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This paper presents a novel method for respiratory motion compensated reconstruction for cone beam computed tomography (CBCT). The reconstruction is based on a time sequence of motion vector fields, which is generated by a dynamic geometrical object shape model. The dynamic model is extracted from the 2D projection images of the CBCT. The process of the motion extraction is converted into an optimal 3D multiple interrelated surface detection problem, which can be solved by computing a maximum flow in a 4D directed graph. The method was tested on 12 mega-voltage (MV) CBCT scans from three patients. Two sets of motion-artifact-free 3D volumes, full exhale (FE) and full inhale (FI) phases, were reconstructed for each daily scan. The reconstruction was compared with three other motion-compensated approaches based on quantification accuracy of motion and size. Contrast-to-noise ratio (CNR) was also quantified for image quality. The proposed approach has the best overall performance, with a relative tumor volume quantification error of 3.39 3.64% and 8.57 8.31% for FE and FI phases, respectively. The CNR near the tumor area is 3.85 0.42 (FE) and 3.58 3.33 (FI). These results show the clinical feasibility to use the proposed method to reconstruct motion-artifact-free MVCBCT volumes.