Graph Matching And Its Application In Left Ventricular Motion Estimation

Cardiovascular diseases(CVDs)have been the leading cause of death worldwide.It has become increasingly important to strengthen early detection and diagnosis of cardiovascular disease.The left ventricle plays an important role in cardiac cycle.It has a strong heart muscle,which can provide power for blood circulation,reflecting the strength of the heart's blood supply,and can provide a reference for diagnosis.Therefore,accurate calculation of the left ventricular deformation function has important reference significance for clinical diagnosis.In many heart motion estimation methods,because the point set matching is relatively low to the initial conditions,the point set matching algorithm is very suitable for solving the heart motion estimation problem.However,the point set matching method only considers the similarity between points,and lacks the consideration of the overall structural relationship of point sets.When calculating the Correspondence using graph matching,the point set is considered as a graph structure,and the Similarity of points and edges is taken into account at the same time,which makes the matching result more robust.The most critical step before calculating graph matches is to extract the points set of the left ventricle contour.We usually use the image segmentation algorithm to extract the key points of the contour.However,in the cardiac MR image,the target edge is often affected by many factors such as signal-to-noise ratio and volumetric effect,resulting in a weak boundary,making the segmentation of the left ventricle of the heart a difficult problem.To solve this problem,we propose a left ventricular segmentation algorithm based on template matching.Firstly,the left ventricular standard template library is built using expert marker data.And pre-processes each template,including downsampling,normalization,and vectorization.The sparse representation algorithm is used to measure the similarity between candidate image patch and template libraries.The particle swarm optimization(PSO)algorithm is used to search for the target.By finding the optimal solution through multiple iterations,we can obtain the left ventricle region of the heart that we want to segment.However,the traditional graph matching model is a quadratic programming model,which is difficult to optimize and has high computational complexity.To solve this problem,we propose a graph matching algorithm CGM with a convex cost function.To solve the GM problem approximately,we prefer the value of the correspondence matrix X between 0 and 1.Due to the convex nature of our cost function,it is easy to solve.In order to make the relaxed solution naturally approximate the original problem solution,we add affine constraints and sparse constraints to the CGM model.In this paper,the alternating direction multiplication method(ADMM)is employed to optimized the cost function.The original problem is factorized into the minimization of three subproblem,and then three variables are alternately optimized until the optimal solution is obtained..Finally,by evaluating the performance of our approach on the public cardiac dataset,experimental results show that our approach is more robust to estimate the correspondence between contours of LV than existed graph matching algorithms,which achieves more accurate motion estimation results.