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15th International Conference in Central Europe on computer graphics, Visualization and computer vision

作者： Shi, Kuangyu Theisel, Holger Weinkauf, Tino Hauser, Helwig Hege, Hans-Christian Seidel, Hans-Peter MPI Informat D-66123 Saarbrucken Germany

ISBN: (纸本)9788086943008

This paper presents an approach to extracting the separation surfaces from periodic 2D time-dependent vector fields based on a recently introduced path line oriented topology. This topology is based on critical path lines which repeat the same spatial cycle per time period. Around those path lines there are areas of similar asymptotic flow behavior (basins) which are captured by a 2D Poincare map as a discrete dynamical system. Due to pseudo discontinuities in this map and the discrete integration scheme, separatrices between the basins can't be obtained as integral curves. Instead we choose a point-wise approach to segment the Poincare map and apply image analysis algorithms to extract the 2D separation curves. Starting from those curves we integrate separation surfaces which partition the periodic 2D time-dependent vector field into areas of similar path line behavior. We apply our approach to a number of data sets to demonstrate its utility.

关键词： Flow Visualization Time-dependent vector fields Topological methods

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Image-based 3D reconstruction of generalized box with user sketches

Image-based 3D reconstruction of generalized box with user s...

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16th International Conference on computer graphics and vision, GraphiCon 2006

作者： Yakubenko, Anton Konouchine, Anton Vezhnevets, Vladimir Graphics and Media Lab Moscow State University Moscow Russia

3d modeling is one of the key problems in computer graphics. Creating 3d models of real world objects is among tasks of 3d modeling problem. One of the approaches to solving it is using images of the object of interest. Images are the most natural and easy to obtain source of information about real-world 3d object. So lots of research is focused on image-based 3d modeling. We propose an algorithm for reconstructing 3d model of object with a specific shape from a sequence of calibrated images with user interaction. The shape of the object is called "generalized box" and describes objects with hexahedron shape, which edges are polylines or curves and faces are curved surfaces. The class of objects described as generalized box is rather wide. It includes technical equipment, machinery or their parts, architectural buildings, a host of common everyday objects. User outlines some edges on several images with known camera calibration. First 3d edges, corresponding to their outlined projections, are reconstructed. Then missing 3d edges are obtained from known 3d edges. At last curved surface is constructed for each face of the model. After 3d model is constructed, the texture is extracted from input images.

关键词： Machinery

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3D-curves and ruled surfaces for graphics and robotics using conformal geometric computing

3D-curves and ruled surfaces for graphics and robotics using...

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IEEE International Conference on Robotics and Automation (ICRA)

作者： L. Falcon-Morales E. Bayro-Corrochano Mathematics Department Tecnológico de Monterrey Guadalajara Jalisco Mexico Computer Science Department CINVESTAV Guadalajara Jalisco Mexico

We present an approach to ruled surfaces and complex 3D-curves using conformal geometric algebra. As robots and mechanisms move, any line attached to them will trace out a ruled surface. In robotics, the arm of a robot usually needs to follow a curve over a ruled surface or over the intersection of some of them. In this paper we present the way to model and to resolve these problems using algebra of incidence and rigid-motion transformations in the context of the conformal geometric algebra

关键词： Algebra Service robots Surface emitting lasers computer vision Physics Robot vision systems Welding computer graphics Mathematics computer science

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A subdivision scheme to model surfaces with spherelike features

A subdivision scheme to model surfaces with spherelike featu...

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13th International Conference in Central Europe on computer graphics, Visualization and computer vision 2005, WSCG'2005 - In Co-operation with EUROgraphics

作者： Beets, Koen Claes, Johan Van Reeth, Frank Limburgs Universitair Centrum Expertise Centre for Digital Media Universitaire Campus B-3590 Diepenbeek Belgium

ISBN: (纸本)8090310079

In this paper, we introduce a novel subdivision method able to generate smooth surfaces which locally tend to minimize variations in curvature. The method is based on a tensor product of a subdivision scheme for circle splines, which is then generalized to arbitrary quadrilateral meshes. Although they involve a geometric construction, our rules are applied in a uniform way, without the need for applying different rules for different vertices or for different stages in the subdivision process. This results in a more general and natural way to obtain circular curvatures, unlike other approaches involving subdivision curves able to generate circles. surfaces of revolution are just a basic example, as circular features can be distributed freely over the surfaces generated via our methods. Copyright UNION Agency - Science Press.

关键词： Tensors

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Evolutionary heuristic optimization for digital curves and surfaces

Evolutionary heuristic optimization for digital curves and s...

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作者： Baig, Meerja Humayun King Fahd University of Petroleum and Minerals (Saudi Arabia)

学位级别：M.S.

Computing curve and surface fitting is the main problem encountered to approximate data in many graphics and image processing applications. For approximation of complex curve and surface fitting, NURBS (Non Uniform Rational B-Spline) is the most popular flexible spline technique. Control points, weight vector and knot vector are the NURBS parameters which effect shape of curve/surface. For different values of these parameters we get different shapes of curves/surfaces. This research is concentrated to a common area among the disciplines of computer graphics, Imaging, and vision. The idea is mainly to optimize the contours obtained from the outline of images. In this research we have applied simulated Evolution (SE) for optimization of control points, weight and knot parameters of NURBS for curve and surface fitting. The main objective is the reduction of fitting error with target curve/surface to obtain a smooth curve/surface in a reasonable time. (Abstract shortened by UMI.)

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Curve-based local surface geometry estimation in polyhedral surfaces

Curve-based local surface geometry estimation in polyhedral ...

