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Shape registration is one of the most challenging problems in computer vision and medical imaging. The process is affected by the way the shape is represented and the form of transformation used to move the source shape. Our paper handles the elastic shape registration by combining the incremental free form deformation (IFFD) with the point-based registration technique using the sum of least squares method. The iterative closest point (ICP) algorithm is used as a criteria to establish point correspondences in each level of the IFFD framework. The free form deformation (FFD) is well known in the literature and works by forming a lattice of control points that can move and hence deform the domain grid points smoothly and uniformly under some shape constrains. The control lattice resolution is increased step by step to achieve a satisfactory deformation of the source shape to exactly match the target boundaries. Our point-based registration is based on least squares that measure the Euclidean distance between source and target boundaries in addition to the shape constrains. The minimization gives a closed form solution of the lattice control points positions. Promising results will be demonstrated for closed and open shapes and structures. The approach can also work for structures that contain multiple parts without any problems.