The fusion of computed tomography (CT) and ultrasound (US) image can enhance lesion detection ability and improve the success rate of liver interventional radiology. The image-based fusion methods encounter the challenge of registration initialization due to the random scanning pose and limited field of view of US. Existing automatic methods those used vessel geometric information and intensity-based metric are sensitive to parameters and have low success rate. The learning-based methods require a large number of registered datasets for training. The aim of this study is to provide a fully automatic and robust US-3D CT registration method without registered training data and user-specified parameters assisted by the revolutionary deep learning-based segmentation, which can further be used for preparing training samples for the study of learning-basedmethods. We propose a fully automatic CT-3D US registration method by two improved registration metrics. We propose to use 3D U-Net-based multi-organ segmentation of US and CT to assist the conventional registration. The rigid transform is searched in the space of any paired vessel bifurcation planes where the best transform is decided by a segmentation overlap metric, which is more related to the segmentation precision than Dice coefficient. In nonrigid registration phase, we propose a hybrid context and edge based image similarity metric with a simple mask that can remove most noisy US voxels to guide the B-spline transform registration. We evaluate our method on 42 paired CT-3D US datasets scanned with two different US devices from two hospitals. We compared our methods with other exsiting methods with both quantitative measures of target registration error (TRE) and the Jacobian determinent with paired t-test and qualitative registration imagingresults. The results show that our method achieves fully automatic rigid registration TRE of 4.895 mm, deformable registration TRE of 2.995 mm in average, which outperforms state-of-the-art automatic linear methods and nonlinear registration metrics with paired t-test's p value less than 0.05. The proposed overlap metric achieves better results than self similarity description (SSD), edge matching (EM), and block matching (BM) with p values of 1.624E-10, 4.235E-9, and 0.002, respectively. The proposed hybrid edge and context-based metric outperforms context-only, edge-only, and intensity statistics-only-based metrics with p values of 0.023, 3.81E-5, and 1.38E-15, respectively. The 3D US segmentation has achieved mean Dice similarity coefficient (DSC) of 0.799, 0.724, 0.788, and precision of 0.871, 0.769, 0.862 for gallbladder, vessel, and branch vessel,respectively. The deep learning-based US segmentation can achieve satisfied result to assist robust conventional rigid registration. The Dice similarity coefficient-based metrics, hybrid context, and edge image similarity metric contribute to robust and accurateregistration.