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This paper presents a method for cardiac deformation recovery from 3D MR image sequences. The main contribution of this work is that the method is mathematically guaranteed to generate incompressible deformations. This is a desirable property since the myocardium has been shown to be close to incompressible. The method is based on an incompressible deformable model that has a relatively small number of parameters. The myocardium needs to be segmented in an initial frame after which the method automatically determines the tissue deformation everywhere in the myocardium throughout the cardiac cycle. The method has been tested with seven 3D cardiac MR image sequences for the left ventricle, and it has been evaluated against manual segmentation and tagged MR image sequences. The volume agreement between the model and the manual segmentation exceeds 95%, the distance between the model and the manually generated endocardial and epicardial surfaces is 1.5mm on average, and the distance between the model and the intersection of the tagged lines is 0.7mm on average.