心脏运动估计中的曲面结构点集匹配算法研究
发布时间：2018-12-14 10:51
【摘要】：随着人们生活水平的提高,心血管疾病已经成为人类的头号杀手,严重威胁着人类的健康。心血管疾病发病急、隐蔽性强、死亡率高,因此对心血管疾病的早期诊断和风险评估尤为重要。左心室心肌的运动情况能够反映心脏的供血功能,为多种心脏疾病的诊断提供重要依据。通过对左心室的运动估计,能够确定每个心肌点的运动轨迹,得到对临床诊断有参考意义的形变函数和可视化图形。点集匹配是常见的左心室运动估计方法,但是现有的点集匹配方法仅仅考虑了点间距离,缺乏对点集形状的考虑。本文针对此问题提出了一种基于曲面结构的点集匹配算法,主要包括以下三个部分:其一,为了描述左心室的曲面结构特征,提出了基于张量投票的曲面特征提取算法。我们将每个点作为投票点,其对应的近似曲面特征方向作为投票方向,向周围的点进行投票,然后每个点对接收到的票数进行累积分解,得出纠正后的方向。模拟数据以及真实的左心室数据实验结果验证了张量投票算法的有效性。其二,针对现有的点集匹配算法仅仅考虑点间距离,缺乏对点集形状的考虑等问题,提出了一种基于曲面结构的点集匹配算法并将其应用于心脏的运动估计。我们将左心室的曲面特征描述引入到点集匹配算法中,提出了一个即约束点间距离又约束点集形状的代价函数,详细推导了拟牛顿法(Quasi-Newton Method,QN)的求解过程以优化该代价函数,得到左心室运动的变换参数,估计左心室心肌点的运动轨迹。多组左心室的实验结果证明我们提出的代价函数是可行的。其三,针对QN算法在高维参数空间出现的发散问题,提出了用随机梯度下降算法(Stochastic Gradient Descent,SGD)来优化代价函数的方法,推导了SGD算法的梯度和算法流程。针对SGD算法收敛精度不如QN算法这个问题,提出了SGD+QN的优化算法,先通过SGD方法来控制变换参数,使收敛于一个较稳定状态,然后运用QN算法来进一步提高其收敛精度。实验结果证明,在高维空间时,SGD+QN的方法即能保证算法的稳定性,又能保证算法的精度。本文针对左心室曲面结构的提取、左心室点集匹配的精确性及稳定性三个方面进行了初步研究,研究成果较好地解决了基于点集匹配的左心室运动估计方法中存在的一些问题。
[Abstract]:With the improvement of people's living standard, cardiovascular disease has become the leading killer of human beings, which is a serious threat to human health. Cardiovascular disease is urgent, hidden and high mortality, so it is very important for early diagnosis and risk assessment of cardiovascular disease. The left ventricular motion can reflect the blood supply function of the heart and provide important basis for the diagnosis of various heart diseases. By estimating the motion of the left ventricle, the motion track of each myocardial point can be determined, and the deformation function and visual figure which are useful for clinical diagnosis can be obtained. Point set matching is a common method for estimating left ventricular motion, but the existing point set matching methods only consider the distance between points, and lack the consideration of point set shape. In this paper, a point set matching algorithm based on curved surface structure is proposed, which includes the following three parts: firstly, in order to describe the surface features of the left ventricle, a surface feature extraction algorithm based on Zhang Liang voting is proposed. We take each point as the polling point, and the corresponding approximate surface characteristic direction as the voting direction, and vote to the surrounding point, and then each point cumulatively decomposes the number of votes received to get the corrected direction. The experimental results of simulated data and real left ventricular data verify the effectiveness of Zhang Liang voting algorithm. Secondly, a point set matching algorithm based on curved surface structure is proposed and applied to the motion estimation of the heart, aiming at the problem that the existing point set matching algorithm only considers the distance between points and the shape of the point set. In this paper, we introduce the curved surface characteristic description of left ventricle into the point set matching algorithm, and propose a cost function of the constraint point set shape as well as the distance between the constrained points. The quasi Newton method (Quasi-Newton Method,) is derived in detail. In order to optimize the cost function, the transformation parameters of left ventricular motion are obtained, and the trajectory of left ventricular motion point is estimated. The experimental results of multiple groups of left ventricle show that the proposed cost function is feasible. Thirdly, aiming at the divergence of QN algorithm in high-dimensional parameter space, a stochastic gradient descent algorithm (Stochastic Gradient Descent,SGD) is proposed to optimize the cost function, and the gradient and algorithm flow of SGD algorithm are deduced. In order to solve the problem that the convergence accuracy of SGD algorithm is lower than that of QN algorithm, the optimization algorithm of SGD QN is proposed. Firstly, the transformation parameters are controlled by SGD method to make it converge to a more stable state, and then the convergence accuracy is further improved by using QN algorithm. The experimental results show that the, SGD QN method can not only guarantee the stability of the algorithm, but also ensure the accuracy of the algorithm in high dimensional space. In this paper, the extraction of the curved structure of the left ventricle, the accuracy and stability of the point set matching of the left ventricle are studied preliminarily. The research results solve some problems in the estimation method of the left ventricular motion based on the point set matching.
