Second order 3D shape features: An exhaustive study

In recent years many techniques for 3D shape retrieval and classification were proposed. Most of them follow the feature vector paradigm, i.e. the shape is extended with some compact feature representation, on which basis the objects are compared and similarity measures are computed. A main demand of such similarity measures is their invariance to Euclidean motion. There are three main direction to obtain such invariances: Matched Filter Approaches, Pose Normalization or Transformation Group Integration. Among those, registration approaches perform best in retrieval accuracy, while their computational expense however is rather high. In contrast, representation obtained by group integration are fast to compute and compare, but show bad retrieval performance due to its loss in information. In this article we try to close this gap and show that it is also possible to obtain meaningful representations of surface models by group integration approaches.