A large number of relaxation schemes for feature mapping, claimed to be invariantto transformation, have been reported. However, most of them can deal with transformations involving only rotation and translation, but not scaling. To stay away from theissue of scaling, unrealistic assumptions have to be imposed, such as the conjectures thatrange data are available so that objects can be rescaled before mapping, and that objectshapes are complete so that ratios between object shapes and prototypes can be figuredout beforehand. In this paper, we propose a relaxation scheme which is able to be invariant at a time to rotation, translation, as well as scaling. In addition, the proposedscheme can also cope with shapes that may be distorted and incomplete. Our schemehas been tested on both synthetic and real data. Experimental results manifest that theproposed scheme is applicable.