Fusing intraoperative 2-D ultrasound (US) frames with preoperative 3-D magnetic resonance (MR) images for guiding interventions has become the clinical gold standard in image-guided prostate cancer biopsy. However, developing an automatic image registration system for this application is challenging because of the modality gap between US/MR and the dimensionality gap between 2-D/3-D data. To overcome these challenges, we propose a novel US frame-to-volume registration (FVReg) pipeline to bridge the dimensionality gap between 2-D US frames and 3-D US volume. The developed pipeline is implemented using deep neural networks, which are fully automatic without requiring external tracking devices. The framework consists of three major components, including one) a frame-to-frame registration network (Frame2Frame) that estimates the current frame's 3-D spatial position based on previous video context, two) a frame-to-slice correction network (Frame2Slice) adjusting the estimated frame position using the 3-D US volumetric information, and three) a similarity filtering (SF) mechanism selecting the frame with the highest image similarity with the query frame. We validated our method on a clinical dataset with 618 subjects and tested its potential on real-time 2-D-US to 3-D-MR fusion navigation tasks. The proposed FVReg achieved an average target navigation error of 1.93 mm at 5-14 fps. Our source code is publicly available at https://github.com/DIAL-RPI/Frame-to-Volume-Registration.