This work proposes an invariant descriptor and a pipeline for the registration of surface range images based on segmentation/reconstruction making use of an edge detection technique combined with a clustering technique using mesh decimation. This novel descriptor is applied to contours and it is invariant to similarity transformations including rotation, translation, uniform scale and it is robust to noise. The proposed feature descriptor makes use of corresponding points extracted from two images and a signature label is assigned specifically to a point considering the geometrical distribution of its neighbourhood, reducing possible areas of overlapping and the ambiguity in the search process. The descriptor was evaluated through a series of tests with various object range images. To validate the candidate transformations, the fitting errors between the two range images are evaluated by the iterative closest point algorithm. This study also presents and discusses results from the application of the developed pipeline in a vision sensor mounted on a robot arm specially built as part of a R&D project to acquire range images by laser scanning over the surface of hydraulic turbine blades. The sensor generates 3D surface models to be registered in the 3D coordinate system of the robot controller.