Scalable 3D shape retrieval using local features and the signature quadratic form distance

We present a scalable and unsupervised approach for content-based retrieval on 3D model collections. Our goal is to represent a 3D shape as a set of discriminative local features, which is important to maintain robustness against deformations such as non-rigid transformations and partial data. However, this representation brings up the problem on how to compare two 3D models represented by feature sets. For solving this problem, we apply the signature quadratic form distance (SQFD), which is suitable for comparing feature sets. Using SQFD, the matching between two 3D objects involves only their representations, so it is easy to add new models to the collection. A key characteristic of the feature signatures, required by the SQFD, is that the final object representation can be easily obtained in a unsupervised manner. Additionally, as the SQFD is an expensive distance function, to make the system scalable we present a novel technique to reduce the amount of features by detecting clusters of key points on a 3D model. Thus, with smaller feature sets, the distance calculation is more efficient. Our experiments on a large-scale dataset show that our proposed matching algorithm not only performs efficiently, but also its effectiveness is better than state-of-the-art matching algorithms for 3D models.