This paper introduces an automatic coarse-to-fine registration method using an implicit volumetric Vector Field representation for 3D point clouds. Highly discriminative correspondence detection for coarse alignment can be extracted by a process such as cascade-filters. In the cascade-filter approach, a number of interest points is first reduced by using curvature signs and connected component labeling to segment a view into convex and concave disjoint regions. The prominent points are selected for each region based on estimated Mean curvature values of each local segmentation. A new point similarity descriptor is then computed for these selected points to select the best ones for final matching. This multidimensional descriptor is a combination of information from a Darboux frame defined by the principal directions and normal vector at the point, and local Mean curvatures of neigbours. A pose refinement process without closest point search is then applied to the rough pose estimation. Both registration processes are supported entirely and uniquely by the Vector Field representation. The reliability of our approach has been validated on multiple real datasets.