Scale-Space processing of point-sampled geometry for efficient 3D object segmentation

In this paper, we present a new framework for analyzing and segmenting point-sampled 3D objects. Our method first computes for each surface point the surface curvature distribution by applying the principal component analysis on local neighborhoods with different sizes. Then we model in the four dimensional space the joint distribution of surface curvature and position features as a mixture of Gaussians using the expectation maximization algorithm. Central to our method is the extension of the scale-space theory from the 2D domain into the three-dimensional space to allow feature analysis and classification at different scales. Our algorithm operates directly on points requiring no vertex connectivity information. We demonstrate and discuss the performance of our framework on a collection of point sampled 3D objects

Scale-Space processing of point-sampled geometry for efficient 3D object segmentation

In this paper, we present a novel framework for analyzing and segmenting point-sampled 3D objects. Our algorithm computes a decomposition of a given point set surface into meaningful components, which are delimited by line features and deep concavities. Central to our method is the extension of the scale-space theory to the three-dimensional space to allow feature analysis and classification at different scales. Then, a new surface classifier is computed and used in an anisotropic diffusion process via partial differential equations (PDEs). The algorithm avoids the misclassifications due to fuzzy and incomplete line features. Our algorithm operates directly on points requiring no vertex connectivity information. We demonstrate and discuss its performance on a collection of point sampled 3D objects including CAD and natural models. Applications include 3D shape matching and retrieval, surface reconstruction and feature preserving simplification

Three Dimensional Nonlinear Statistical Modeling Framework for Morphological Analysis

This dissertation describes a novel three-dimensional (3D) morphometric analysis framework for building statistical shape models and identifying shape differences between populations. This research generalizes the use of anatomical atlases on more complex anatomy as in case of irregular, flat bones, and bones with deformity and irregular bone growth. The foundations for this framework are: 1) Anatomical atlases which allow the creation of homologues anatomical models across populations; 2) Statistical representation for output models in a compact form to capture both local and global shape variation across populations; 3) Shape Analysis using automated 3D landmarking and surface matching. The proposed framework has various applications in clinical, forensic and physical anthropology fields. Extensive research has been published in peer-reviewed image processing, forensic anthropology, physical anthropology, biomedical engineering, and clinical orthopedics conferences and journals. The forthcoming discussion of existing methods for morphometric analysis, including manual and semi-automatic methods, addresses the need for automation of morphometric analysis and statistical atlases. Explanations of these existing methods for the construction of statistical shape models, including benefits and limitations of each method, provide evidence of the necessity for such a novel algorithm. A novel approach was taken to achieve accurate point correspondence in case of irregular and deformed anatomy. This was achieved using a scale space approach to detect prominent scale invariant features. These features were then matched and registered using a novel multi-scale method, utilizing both coordinate data as well as shape descriptors, followed by an overall surface deformation using a new constrained free-form deformation. Applications of output statistical atlases are discussed, including forensic applications for the skull sexing, as well as physical anthropology applications, such as asymmetry in clavicles. Clinical applications in pelvis reconstruction and studying of lumbar kinematics and studying thickness of bone and soft tissue are also discussed