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This paper presents a general and efficient method for geometrical calibration of industrial X-ray tomography systems without the use of any phantom. In the field of nondestructive testing (NDT), an accurate numerical model of the object is usually available. By extending the classical volume-to-image registration framework, the method estimates both the parameters related to the position of the object, and those related to the positions and the orientations of the X-ray source, the detector and the rotation axis. Only using the projections data and the numerical model of the object, the values of the geometrical parameters are estimated with a good accuracy. Numerical experiments show that the method provides good results, even if the initialization of the process is far from the real values.