| Over the past decade, 3D models are broadly obtainable in various science and technology areas and make 3D model shape retrieval and analysis receiving increasing attention. Content based 3D shape retrieval methods by extracting shape characteristics of the 3D models have competitive potential to generate satisfactory retrieval results. Defining a good shape descriptor becomes an essential problem. Feature based descriptors have been extendedly studied for their capability of accurate describing the characteristics of 3D shape.; Curvature tensor, due to its invariance with respect to rotation, translation, and viewpoint, is a natural way for identification of intrinsic surface characteristics. Estimating principal curvatures and principal directions of a surface from a polyhedral approximation has become a basic step in many computer vision and computer graphics applications. While curvature computation is well known for both continuous curves and smooth surfaces, there is no agreement on the counterpart in a discrete situation.; In this thesis, approaches for accurate curvature tensor estimation in mesh surfaces, curvature line extraction, and content based 3D shape descriptors are described. The proposed curvature tensor estimation approach is based on local directional curve sampling of the surface where the sampling frequency can be selected based on the characteristics of the observed surface. Based on accurate curvature tensor estimation on arbitrary location, two local feature based 3D shape descriptors are proposed for object recognition and retrieval. They utilize the normal curvature and principal curvatures of neighbors to describe the local shape feature. A curvature line extraction approach is also proposed based on accurate estimation of the principal direction at arbitrary position on the surface.; The improved accuracy of the proposed approaches is demonstrated in quantitative experimental evaluation results in which the proposed approaches are compared to known techniques. The evaluation is performed on randomly generated Bezier surfaces with additive Gaussian noise, other synthetic surfaces, and real non-uniform sampled surfaces. |
