In this paper, a shape-constrained iterative algorithm is proposed to register a rigid template point-cloud to a given reference point-cloud. The algorithm embeds a shape-based similarity constraint into the principle of gravitation. The shape-constrained gravitation, as induced by the reference, controls the movement of the template such that at each iteration, the template better aligns with the reference in terms of shape. This constraint enables the alignment in difficult conditions indtroduced by change (presence of outliers and/or missing parts), translation, rotation and scaling. We discuss efficient implementation techniques with least manual intervention. The registration is shown to be useful for change detection in the 3D point-cloud. The algorithm is compared with three state-of-the-art registration approaches. The experiments are done on both synthetic and real-world data. The proposed algorithm is shown to perform better in the presence of big rotation, structured and unstructured outliers and missing data.