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Conference on vision Geometry XII

作者： Tang, XJ Agam, G IIT Dept Comp Sci Chicago IL 60616 USA

ISBN: (纸本)0819452033

Accurate curvature estimation in mesh surfaces is an important problem with numerous applications. Curvature is a significant indicator of ridges and can be used in applications such as: recognition, adaptive smoothing, and compression. Common methods for curvature estimation are based on quadric surface fitting to local neighborhoods. While the use of quadric surface patches simplifies computations, due to its simplicity the quadric surface model is incapable of modeling accurately the local surface geometry and introduces a strong element of smoothing into the computations. Hence, reducing the accuracy of the curvature estimation. The method proposed in this paper models the local surface geometry by using a set of quadratic curves. Consequently, as the proposed model has a large number of degrees of freedom, it is capable of modeling the local surface geometry much more accurately compared to quadric surface fitting. The experimental setup for evaluating the proposed approach is composed of randomly generated Bezier surfaces for which the curvature is known with various levels of additive Gaussian noise. We compare the results obtained by the proposed approach to those obtained by other techniques. It is demonstrated that the proposed approach produces significantly improved estimation results which are less sensitive to noise.

关键词： computer graphics computer vision geometric modeling vision geometry polyhedral surfaces local geometry estimation curvature estimation

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Industrial geometry: Recent advances and applications in CAD

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computer-Aided Design and Applications 2004年第1-4期1卷 513-522页

作者： Pottmann, Helmut Leopoldseder, Stefan Hofer, Michael Wang, Wenping Vienna University of Technology Austria University of Hong Kong Hong Kong

Industrial Geometry aims at unifying existing and developing new methods and algorithms for a variety of application areas with a strong geometric component. These include CAD, CAM, Geometric Modeling, Robotics, computer vision and Image Processing, computer graphics and Scientific Visualization. The methods are mainly taken from classical geometry, computational geometry, CAGD and various branches of applied and industrial mathematics. In this paper, Industrial Geometry is illustrated via the fruitful interplay of the areas indicated above in the context of novel solutions of CAD related, geometric optimization problems: approximation with general NURBS curves and surfaces, approximation with special surfaces for applications in architecture and manufacturing, and registration problems for industrial inspection and 3D model generation from measurement data.

关键词： computer aided design

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A realization of intelligent control for freedom surface modeling system

A realization of intelligent control for freedom surface mod...

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International Conference on Machine Learning and Cybernetics (ICMLC)

作者： Xu-Min Liu Hou-Kuan Huang Wei-Xiang Xu School of Information Engineering Capital Normal University Beijing China School of Computer and Information Technology Beijing Jiaotong University Beijing China School of Traffic and Transportation Beijing Jiaotong University Beijing China

ISBN: (纸本)0780384032

The freedom surfaces modeling technology is very important and widely applied. We discuss a realization technology of intelligent control for freedom surfaces modeling system. We firstly present the principle and realization algorithm of a surface produced by beta-spline curves. Secondly, on the basis of the coordinate projection of bibeta-spline surface, the automatic adjustment and display principle of graphics on the screen are discussed, and a specific algorithm is given. Finally, we focus on the basic thought and fast algorithm of hidden surface elimination. The algorithm puts each surface fragment in a small-to-big order according to the vision depth information, and outputs the quadrangles filled with colors on the screen. Applying the algorithm mentioned above to the freedom surface geometric modeling, we have got some satisfying results. The algorithm needs less computation and the results are reliable.

关键词： Intelligent control Shape control Spline Displays Solid modeling Marine technology Information technology Traffic control Transportation graphics

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Computation of the shock scaffold for unorganized point clouds in 3D

Computation of the shock scaffold for unorganized point clou...

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2003 IEEE computer Society Conference on computer vision and Pattern Recognition, CVPR 2003

作者： Leymarie, Frederic F. Kimia, Benjamin B. Brown University Division of Engineering Providence RI United States

The shock scaffold is a hierarchical organization of the medial axis in 3D consisting of special medial points and curves connecting these points, thereby forming a geometric directed graph, which is key in applications such as object recognition. In this paper we describe a method for computing the shock scaffold of realistic datasets, which involve tens or hundreds of thousands of points, in a practical time-frame. Our approach is based on propagation along the scaffold from initial sources of flow by considering pairs of input points. We present seven principles which avoid the consideration of those pairs of points which cannot possibly lead to a shock flow;they involve: (i) the "visibility" of a point from another, (ii) the clustering of points, (iii) the visibility of a cluster from another, (iv) the convex hull of a cluster, (v) the vertices of such convex hulls as "virtual" points, (vi) a mult-resolution framework, and, finally, (vii) a search strategy-organized in layers.

关键词： Three dimensional computer graphics

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Approximation with active B-spline curves and surfaces 10

Approximation with active B-spline curves and surfaces

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10th Pacific Conference on computer graphics and Applications

作者： Pottmann, H Leopoldseder, S Hofer, M Vienna Univ Technol Inst Geometry Vienna Austria

ISBN: (纸本)0769517846;0769517854

An active contour model for parametric curve and surface approximation is presented. The active curve or surface adapts to the model shape to be approximated in an optimization algorithm. The quasi-Newton optimization procedure in each iteration step minimizes a quadratic function which is built up with help of local quadratic approximants of the squared distance function of the model shape and an internal energy which has a smoothing and regularization effect. The approach completely avoids the parametrization problem. We also show how to use a similar strategy for the solution of variational problems for curves on surfaces. Examples are the geodesic path connecting two points on a surface and interpolating or approximating spline curves on surfaces. Finally we indicate how the latter topic leads to the variational design of smooth motions which interpolate or approximate given positions.

关键词： Active contours Application software Character generation computer vision Geometry Least squares approximation Parameter estimation Polynomials Smoothing methods Spline

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