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37
RidgeValley Lines on Meshes via Implicit Surface Fitting
 ACM TRANS. GRAPH
, 2004
"... We propose a simple and effective method for detecting view and scaleindependent ridgevalley lines defined via first and secondorder curvature derivatives on shapes approximated by dense triangle meshes. A highquality estimation of highorder surface derivatives is achieved by combining multil ..."
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Cited by 123 (8 self)
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We propose a simple and effective method for detecting view and scaleindependent ridgevalley lines defined via first and secondorder curvature derivatives on shapes approximated by dense triangle meshes. A highquality estimation of highorder surface derivatives is achieved by combining multilevel 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.
Consolidation of Unorganized Point Clouds for Surface Reconstruction
"... We consolidate an unorganized point cloud with noise, outliers, nonuniformities, and in particular interference between closeby surface sheets as a preprocess to surface generation, focusing on reliable normal estimation. Our algorithm includes two new developments. First, a weighted locally optim ..."
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Cited by 47 (10 self)
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We consolidate an unorganized point cloud with noise, outliers, nonuniformities, and in particular interference between closeby 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, outlierfree 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 prioritydriven normal propagation scheme based on a new priority measure and an orientationaware 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 closeby 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
A comparison of Gaussian and mean curvatures estimation methods on triangular meshes
 In: ICRA
, 2003
"... 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 s ..."
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Cited by 47 (0 self)
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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 Bspline (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.
Fast and robust detection of crest lines on meshes
 Proc. of ACM Symposium on Solid and Physical Modeling
, 2005
"... 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 secondorder curvature derivatives, are widely used for shape matching and interrogation purposes. Their practical extract ..."
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Cited by 39 (3 self)
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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 secondorder curvature derivatives, are widely used for shape matching and interrogation purposes. Their practical extraction is difficult because it requires good estimation of highorder 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 socalled MVS functional of Moreton and Sequin, and Dupin cyclides, An application of the crest lines to adaptive mesh simplification is also considered.
SAFER vehicle inspection: a multimodal robotic sensing platform
 in Proc. SPIE Unmanned Ground Vehicle Technology VI
, 2004
"... 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 In ..."
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Cited by 13 (11 self)
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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, standoff checkpoint inspections, scout surveillance, intruder detection, obstaclebreach situations, and rendersafe 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.
Segmenting geometric reliefs from textured background surfaces
 ComputerAided Design and Applications
, 2007
"... 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 b ..."
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Cited by 5 (2 self)
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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 userdrawn 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.
Unconstrained 3DMesh Generation Applied to Map Building
 9th Iberoamerican Congress on Pattern Recognition
, 2004
"... 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 3Dmesh generation from a ..."
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Cited by 2 (1 self)
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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 3Dmesh generation from a notuniformly distributed point cloud. 1
SALIENT POINT CHARACTERIZATION FOR LOW RESOLUTION MESHES
"... This paper deals with edge detection and vertex characterization of 3D meshes. First, a new measure is introduced, the saliency degree, which provide directly the shape information of a vertex of the mesh without any curvature computation. The relationship between the saliency degree and the curvatu ..."
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Cited by 2 (2 self)
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This paper deals with edge detection and vertex characterization of 3D meshes. First, a new measure is introduced, the saliency degree, which provide directly the shape information of a vertex of the mesh without any curvature computation. The relationship between the saliency degree and the curvature is demonstrated for continuous and discontinuous 2D curves. Then, a description of the 3D operator is given. Finally, results on geometric and real objects are shown. The contributions of this work are the definition of a new 3D operator which is able to extract point characteristic on 3D low resolution mesh. Index Terms — 3D Salient point detection, saliency
Shape Interrogation
"... 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 ..."
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Cited by 1 (0 self)
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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 stateoftheart 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.