EC-EGI: enriched complex EGI for 3D shape registration

Abstract

Extended Gaussian image (EGI) and complex EGI (CEGI) have been widely used as the representation of 3D shapes for shape recognition and pose estimation. In this work, we extend the representations and present a new representation named enriched complex extended Gaussian image (EC-EGI). The representation follows the same framework of EGI and CEGI, which is to represent each surface patch of the target 3D shape as a weight at the associated spot on the surface of the Gaussian sphere. However, while the original CEGI uses a single complex number as the weight, the new representation uses three complex numbers, which are related to the centroid position of the surface patch in 3D. With the inclusion of more information in the new representation, not only could object pose be determined more accurately, but also some key ambiguities of shape representation that CEGI and EGI have also removed. The translation parameters in the pose estimation application could also be determined in a simpler and more accurate way. In addition, the Gaussian sphere partition problem of CEGI is no longer present. Experimental results on synthetic and real image data are shown to illustrate the performance of the proposed representation in pose estimation.