This work describes a degree reduction method for Bezier simplexes with the following properties: (1) Symmetry: The degree reduction method is symmetric with respect to the corner points of the Bezier simplex. (2) Res...
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ISBN:
(纸本)0819410314
This work describes a degree reduction method for Bezier simplexes with the following properties: (1) Symmetry: The degree reduction method is symmetric with respect to the corner points of the Bezier simplex. (2) Restriction: The degree reduction method restricted to the boundary of a Bezier simplex yields the same result as the boundary of the degree-reduced Bezier simplex. (3) Interpolation: The degree-reduced simplex of degree e interpolates the value and the first [e-1/2] derivatives at the corner points of the original Bezier simplex. (4) Optimal order of approximation: The order of approximation of the given simplex by the degree-reduced simplex is O(he+1), (where h is the diameter of the domain simplex), which is optimal for functional approximation. The method, restricted to Bezier surface, yields a new technique for degree reduction, which is easy to implement.
The three-dimensional (3D) skeleton is developed as a geometric modeling tool. The relationship of the Voronoi diagram to the skeleton is exploited to produce a new 3D skeleton algorithm. This algorithm has several su...
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ISBN:
(纸本)0819410314
The three-dimensional (3D) skeleton is developed as a geometric modeling tool. The relationship of the Voronoi diagram to the skeleton is exploited to produce a new 3D skeleton algorithm. This algorithm has several substantial advantages over existing 3D skeleton computation techniques. For instance, the resulting skeleton is a graph that contains coordinate and disk radius information sufficient for exact regeneration, yet it is also amenable to graphical display and further analysis. The resulting skeleton is also homotopically equivalent to the original shape. It is based on the Euclidean metric and requires only a discrete sample set of the shape boundary as input. The new algorithm also reveals deficiencies in the underlying theory of the 3D skeleton. The process of removing these deficiencies leads to the discovery of a new general relationship between local skeleton structure and boundary features which is then exploited to classify and simplify the skeleton.
In this paper we examine the localization criterion for edge detection and determine the density function describing the edge location error, i.e. the displacement of the detected edge position from the true edge loca...
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ISBN:
(纸本)0819410314
In this paper we examine the localization criterion for edge detection and determine the density function describing the edge location error, i.e. the displacement of the detected edge position from the true edge location. Canny defines the measure of localization as the reciprocal of the root-mean-square edge location error and formulates an expression of this measure for local maximum detectors. However, Tagare and deFigueiredo point out that an incorrect assumption is made in the calculation. The same procedure is used by Sarkar and Boyer for their localization measure for zero-crossing detectors. We modify the analysis and obtain a closed form solution of the probability density function of the edge location error. Examination of the density function indicates the variance of the edge location error does not exist, and hence can not be used as a measure of localization. A new localization measure is proposed, characterized by a percentile level on the absolute value of the edge location error.
Traditional modeling techniques, with roots in CAD systems, do not provide a rich enough modeling environment for computervision. The models themselves describe the structure rather than appearance of objects, and ra...
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ISBN:
(纸本)0819410314
Traditional modeling techniques, with roots in CAD systems, do not provide a rich enough modeling environment for computervision. The models themselves describe the structure rather than appearance of objects, and rarely provide facilities for the recording of the additional information required by a vision system. Encoding appearance explicitly ensures quick access and use of the model, and yields model features that correspond to observable data features. We describe the Suggestive Modelling System (SMS) which has been designed specifically for vision applications, combining the geometric object model with vision-specific annotations. Among SMS's features are: (1) A novel separation of surface shape, extent and position;(2) Encoding of underconstrained positions for subcomponents such as spheres and discs;(3) Incorporation of uncertain property values;(4) Cheap encoding of viewpoint- dependent information in addition to the body-centered model;(5) Hierarchical models;(6) Symbolic labels for each primitive;and (7) Parallel curve, surface, and volume-based representations simplify project management. We will describe how this approach reflects more faithfully the capabilities of current scene analysis algorithms than traditional methods. Results from the Imagine 2 vision system demonstrate the applicability of the models to complex real-world industrial inspection and recognition tasks. In addition a number of other vision-related applications in which the SMS paradigm has proved useful will be discussed.
The problem of numerical robustness in Solid Modelling involves proving theorems about the subset of E3 defined by the output of an algorithm using finite-precision floating point arithmetic. However, both input and o...
