scholarly journals 3D Reconstruction with Coronary Artery Based on Curve Descriptor and Projection Geometry-Constrained Vasculature Matching

Information ◽  
2022 ◽  
Vol 13 (1) ◽  
pp. 38
Author(s):  
Jijun Tong ◽  
Shuai Xu ◽  
Fangliang Wang ◽  
Pengjia Qi
Keyword(s):  
Coronary Artery ◽  
3D Reconstruction ◽  
Trust Region Method ◽  
Trust Region ◽  
Geometric Transformation ◽  
Error Matrix ◽  
Point Pair ◽  
Marquardt Algorithm ◽  
Projection Geometry ◽  
Point Set

This paper presents a novel method based on a curve descriptor and projection geometry constrained for vessel matching. First, an LM (Leveberg–Marquardt) algorithm is proposed to optimize the matrix of geometric transformation. Combining with parameter adjusting and the trust region method, the error between 3D reconstructed vessel projection and the actual vessel can be minimized. Then, CBOCD (curvature and brightness order curve descriptor) is proposed to indicate the degree of the self-occlusion of blood vessels during angiography. Next, the error matrix constructed from the error of epipolar matching is used in point pairs matching of the vascular through dynamic programming. Finally, the recorded radius of vessels helps to construct ellipse cross-sections and samples on it to get a point set around the centerline and the point set is converted to mesh for reconstructing the surface of vessels. The validity and applicability of the proposed methods have been verified through experiments that result in the significant improvement of 3D reconstruction accuracy in terms of average back-projection errors. Simultaneously, due to precise point-pair matching, the smoothness of the reconstructed 3D coronary artery is guaranteed.

Shape context and projection geometry constrained vasculature matching for 3D reconstruction of coronary artery

2016 ◽  
Vol 195 ◽  
pp. 65-73 ◽  
Author(s):  
Ruoxiu Xiao ◽  
Jian Yang ◽  
Jingfan Fan ◽  
Danni Ai ◽  
Guangzhi Wang ◽  
...  
Keyword(s):  
Coronary Artery ◽  
3D Reconstruction ◽  
Shape Context ◽  
Projection Geometry

scholarly journals An Active Set Trust-Region Method for Bound-Constrained Optimization

2021 ◽  
Author(s):  
Morteza Kimiaei
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Positive Definiteness ◽  
Active Set ◽  
Sufficient Descent Condition ◽  
Critical Measure ◽  
Complexity Result ◽  
Bound Constrained Optimization

AbstractThis paper discusses an active set trust-region algorithm for bound-constrained optimization problems. A sufficient descent condition is used as a computational measure to identify whether the function value is reduced or not. To get our complexity result, a critical measure is used which is computationally better than the other known critical measures. Under the positive definiteness of approximated Hessian matrices restricted to the subspace of non-active variables, it will be shown that unlimited zigzagging cannot occur. It is shown that our algorithm is competitive in comparison with the state-of-the-art solvers for solving an ill-conditioned bound-constrained least-squares problem.

Based on GA Mixed with Trust Region Method Solving Nonlinear Least Square Problems

2011 ◽  
Vol 141 ◽  
pp. 92-97
Author(s):  
Miao Hu ◽  
Tai Yong Wang ◽  
Bo Geng ◽  
Qi Chen Wang ◽  
Dian Peng Li
Keyword(s):  
Genetic Algorithm ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Least Square ◽  
Search Range ◽  
Genetic Search ◽  
Region Method ◽  
Unconstrained Optimization Problems ◽  
Least Square Problems

Nonlinear least square is one of the unconstrained optimization problems. In order to solve the least square trust region sub-problem, a genetic algorithm (GA) of global convergence was applied, and the premature convergence of genetic algorithms was also overcome through optimizing the search range of GA with trust region method (TRM), and the convergence rate of genetic algorithm was increased by the randomness of the genetic search. Finally, an example of banana function was established to verify the GA, and the results show the practicability and precision of this algorithm.

A BFGS trust-region method for nonlinear equations

Computing ◽  
2011 ◽  
Vol 92 (4) ◽  
pp. 317-333 ◽  
Author(s):  
Gonglin Yuan ◽  
Zengxin Wei ◽  
Xiwen Lu
Keyword(s):  
Nonlinear Equations ◽  
Trust Region Method ◽  
Trust Region ◽  
Region Method

scholarly journals A Nonmonotone Weighting Self-Adaptive Trust Region Algorithm for Unconstrained Nonconvex Optimization

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Yunlong Lu ◽  
Weiwei Yang ◽  
Wenyu Li ◽  
Xiaowei Jiang ◽  
Yueting Yang
Keyword(s):  
Nonconvex Optimization ◽  
Line Search ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Search Technique ◽  
Trust Region Algorithm ◽  
Unconstrained Optimization Problems ◽  
Line Search Technique ◽  
Self Adaptive

A new trust region method is presented, which combines nonmonotone line search technique, a self-adaptive update rule for the trust region radius, and the weighting technique for the ratio between the actual reduction and the predicted reduction. Under reasonable assumptions, the global convergence of the method is established for unconstrained nonconvex optimization. Numerical results show that the new method is efficient and robust for solving unconstrained optimization problems.

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