【学位授予单位】：深圳大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：R54;TP391.41
[Abstract]:With the improvement of people's living standard, cardiovascular disease has become the leading killer of human beings, which is a serious threat to human health. Cardiovascular disease is urgent, hidden and high mortality, so it is very important for early diagnosis and risk assessment of cardiovascular disease. The left ventricular motion can reflect the blood supply function of the heart and provide important basis for the diagnosis of various heart diseases. By estimating the motion of the left ventricle, the motion track of each myocardial point can be determined, and the deformation function and visual figure which are useful for clinical diagnosis can be obtained. Point set matching is a common method for estimating left ventricular motion, but the existing point set matching methods only consider the distance between points, and lack the consideration of point set shape. In this paper, a point set matching algorithm based on curved surface structure is proposed, which includes the following three parts: firstly, in order to describe the surface features of the left ventricle, a surface feature extraction algorithm based on Zhang Liang voting is proposed. We take each point as the polling point, and the corresponding approximate surface characteristic direction as the voting direction, and vote to the surrounding point, and then each point cumulatively decomposes the number of votes received to get the corrected direction. The experimental results of simulated data and real left ventricular data verify the effectiveness of Zhang Liang voting algorithm. Secondly, a point set matching algorithm based on curved surface structure is proposed and applied to the motion estimation of the heart, aiming at the problem that the existing point set matching algorithm only considers the distance between points and the shape of the point set. In this paper, we introduce the curved surface characteristic description of left ventricle into the point set matching algorithm, and propose a cost function of the constraint point set shape as well as the distance between the constrained points. The quasi Newton method (Quasi-Newton Method,) is derived in detail. In order to optimize the cost function, the transformation parameters of left ventricular motion are obtained, and the trajectory of left ventricular motion point is estimated. The experimental results of multiple groups of left ventricle show that the proposed cost function is feasible. Thirdly, aiming at the divergence of QN algorithm in high-dimensional parameter space, a stochastic gradient descent algorithm (Stochastic Gradient Descent,SGD) is proposed to optimize the cost function, and the gradient and algorithm flow of SGD algorithm are deduced. In order to solve the problem that the convergence accuracy of SGD algorithm is lower than that of QN algorithm, the optimization algorithm of SGD QN is proposed. Firstly, the transformation parameters are controlled by SGD method to make it converge to a more stable state, and then the convergence accuracy is further improved by using QN algorithm. The experimental results show that the, SGD QN method can not only guarantee the stability of the algorithm, but also ensure the accuracy of the algorithm in high dimensional space. In this paper, the extraction of the curved structure of the left ventricle, the accuracy and stability of the point set matching of the left ventricle are studied preliminarily. The research results solve some problems in the estimation method of the left ventricular motion based on the point set matching.
【学位授予单位】：深圳大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：R54;TP391.41
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