Application of Jacobian determinant of reverse deformation field to evaluation of deformation registration algorithm
Objective To effectively quantify and evaluate the quality of different deformation registration algorithms,in order to enhance the possibility of implementing deformation registration in clinical practice.Methods The Jacobian determinant mean(JDM)is proposed based on the Jacobian determinant(JD)of displacement vector field(DVF),and the Jacobian determinant error(DJDE)is introduced by incorporating the JD of the inverse DVF.The optical flow method(OF-DIR)and fast demons method with elastic regularization(FD-DIR)were tested on nasopharyngeal and lung cancer datasets.Finally,JDM and DJDE with the Jacobian determinant negative percentage(JDNP),inverse consistency error(ICE)and normalized mean square error(NMSE)were used to evaluate the registration algorithms and compare the differences evaluation indicators in different tumor images and different algorithms,and the receiver operating curve(ROC)was analyzed in evaluation.Results In lung cancer,OF-DIR outperformed FD-DIR in terms of JDM,NMSE,DJDE and ICE,and the difference was statistically significant(z=-2.24,-4.84,t=4.01,6.54,P＜0.05).In nasopharyngeal carcinoma,DJDE,ICE and NMSE of OF-DIR were superior to FD-DIR,and the difference was statistically significant(t=4.46,-7.49,z=-2.22,P＜0.05),but there was no significant difference in JDM(P＞0.05).In lung cancer and nasopharyngeal carcinoma,JDNP of OF-DIR was worse than that of FD-DIR,and the difference was statistically significant(z=-4.29,-4.02,P＜0.01).In addition,DJDE is more specific and sensitive on ROC curve(AUC=0.77),and has different performance result for tumor images at different sites.Conclusions The JDM and DJDE evaluation metrics proposed are effective for deformation registration algorithms.OF-DIR is suitable for both lung cancer and nasopharyngeal carcinoma,while the influence of organ motion on the registration effect should be considered when using FD-DIR.
Jacobian determinantDeformation registration algorithm evaluationLung cancerNasopharyngeal carcinomaDisplacement vector field
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