Three-dimensional shape analysis for quantification, classification, and retrieval

Three-dimensional objects are now commonly used in a large number of applications including games, mechanical engineering, archaeology, culture, and even medicine. As a result, researchers have started to investigate the use of 3D shape descriptors that aim to encapsulate the important shape properties of the 3D objects. This thesis presents new 3D shape representation methodologies for quantification, classification and retrieval tasks that are flexible enough to be used in general applications, yet detailed enough to be useful in medical craniofacial dysmorphology studies. The methodologies begin by computing low-level features at each point of the 3D mesh and aggregating the features into histograms over mesh neighborhoods. Two different methodologies are defined. The first methodology begins by learning the characteristics of salient point histograms for each particular application, and represents the points in a 2D spatial map based on longitude-latitude transformation. The second methodology represents the 3D objects by using the global 2D histogram of the azimuth-elevation angles of the surface normals of the points on the 3D objects.;Four datasets, two craniofacial datasets and two general 3D object datasets, were obtained to develop and test the different shape analysis methods developed in this thesis. Each dataset has different shape characteristics that help explore the different properties of the methodologies. Experimental results on classifying the craniofacial datasets show that our methodologies achieve higher classification accuracy than medical experts and existing state-of-the-art 3D descriptors. Retrieval and classification results using the general 3D objects show that our methodologies are comparable to existing view-based and feature-based descriptors and outperform these descriptors in some cases. Our methodology can also be used to speed up the most powerful general 3D object descriptor to date.