We present tools for 3D object retrieval in which a model, a polygonal mesh, serves as a query and similar objects are retrieved from a collection of 3D objects. Algorithms proceed first by a normalization step (pose estimation) in which models are transformed into a canonical coordinate frame. Second, feature vectors are extracted and compared with those derived from normalized models in the search space. Using a metric in the feature vector space nearest neighbors are computed and ranked. Objects thus retrieved are displayed for inspection, selection, and processing. For the pose estimation we introduce a modified Karhunen-Loeve transform that takes into account not only vertices or polygon centroids from the 3D models but all points in the polygons of the objects. Some feature vectors can be regarded as samples of functions on the 2-sphere. We use Fourier expansions of these functions as uniform representations allowing embedded multi-resolution feature vectors. Our implementation demonstrates and visualizes these tools.

The development of effective content-based multimedia search systems is an important research issue, due to the growing amount of digital audiovisual information. In the case of images and video, the growth of digital data has been observed since the introduction of 2D capture devices. A similar development is expected for 3D data, as acquisition and dissemination technology of 3D models is constantly improving. 3D objects are becoming an important type of multimedia data, with many promising application possibilities. Defining the aspects that constitute the similarity among 3D objects, and designing algorithms that implement such similarity definitions, is a difficult problem. Over the last few years, a strong interest in methods for 3D similarity search has arisen, and a growing number of competing algorithms for content-based retrieval of 3D objects have been proposed. We survey feature-based methods for 3D retrieval, and we propose a taxonomy for these methods. We also present experimental results, comparing the effectiveness of some of the surveyed methods.

Abstract. We consider 3D object retrieval in which a polygonal mesh serves as a query and similar objects are retrieved from a collection of 3D objects. Algorithms proceed first by a normalization step in which models are transformed into canonical coordinates. Second, feature vectors are extracted and compared with those derived from normalized models in the search space. In the feature vector space nearest neighbors are computed and ranked. Retrieved objects are displayed for inspection, selection, and processing. Our feature vectors are based on rays cast from the center of mass of the object. For each ray the object extent in the ray direction yields a sample of a function on the sphere. We compared two kinds of representations of this function, namely spherical harmonics and moments. Our empirical comparison using precision-recall diagrams for retrieval results in a data base of 3D models showed that the method using spherical harmonics performed better.

In this paper, we consider 3D-shape descriptors generated by using functions on a sphere. The descriptors are engaged for retrieving polygonal mesh models. Invariance of descriptors with respect to rotation of a model can be achieved either by using the Principle Component Analysis (PCA) or defining features in which the invariance exists. The contribution of the paper is twofold: firstly, we define a new rotation invariant feature vector based on functions on concentric spheres, that outperforms a recently proposed descriptor; secondly, we compare the two approaches for achieving rotation invariance as well as options to use a single function or several functions on concentric spheres to generate feature vectors.We conclude that descriptors, which use the PCA, outperform others, while capturing the internal structure of a 3D-model with functions on concentric spheres can improve retrieval effectiveness.

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