高斯过程下的CMA-ES在医学图像配准中的应用
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摘要
为了改进协方差矩阵自适应进化策略(CMA-ES)的性能,提出了一种高斯过程协助下的协方差矩阵自适应进化策略(GPACMA-ES)。该策略利用CMA-ES中的协方差矩阵构建核函数,引入高斯过程,在线学习历史经验,并根据历史经验预测全局最优解的最有前景区域,有效地降低了适应度函数的评价次数。同时,为了提高群体的搜索效率,引入了置信区间。群体在置信区间内更高效地采样,使得算法具备更快的收敛速度和全局寻优能力。最后,将GPACMA-ES算法应用于医学图像配准中,配准精度和效率均高于标准的CMA-ES算法。
A gaussian process assisted covariance matrix adaptation evolution strategy(GPACMA-ES)optimization algorithm was proposed in this paper.The kernel function used in the GPACMA-ES algorithm is constructed by the covariance matrix.Taking advantage of the Gaussian process,which plays a key role in both online learning about the historic experience and predicting the promising region which contains globally optimal solution,the frequency of calculating fitness function in the algorithm is reduced markedly.Meanwhile,in order to improve the efficiency of the algorithm,GPACMA-ES is sampling in the trust region.So it has rapid convergence and good global search capacity.Finally,a case study of medical image registration is examined to demonstrate the ability and applicability of the GPACMA-ES.Experiment results show that GPACMA-ES is proper for medical image registration than CMA-ES,and it has a better effect on the precision of registration while reducing the number of calculation of the fitness function.
A gaussian process assisted covariance matrix adaptation evolution strategy(GPACMA-ES)optimization algorithm was proposed in this paper.The kernel function used in the GPACMA-ES algorithm is constructed by the covariance matrix.Taking advantage of the Gaussian process,which plays a key role in both online learning about the historic experience and predicting the promising region which contains globally optimal solution,the frequency of calculating fitness function in the algorithm is reduced markedly.Meanwhile,in order to improve the efficiency of the algorithm,GPACMA-ES is sampling in the trust region.So it has rapid convergence and good global search capacity.Finally,a case study of medical image registration is examined to demonstrate the ability and applicability of the GPACMA-ES.Experiment results show that GPACMA-ES is proper for medical image registration than CMA-ES,and it has a better effect on the precision of registration while reducing the number of calculation of the fitness function.
引文
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[18]SHAHRIARI B,SWERSKY K,WANG Z,et al.Taking the Human Out of the Loop:A Review of Bayesian Optimization[J].Proceedings of the IEEE,2015,104(1):1-24.
[19]SNOEK J,LAROCHELLE H,ADAMS R P.Practical bayesian optimization of machine learning algorithms[C]∥Advances in Neural Information Processing Systems.MIT Press,2012:2951-2959.
[20]COLLINS D L,ZIJDENBOS A P,KOLLOKIAN V,et al.Design and construction of a realistic digital brain phantom[J].IEEE Transactions on Medical Imaging,1998,17(3):463-468.
[2] SONG G,HAN J,ZHAO Y,et al.A Review on Medical Image Registration as an Optimization Problem[J].Current Medical Imaging Reviews,2017,13(3):274-283.
[3] PANDA R,AGRAWAL S,SAHOO M,et al.A novel evolutionary rigid body docking algorithm for medical image registration[J].Swarm&Evolutionary Computation,2017,33:108-118.
[4] WINTER S,BRENDEL B,PECHLIVANIS I,et al.Registration of CT and intraoperative 3-D ultrasound images of the spine using evolutionary and gradient-based methods[J].IEEE Transactions on Evolutionary Computation,2008,12(3):284-296.
[5]刘哲,宋余庆,王栋栋.自适应变异差分算法与Powell算法相结合的医学图像配准[J].计算机科学,2017,44(11):297-300.
[6] HANSEN N.The CMA Evolution Strategy:A Tutorial[J/OL].http://www2.fiit.stuba.sk/~kvasnicka/Seminar_of_AI/Hansen_CMA_tutorial.pdf.
[7]李焕哲,吴志健,汪慎文,等.协方差矩阵自适应演化策略学习机制综述[J].电子学报,2017,45(1):238-245.
[8] NISHID K,AKIMOTO Y.Population Size Adaptation for the CMA-ES Based on the Estimation Accuracy of the Natural Gradient[C]∥Genetic and Evolutionary Computation Conference.ACM,2016:237-244.
[9] MOHAMMADI H,RICHE R L,TOUBOUL E.Making EGO and CMA-ES Complementary for Global Optimization[M]∥Learning and Intelligent Optimization.Springer International Publishing,2015:287-292.
[10]BOUZARKOUNA Z,AUGER A,DING D Y.Investigating the Local-Meta-Model CMAES for Large Population Sizes[M]∥Applications of Evolutionary Computation.Springer Berlin Heidelberg,2010:402-411.
[11]LOSHCHILOV I,SCHOENAUER M.Comparison-based optimizers need comparison-based surrogates[C]∥International Conference on Parallel Problem Solving From Nature.SpringerVerlag,2010:364-373.
[12]KRUISSELBRINK J W,EMMERICH M T M,DEUTZ A H,et al.A robust optimization approach using Kriging metamodels for robustness approximation in the CMAES[C]∥Evolutionary Computation.IEEE,2010:1-8.
[13]别术林.基于互信息的医学图像配准算法研究[D].北京:北京交通大学,2014.
[14]HANSEN N,OSTERMEIER A.Adapting arbitrary normal mutation distributions in evolution strategies:the covariance matrix adaptation[C]∥IEEE International Conference on Evolutionary Computation.IEEE,1996:312-317.
[15]HOWARD W R.Pattern Recognition and Machine Learning[M]∥Pattern Recognition and Machine Learning.Springer,2006:461-462.
[16]SEEGER M.Gaussian processes for machine learning[J].International Journal of Neural Systems,2004,14(2):69-106.
[17]LOSHCHILOV I,SCHOENAUER M,SEBAG M.Self-adaptive surrogate-assisted covariance matrix adaptation evolution strategy[C]∥Conference on Genetic and Evolutionary Computation.ACM,2012:321-328.
[18]SHAHRIARI B,SWERSKY K,WANG Z,et al.Taking the Human Out of the Loop:A Review of Bayesian Optimization[J].Proceedings of the IEEE,2015,104(1):1-24.
[19]SNOEK J,LAROCHELLE H,ADAMS R P.Practical bayesian optimization of machine learning algorithms[C]∥Advances in Neural Information Processing Systems.MIT Press,2012:2951-2959.
[20]COLLINS D L,ZIJDENBOS A P,KOLLOKIAN V,et al.Design and construction of a realistic digital brain phantom[J].IEEE Transactions on Medical Imaging,1998,17(3):463-468.