We propose a simple and effective method for detecting view- and scale-independent ridge-valley lines defined via first- and secondorder curvature derivatives on shapes approximated by dense triangle meshes. A high-quality estimation of high-order surface derivatives is achieved by combining multi-level implicit surface fitting and finite difference approximations. We demonstrate that the ridges and valleys are geometrically and perceptually salient surface features and, therefore, can be potentially used for shape recognition, coding, and quality evaluation purposes.

Estimating intrinsic geometric properties of a surface from a polygonal mesh obtained from range data is an important stage of numerous algorithms in computer and robot vision, computer graphics, geometric modeling, industrial and biomedical engineering. This work considers different computational schemes for local estimation of intrinsic curvature geometric properties. Five different algorithms and their modifications were tested on triangular meshes that represent tesselations of synthetic geometric models. The results were compared with the analytically computed values of the Gaussian and mean curvatures of the non uniform rational B-spline (NURBs) surfaces, these meshes originated from. This work manifests the best algorithms suited for total (Gaussian) and mean curvature estimation, and shows that indeed different alogrithms should be employed to compute the Gaussian and mean curvatures.

We propose a fast and robust method for detecting crest lines on surfaces approximated by dense triangle meshes. The crest lines, salient surface features defined via first- and second-order curvature derivatives, are widely used for shape matching and interrogation purposes. Their practical extraction is difficult because it requires good estimation of high-order surface derivatives. Our approach to the crest line detection is based on estimating the curvature tensor and curvature derivatives via local polynomial fitting. Since the crest lines are not defined in the surface regions where the surface focal set (caustic) degenerates, we introduce a new thresholding scheme which exploits interesting relationships between curvature extrema, the so-called MVS functional of Moreton and Sequin, and Dupin cyclides, An application of the crest lines to adaptive mesh simplification is also considered.

We consolidate an unorganized point cloud with noise, outliers, non-uniformities, and in particular interference between close-by surface sheets as a preprocess to surface generation, focusing on reliable normal estimation. Our algorithm includes two new developments. First, a weighted locally optimal projection operator produces a set of denoised, outlier-free and evenly distributed particles over the original dense point cloud, so as to improve the reliability of local PCA for initial estimate of normals. Next, an iterative framework for robust normal estimation is introduced, where a priority-driven normal propagation scheme based on a new priority measure and an orientation-aware PCA work complementarily and iteratively to consolidate particle normals. The priority setting is reinforced with front stopping at thin surface features and normal flipping to enable robust handling of the close-by surface sheet problem. We demonstrate how a point cloud that is wellconsolidated by our method steers conventional surface generation schemes towards a proper interpretation of the input data. 1

The current threats to U.S. security both military and civilian have led to an increased interest in the development of technologies to safeguard national facilities such as military bases, federal buildings, nuclear power plants, and national laboratories. As a result, the Imaging, Robotics, and Intelligent Systems (IRIS) Laboratory at The University of Tennessee (UT) has established a research consortium, known as SAFER (Security Automation and Future Electromotive Robotics), to develop, test, and deploy sensing and imaging systems for unmanned ground vehicles (UGV). The targeted missions for these UGV systems include—but are not limited to—under vehicle threat assessment, stand-off check-point inspections, scout surveillance, intruder detection, obstaclebreach situations, and render-safe scenarios. This paper presents a general overview of the SAFER project. Beyond this general overview, we further focus on a specific problem where we collect 3D range scans of under vehicle carriages. These scans require appropriate segmentation and representation algorithms to facilitate the vehicle inspection process. We discuss the theory for these algorithms and present results from applying them to actual vehicle scans.

Segmentation of geometric reliefs from a textured background has various applications in reverse engineering. We consider two approaches to solve this problem. The first classifies parts of a surface mesh as relief or background, and then uses a snake which moves inwards towards the desired relief boundary, which is coarsely located using an energy based on the classification. The second approach initially smoothes the surface to eliminate the background texture, and locates the snake at the relief boundary using an energy based on the step between the background and the relief. Both snakes start at simple user-drawn contours, and are driven towards the relief boundaries by the snake energy functional. In both cases, the snake has different evolution phases with different energy terms, to initially rapidly drive the snake towards the relief boundary, and to later accurately match it. To describe geometric textures, we analyze surface differential properties, and integral and statistical quantities based upon them, computed at multiple scales taken over local neighborhoods, following similar ideas from image texture processing. For classification, we use a support vector machine together with sequential forward floating search for feature selection. A straightforward Laplacian method is used for smoothing. We use example scanned models to demonstrate that both approaches are useful, but are suitable for different types of model.

Abstract. 3D map building is a complex robotics task which needs mathematical robust models. From a 3D point cloud, we can use the normal vectors to these points to do feature extraction. In this paper, we will present a robust method for normal estimation and unconstrained 3D-mesh generation from a not-uniformly distributed point cloud. 1

Shape interrogation methods are of increasing interest in geometric modeling as well as in computer graphics. Originating 20 years ago from CAD/CAM applications where ”class A” surfaces are required and no surface imperfections are allowed, shape interrogation has become recently an important tool for various other types of surface representations such as triangulated or polygonal surfaces, subdivision surface, and algebraic surfaces. In this paper we present the state-of-the-art of shape interrogation methods including methods for detecting surface imperfections, surface analysis tools and methods for visualizing intrinsic surface properties. Furthermore we focus on stable numerical and symbolic solving of algebraic systems of equations, a problem that arises in most shape interrogation methods.

This paper used surface curvatures and support vector machines for the identification of manufacturing processes in a database of mesh based CAD artifacts. The target is to classify prismatic machined and cast-then-machined parts into their respective classification to assist the manufacturing cost estimation. Current research on shape matching techniques have used shape functions to match the gross shapes of mesh models. However, they do not adequately discrimate artifacts manufactured by different processes. Our approach shows how different kinds of surfaces can distinguish different manufacturing processes. Statistics on surface curvatures are used to construct shape descriptors; then supervised machine learning classifier support vector machines are applied to separate the two classifications. 1.

A local parametrization based curvature computation technique for triangular meshes is presented. The computation process starts with interpolating the interested region of the given mesh with a Loop subdivision surface. The interpolation technique guarantees that the resulting surface reflects the local shape of the mesh, including features such as edges and corners; no data simplification is necessary. A blending technique is then applied to vicinities of extra-ordinary vertices to ensure continuity and boundedness of curvature at each extra-ordinary vertex. This blending process does not change the value of the surface at the extra-ordinary points. Curvatures for each given point are subsequently computed based on standard parametrization for Loop surfaces. Advantages of the new technique include that curvature can be computed in any direction for any point of the given mesh and higher accuracy of the computed results due to precise representation obtained by the interpolation process. Test results showing the effectiveness of the new technique are included.