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A method for prospective motion correction of X-ray imaging of the heart is presented. A 3D+t coronary model is reconstructed from a biplane coronary angiogram obtained during free breathing. The deformation field is parameterized by cardiac and respiratory phase, which enables the estimation of the state of the arteries at any phase of the cardiac-respiratory cycle. The motion of the three-dimensional (3-D) coronary model is projected onto the image planes and used to compute a dewarping function for motion correcting the images. The use of a 3-D coronary model facilitates motion correction of images acquired with the X-ray system at arbitrary orientations. The performance of the algorithm was measured by tracking the motion of selected left coronary landmarks using a template matching cross-correlation. In three patients, we motion corrected the same images used to construct their 3D+t coronary model. In this best case scenario, the algorithm reduced the motion of the landmarks by 84%-85%, from mean RMS displacements of 12.8-14.6 pixels to 2.1-2.2 pixels. Prospective motion correction was tested in five patients by building the coronary model from one dataset, and correcting a second dataset. The patient's cardiac and respiratory phase are monitored and used to calculate the appropriate correction parameters. The results showed a 48%-63% reduction in the motion of the landmarks, from a mean RMS displacement of 11.5-13.6 pixels to 4.4-7.1 pixels.