骤(1)中，用激光扫描仪获得的点云和CT获得的点云采用基于高斯混合模型的全局优化点集配准方法实现配准。2. method according to claim 1, is characterized in that, in described step (1), the point cloud that obtains with laser scanner and the point cloud that CT obtains adopts the global optimization point set registration method based on Gaussian mixture model to realize Registration.3.根据权利要求1所述的方法，其特征在于，所述步骤(2)中，将初步配准结果与神经导航中通过CT重建出来的病人空间采用无序点自动配准的方法再次进行配准。3. The method according to claim 1, characterized in that, in the step (2), the preliminary registration result and the patient space reconstructed by CT in neuronavigation are carried out again using the method of automatic registration of disordered points Registration.4.根据权利要求1所述的方法，其特征在于，所述步骤(1)中基于高斯混合模型的全局优化点集配准方法为，将进行配准的点集看作一个整体，将点集内点与点在整体空间和子空间的相关性作为点集的特征，实施配准；4. method according to claim 1, is characterized in that, in the described step (1), the global optimization point set registration method based on Gaussian mixture model is, regards the point set that registers as a whole, regards the point set The correlation between the inner point and the point in the overall space and subspace is used as the feature of the point set, and the registration is implemented;高斯混合模型的概率密度函数表示为：The probability density function of the Gaussian mixture model is expressed as:$\mathrm{<span><span>f</span>f</span>}<span><span>(</span>(</span>\mathrm{<span><span>X</span>x</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>i</span>i</span>}}\mathrm{<span><span>\&phi;</span>\&phi;</span>}<span><span>(</span>(</span>\mathrm{<span><span>X</span>x</span>}<span><span>|</span>|</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>$其中，$\mathrm{\&phi;}\left(X\right|{\mathrm{\&mu;}}_i,{\mathrm{\&Sigma;}}_i)=\frac{\exp [-\frac{1}{2}{(X-{\mathrm{\&mu;}}_i)}^T{\mathrm{\&Sigma;}}_i^{-1}(X-{\mathrm{\&mu;}}_i)]}{\sqrt{{\left(2\mathrm{\&pi;}\right)}^d\left|\det \left({\mathrm{\&Sigma;}}_i\right)\right|}}---\left(2\right)$in,$\mathrm{\&phi;}\left(x\right|{\mathrm{\&mu;}}_i,{\mathrm{\&Sigma;}}_i)=\frac{\exp [-\frac{1}{2}{(x-{\mathrm{\&mu;}}_i)}^T{\mathrm{\&Sigma;}}_i^{-1}(x-{\mathrm{\&mu;}}_i)]}{\sqrt{{\left(2\mathrm{\&pi;}\right)}^d\left|\det \left({\mathrm{\&Sigma;}}_i\right)\right|}}---\left(2\right)$根据高斯混合模型的定义，定义点集所表示的数据空间中点与点之间的相关性，表示为：According to the definition of the Gaussian mixture model, define the correlation between points in the data space represented by the point set, expressed as:$\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>i</span>i</span>}}\mathrm{<span><span>\&phi;</span>\&phi;</span>}<span><span>(</span>(</span>\mathrm{<span><span>X</span>x</span>}<span><span>|</span>|</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span>\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>j</span>j</span>}}\mathrm{<span><span>\&phi;</span>\&phi;</span>}<span><span>(</span>(</span>\mathrm{<span><span>X</span>x</span>}<span><span>|</span>|</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>j</span>j</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>j</span>j</span>}}<span><span>)</span>)</span>$$<span><span>(</span>(</span>\mathrm{<span><span>3</span>3</span>}<span><span>)</span>)</span>$$<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>i</span>i</span>}}{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>j</span>j</span>}}\mathrm{<span><span>\&phi;</span>\&phi;</span>}<span><span>(</span>(</span>\mathrm{<span><span>X</span>x</span>}<span><span>|</span>|</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span>\mathrm{<span><span>\&phi;</span>\&phi;</span>}<span><span>(</span>(</span>\mathrm{<span><span>X</span>x</span>}<span><span>|</span>|</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>j</span>j</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>j</span>j</span>}}<span><span>)</span>)</span>$对于点集P所表示的整个数据空间中所有点相关性总和，即该数据空间的全局特征表示为：For the sum of all point correlations in the entire data space represented by the point set P, that is, the global feature of the data space is expressed