The purpose of this work is to develop a method of estimation of the field of vector velocity to evaluate motion of the heart in view of an assistance with the medical diagnosis. This method is based on the application of a new functional of motion estimation for density images like X- ray CT. Assuming that the images are proportional to some conserved quantity, a new penalty function is defined for motion estimation of a deforming body. We use the theory of linear elasticity to propose a new constraining term. We choose to solve the penalty function with a finite element method. Examples of experiments using simulated images of deforming body are presented. The method is able to take into account compressible or incompressible motion according to the parameter's values.
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