Conventional registration algorithms are mostly concerned with rigid-body transformation parameters between a pair of 3D range images. Our proposed framework aims to determine, in a unified manner, not only such rigid transformation parameters but also various deformation parameters, assuming that the deformation we handle here is strictly defined by some parameterized formulation derived from the deformation mechanism. While conventional registration algorithms usually calcurate six parameters (three translation and three rotation parameters), our proposed algorithm estimates deformation parameters as well. In this paper, we describe how we formulated such an algorithm, implemented it, and evaluated its performance.