In this paper, we present a method for coronary artery motion estimation from 4D cardiac CT angiogram (CTA) data sets. The proposed method potentially allows the construction of patient-specific 4D coronary motion model from pre-operative CTA which can be used for guiding totally endoscopic coronary artery bypass surgery (TECAB). The proposed approach consists of three steps: Firstly, prior to motion tracking, we form a coronary probability atlas from manual segmentations of the CTA scans of a number of subjects. Secondly, the vesselness response image is calculated and enhanced for end-diastolic and end-systolic CTA images in each 4D sequence. Thirdly, we design a special purpose registration framework for tracking the highly localized coronary motion. It combines the coronary probability atlas, the intensity information from the CTA image and the corresponding vesselness response image to fully automate the coronary motion tracking procedure and improve its accuracy. We performed pairwise 3D registration of cardiac time frames by using a multi-channel implementation of the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework, where each channel contains a given level of description of the registered shapes. For validation, we compare the automatically tracked coronaries with those segmented manually at end-diastolic phase for each subject.