In this paper, we investigate conventional registration implementation, consisting of rotation and translation, to design the most precise registration so as to accurately restore the 3D shape of an object. To achieve the most accurate registration, our registration implementation needs robustness against data noise, or initial pose and position of data. To verify the accuracy of our implemented registration, we compare the registration behavior with the registration behavior of conventional methods, and evaluate the numerical accuracy of transformation parameter obtained by our registration. However, registration by rigid-body transformation is not enough for modeling and shape comparison: registration with deformation is needed. In this paper, we extend our robust registration to simultaneously estimate the shape parameter as well as the rigid-body transformation parameter. This extension method assumes that the deformation is formulated strictly from the deformation mechanism. We additionally introduce the applications of our extension method.