as:$\mathrm{<span><span>gmm</span>gmm</span>}<span><span>\_</span>\_</span>\mathrm{<span><span>correlation</span>correlation</span>}<span><span>(</span>(</span>\mathrm{<span><span>P</span>P</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>i</span>i</span>}}{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>j</span>j</span>}}<span><span>\&Integral;</span>\&Integral;</span>\mathrm{<span><span>\&phi;</span>\&phi;</span>}<span><span>(</span>(</span>\mathrm{<span><span>X</span>x</span>}<span><span>|</span>|</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span>\mathrm{<span><span>\&phi;</span>\&phi;</span>}<span><span>(</span>(</span>\mathrm{<span><span>X</span>x</span>}<span><span>|</span>|</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}_{\mathrm{<span><span>j</span>j</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>j</span>j</span>}}<span><span>)</span>)</span>\mathrm{<span><span>dX</span>wxya</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4</span>4</span>}<span><span>)</span>)</span>$对于3维点集P表示的3维数据空间经过投影变换，形成3个1维数据空间；每个1维数据空间可使用混合高斯模型进行表示，其表示形式与上述公式(4)一致；The 3-dimensional data space represented by the 3-dimensional point set P undergoes projection transformation to form three 1-dimensional data spaces; each 1-dimensional data space can be represented by a mixed Gaussian model, and its representation form is consistent with the above formula (4);进行配准的两个点集，分别是同一数据空间不同的采样结果，其代表了同一的数据空间，其相应的投影变换形成的子空间也是一致的，对应子空间的点与点之间相关性总和也是接近相等；刚体点集配准转变为最小化式(6)所表示的目标函数，M_l和S_l分别表示两个点集代表的对应子空间，The two point sets for registration are different sampling results of the same data space, which represent the same data space, and the subspace formed by the corresponding projection transformation is also consistent, and the points corresponding to the subspace are related to each other. The sum of the properties is also close to equal; the registration of the rigid body point set is transformed into the objective function represented by the minimization formula (6), M_l and S_l respectively represent the corresponding subspaces represented by the two point sets,dRMS_l＝(gmm_correlation(M_l)-gmm_correlation(S_l))²         (6)dRMS_l ＝(gmm_correlation(M_l )-gmm_correlation(S_l ))² (6)在进行点集配准的过程中，表示整个数据空间的高斯混合模型各个混合分量是均匀分布的，即式(4)中的同时，各个混合分量的协方差矩阵是一致的，即式(4)中的∑_i＝∑_j。In the process of point set registration, each mixed component of the Gaussian mixture model representing the entire data space is uniformly distributed, that is, in formula (4) At the same time, the covariance matrix of each mixed component is consistent, that is, ∑_i =∑_j in formula (4).5.根据权利要求1所述的方法，其特征在于，所述步骤(2)中无序点自动匹配方法为，将待匹配的点集按照点与点之间的距离关系映射到新的点集空间，然后根据距离阈值与目标点集通过剪枝的方法获得最终的匹配关系，其包括步骤为：5. The method according to claim 1, wherein the automatic matching method of disordered points in the step (2) is to map the point set to be matched to a new point according to the distance relationship between points and points set space, and then according to the distance threshold and the target point set, the final matching relationship is obtained by pruning, which includes the following steps:①获取手术真实场景中标记点做为目标点集，获取所述步骤(1)中初步配准结果中的特征点做为待匹配点集；① Obtain the marked points in the real scene of the operation as the target point set, and obtain the feature points in the preliminary registration result in the step (1) as the point set to be matched;②从待匹配点集中取出四个点，对其中每一个点获得与其他三个点之间的距离关系并按照一定的顺序进行排列，形成一个新的点的空间描述；② Take four points from the set of points to be matched, and obtain the distance relationship between each point and the other three points and arrange them in a certain order to form a new spatial description of points;③对四个点的新的空间描述做如下处理：每两个点对应元素之间做差值并取绝对值然后求和；取所有和值中的最小值；③The new spatial description of the four points is processed as follows: make a difference between the corresponding elements of each two points and take the absolute value and then sum; take the minimum value of all sums;④对待匹配点集中所有的四个点的组合重复上述步骤②和步骤③中的操作，获得步骤③中所有最小值中的最大值对应的四个点的组合；④Repeat the operations in the above steps ② and ③ for the combination of all four points in the matching point set to obtain the combination of four points corresponding to the maximum value among all the minimum values in step ③;⑤对目标点集做四个点的排列，每一组排列分别与上述步骤④中获得的四个点的组合做剪枝，逐步排除不符合阈值判定的目标点集的排列；⑤ Arrangement of four points on the target point set, and each group of arrangement is pruned with the combination of the four points obtained in the above step ④, and gradually excludes the arrangement of the target point set that does not meet the threshold judgment;⑥最后获得与待匹配点集相对应的目标点集的一组排列。⑥Finally, a set of arrangement of the target point set corresponding to the point set to be matched is obtained.