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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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Tensorial rational surfaces with base points via massic vectors

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SIAM JOURNAL ON NUMERICAL ANALYSIS 2004年第4期42卷 1415-1434页

作者： Gibaru, O Ecole Natl Super Arts & Metiers Lille Lab L2MA F-59046 Lille France

Let S be a tensorial rational surface defined by a rational function from [0, 1](2) onto R-3 with a base point at (u, v) = (0, 0). We demonstrate that the image of this base point is a set of rational curves;a base point is a parameter value for which the rational parametrization takes the value (0/0, 0/0, 0/0). This result was established by Clebsch [Ueber die abbildung algebraischer. flachen, insbesondere der vierten und funften ordnung, Math. Ann., 1 (1869), pp. 253-316]. Base points were first introduced in the context of geometric design by Chionh [Base Points, Resultants and the Implicit Representation of Rational surfaces, Ph. D. thesis, Department of computer Science, University of Waterloo, Waterloo, Ontario, 1990] and Manocha and Canny [Implicitizing Rational Parametric surfaces, Tech. report 90/592, computer Science Division, University of California, Berkeley, 1990] and were used by Warren [ACM Trans. graphics, 11 (1992), pp. 127-139] to define multisided rational Bezier patches. We give here a constructive approach of this result to exploit it directly in the industrial scope of computer aided design. We show that these rational curves are placed end to end by using the formalism of massic vectors introduced by Fiorot and Jeannin [Courbes et surfaces Rationnelles. Applications a la CAO, R. M. A. 12, Masson, Paris, 1989]. Furthermore, we give the relations between the massic vectors which define these curves and the massic vectors which define S. Finally, we give an algorithm to draw on a computer a surface having base points.

关键词： base point Newton polygon SBR-surfaces BR-curves blow up blow down

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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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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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Approximation with active B-spline curves and surfaces

Approximation with active B-spline curves and surfaces

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Pacific Conference on computer graphics and Applications

作者： H. Pottmann S. Leopoldseder M. Hofer Institute of Geometry University of Technology Vienna Vienna Austria

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

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Perceptual geometry of space and form: Visual perception of natural scenes and their virtual representation

Perceptual geometry of space and form: Visual perception of ...

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Conference on vision Geometry X

作者： Assadi, AH Univ Wisconsin Madison WI 53706 USA

ISBN: (纸本)0819441902

Perceptual geometry is an emerging field of interdisciplinary research whose objectives focus on study of geometry from the perspective of visual perception, and in turn, apply such geometric findings to the ecological study of vision. Perceptual geometry attempts to answer fundamental questions in perception of form and representation of space through synthesis of cognitive and biological theories of visual perception with geometric theories of the physical world. Perception of form and space are among fundamental problems in vision science. In recent cognitive and computational models of human perception, natural scenes are used systematically as prefer-red visual stimuli. Among key problems in perception of form and space, we have examined perception of geometry of natural surfaces and curves, e.g. as in the observer's environment. Besides a systematic mathematical foundation for a remarkably general framework, the advantages of the Gestalt theory of natural surfaces include a concrete computational approach to simulate or "recreate images" whose geometric invariants and quantities might be perceived and estimated by an observer. The latter is at the very foundation of understanding the nature of perception of space and form, and the (computer graphics) problem of rendering scenes to visually invoke virtual presence.

关键词： Gestalt human vision surfaces texture spatial representation cognitive science learning theory

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Dynamic models of planar algebraic curves

Dynamic models of planar algebraic curves

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40th IEEE Conference on Decision and Control

作者： Unel, M Ghosh, BK Bogazici Univ Dept Elect & Elect Engn Istanbul Turkey

ISBN: (纸本)0780370619

There has been a growing interest in the use of implicit representations for curves and surfaces. Applications arise in numerous areas of physical sciences, such as engineering, robotics, vision, graphics, geometric optics, and in many areas of pure mathematics such as differential geometry, complex analysis, number theory and differential equations. Motivated from problems in mobile robotics and computer vision, in this paper we are interested in the study of how to model and describe the dynamics of planar algebraic curves.

关键词： Curve fitting

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Dynamic models of planar algebraic curves

Dynamic models of planar algebraic curves

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IEEE Conference on Decision and Control

作者： M. Unel B.K. Ghosh Department of Electrical and Electronics Engineering Bogazici University Istanbul Turkey Department of Systems Science and Mathematics Washington University Saint Louis MO USA

ISBN: (纸本)0780370619

There has been a growing interest in the use of implicit representations for curves and surfaces. Applications arise in numerous areas of physical sciences, such as engineering, robotics, vision, graphics, geometric optics, and in many areas of pure mathematics such as differential geometry, complex analysis, number theory and differential equations. Motivated from problems in mobile robotics and computer vision, we are interested in the study of how to model and describe the dynamics of planar algebraic curves.

关键词： Robot vision systems Geometrical optics Application software computer graphics Mathematics Computational geometry Differential equations Mobile computing Mobile robots computer vision

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