Marcin Novotni

3D zernike descriptors for content based shape retrieval

Content based 3D shape retrieval for broad domains like the World Wide Web has recently gained considerable attention in Computer Graphics community. One of the main challenges in this context is the mapping of 3D objects into compact canonical representations referred to as descriptors, which serve as search keys during the retrieval process. The descriptors should have certain desirable properties like invariance under scaling, rotation and translation. Very importantly, they should possess descriptive power providing a basis for similarity measure between three-dimensional objects which is close to the human notion of resemblance.In this paper we advocate the usage of so-called 3D Zernike invariants as descriptors for content based 3D shape retrieval. The basis polynomials of this representation facilitate computation of invariants under the above transformations. Some theoretical results have already been summarized in the past from the aspect of pattern recognition and shape analysis. We provide practical analysis of these invariants along with algorithms and computational details. Furthermore, we give a detailed discussion on influence of the algorithm parameters like type and resolution of the conversion into a volumetric function, number of utilized coefficients, etc. As is revealed by our study, the 3D Zernike descriptors are natural extensions of spherical harmonics based descriptors, which are reported to be among the most successful representations at present. We conduct a comparison of 3D Zernike descriptors against these regarding computational aspects and shape retrieval performance.

Shape retrieval using 3D Zernike descriptors

Abstract We advocate the usage of 3D Zernike invariants as descriptors for 3D shape retrieval. The basis polynomials of this representation facilitate computation of invariants under rotation, translation and scaling. Some theoretical results have already been summarized in the past from the aspect of pattern recognition and shape analysis. We provide practical analysis of these invariants along with algorithms and computational details. Furthermore, we give a detailed discussion on influence of the algorithm parameters like the conversion into a volumetric function, number of utilized coefficients, etc. As is revealed by our study, the 3D Zernike descriptors are natural extensions of recently introduced spherical harmonics based descriptors. We conduct a comparison of 3D Zernike descriptors against these regarding computational aspects and shape retrieval performance using several quality measures and based on experiments on the Princeton Shape Benchmark.

A geometric approach to 3D object comparison

Along with the development of 3D acquisition devices and methods and the increasing number of available 3D objects, new tools are necessary to automatically analyze, search and interpret these models. In this paper, we describe a novel geometric approach to 3D object comparison and analysis. To compare two objects geometrically, we first properly position and align the objects. After solving this pose estimation problem, we generate specific distance histograms that define a measure of the geometric similarity of the inspected objects. The geometric approach is very well-suited for structures with moderate variance, e.g. bones, fruits, etc. The strength of the approach is proven through the results of several tests that we performed on different data sets.

Progressive Gap Closing for MeshRepairing

Modern 3D acquisition and modeling tools generate high-quality, detailed geometric models. However, in order to cope with the associated complexity, several mesh decimation methods have been developed in the recent years. On the other hand, a common problem of geometric modeling tools is the generation of consistent three-dimensional meshes. Most of these programs output meshes containing degenerate faces, T-vertices, narrow gaps and cracks. Applying well-established decimation methods to such meshes results in severe artifacts due to lack of consistent connectivity information. The industrial relevance of this problem is emphasized by the fact that as an output of most of the commercial CAD/CAM and other modeling tools, the user usually gets consistent meshes only for separate polygonal patches as opposed to the whole mesh.

Enhancing Fourier Volume Rendering Using Contour Extraction

Fourier Volume Rendering (FVR) has received considerable attention in volume visualization during the last decade due its O(N 2 logN) rendering time complexity, where O(N 3) is the volume size. Nevertheless, FVR currently suffers from some quality limiting its usefulness in particular medical applications. The main reason for this is the lack of weighting sample points in dependence of the samples along the integration path. In this work we propose a solution for a special class of problems, namely the extraction and emphasis of contours in volumetric datasets. The accuracy of the illumination of the extracted contours can be derived in an exact manner. Main applications of our method include contour extraction and enhancement of features, noise removal and revealing of important spatial relationships between interior and exterior structures, making it an attractive tool for improved X-ray-like investigations of the given dataset.