Shape Representations and Algorithms for 3D Model Retrieval (Thesis)

Abstract:

With recent improvements in methods for the acquisition and rendering
of 3D models, the need for retrieval of models from large repositories
of 3D shapes has gained prominence in the graphics and vision communities.
A variety of methods have been proposed that enable the efficient querying
of model repositories for a desired 3D shape. Many of these methods use a
3D model as a query and attempt to retrieve models from the database that
have a similar shape.

In this thesis, we begin by introducing a new shape descriptor that is well
suited to the task of 3D model retrieval. The descriptor is designed to enable
efficient and meaningful comparison of 3D shapes, thereby satisfying the
requirements of efficiency and discriminability that are necessary for an effective,
real-time shape retrieval system. We compare our descriptor to other existing
descriptors in empirical retrieval experiments, demonstrating that the new shape
descriptor provides improved retrieval accuracy and is better suited to the task of
shape matching.

One of the specific challenges in matching 3D shapes arises from the fact that
in many applications, models should be considered to be the same if they
differ by a similarity transformation. Thus in order to match two models, a
measure of similarity needs to be computed at the optimal translation, scale
and rotation. In this thesis, we review a number of approaches for addressing
the alignment challenge and provide new methods for addressing this issue that
give rise to better shape matching algorithms.

Additionally, we present two general methods for improving the
performance of many extant 3D model matching algorithms by providing
a general framework for augmenting existing shape representations with
global shape information characterizing salient shape properties. The first
approach leverages symmetry information to augment existing representations
with information characterizing a model's self-similarity. The second
approach factors the shape matching equation as the disjoint product of
anisotropy and geometric comparisons --- improving the matching performance
of many shape metrics by facilitating the task of shape registration.