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ISBN:
(纸本)0819410314
The problem of numerical robustness in Solid Modelling involves proving theorems about the subset of E3 defined by the output of an algorithm using finite-precision floating point arithmetic. However, both input and output sets are usually specified by symbolic data and geometric data that are possibly inconsistent, and the latter comprise geometric vertices in E3, surface intersection curves, and surface patches defined by approximation techniques that leads to the definition of precise subsets of E3, such that the stored input sets are consistent with the symbolic data, and typically closer to the user's input sets that can be warranted by the inherent uncertainty in the data. This definition will permit rigorous proofs, based on the fundamental equation fl(xoy) = xoy(1 + η), of theorems providing a backward error analysis;that is, it will be possible to show that, if a problem is well conditioned, we have the exact solution for a problem defined by slightly perturbed sets. Here, the perturbation is measured by the maximum of the Hausdorff distance between the exact and the perturbed sets, and the Hausdorff distance between the boundaries of these two sets. It will also be possible to show that the error is small as measured by a certain pseudo-distance reflecting relative variation of the boundaries. Furthermore, in circumstances where the piecewise linear Schoenflies theorem in E3 is true, it will follow that there is a space homeomorphism from E3 onto E3 relating the two sets;that is, in a very strong sense, they have the same topological form. The interpolatory technique is described in the curvilinear case, but so far we have used this approach only to prove results about stability of algorithms for sets defined by planar surface patches with inconsistent geometric vertex information. An illustrative example is given.
The proceedings contain 34 papers. The topic discussed include: simplification of digital filtering algorithms using multirate concepts;controlled redundancy in interpolation-based neural nets;morphological decomposit...
The proceedings contain 34 papers. The topic discussed include: simplification of digital filtering algorithms using multirate concepts;controlled redundancy in interpolation-based neural nets;morphological decomposition of natural surfaces;modeling with multivariate B-spline surfaces over arbitrary triangulations;resolvents and their applications in computer-aided geometric design;fast space-variant texture-filtering techniques;and range image segmentation by controlled-continuity spline approximation for parallel computation.
This paper reviews an evolving family of surface modeling primitives for use in computervision, graphics, CAGD, and data analysis. Dynamic surfaces offer significantly greater power to these applications domains than...
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ISBN:
(纸本)0819410314
This paper reviews an evolving family of surface modeling primitives for use in computervision, graphics, CAGD, and data analysis. Dynamic surfaces offer significantly greater power to these applications domains than do conventional, geometric surface modeling primitives. The benefits stem from computational physics: Simulated forces influence the shapes and motions of dynamic surface according to the basic mechanical principles of nonrigid bodies with given mass and damping distributions and deformation energies. Dynamic surfaces are applicable both to static surface reconstruction problems and to more general surface estimation from structured or unstructured time-varying data. In particular, efficient, recursive solutions to time dependent problems result from a Kalman estimation approach in which dynamic surfaces serve as nonstationary system models.
The problems of computing the intersection of curves and surfaces are fundamental to computergraphics and geometric and solid modeling. Earlier algorithms were based either on subdivision methods or algebraic techniq...
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ISBN:
(纸本)0819410314
The problems of computing the intersection of curves and surfaces are fundamental to computergraphics and geometric and solid modeling. Earlier algorithms were based either on subdivision methods or algebraic techniques. They are generally restricted to simple intersections. It has been generally regarded that algebraic approach is impractical due to numerical problems on higher degree curves and surfaces (beyond cubics). In our earlier work we have applied Elimination theory and reduced the problem of intersections of curves and surfaces to matrix computations. These include Gauss elimination, matrix inversion, singular value decomposition, eigenvalues and eigenvectors etc. In this paper, we present robust algorithms based on techniques from linear algebra and numerical analysis for computing the zero dimensional intersections of curves and surface. These include intersection of parametric and algebraic curves and curve-surface intersections. In particular, we present a robust algorithm for computer higher order intersections.
We present the foundations of a method to generate blend surfaces. The idea of this method is to consider functionals depending on parametrized surfaces and their partial derivatives up to order two. The blend surface...
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ISBN:
(纸本)0819410314
We present the foundations of a method to generate blend surfaces. The idea of this method is to consider functionals depending on parametrized surfaces and their partial derivatives up to order two. The blend surface then is the surface which minimizes the functional. In section 2 we briefly describe the mathematical foundation. We discuss the variational problem associated to certain bilinear functionals in the Sobolov space of order 2. In section 2 we outline in detail the procedure how to generate blend surfaces by this method. Starting with a primary parameter space and a primary bilinear functional, one has to determine the final bilinear functional. The blend surface then is chosen as the tensor spline surface which minimizes the quadratic form corresponding to this bilinear functional.
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