A computational model for generating a graphical deformation process of a 3-D object from an initial state to a final state is proposed. The deformation process is represented by several intermediate states which are ...
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ISBN:
(纸本)0819410314
A computational model for generating a graphical deformation process of a 3-D object from an initial state to a final state is proposed. The deformation process is represented by several intermediate states which are interpolated from the two original states of an object. The generated processes can be used for filling the missing information between two given states, visualizing the changing process, or conveying the underlying idea more clearly through a pictorial sequence. The model includes a generic scheme for correspondence establishment and a physically-based process generator.
In surface reconstruction a mathematical description is created from sampled data points. While the displayed image may appear to be correct, there remains the analytical question as to whether it can be proven that t...
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ISBN:
(纸本)0819410314
In surface reconstruction a mathematical description is created from sampled data points. While the displayed image may appear to be correct, there remains the analytical question as to whether it can be proven that the stored surface model and the original artifact have the same topology. Previous approaches to investigate all possible topological configurations were cumbersome and offered little insight as to how those topological configurations were generated. An alternative algorithm is offered, where the mathematics of the algorithm does offer insight into the structure of these configurations.
This paper presents an efficient technique to compress chain-encoded line drawings. The technique, called the address chain code, constructs a codebook containing vectors of chains which recur frequently in the chain-...
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ISBN:
(纸本)0819410314
This paper presents an efficient technique to compress chain-encoded line drawings. The technique, called the address chain code, constructs a codebook containing vectors of chains which recur frequently in the chain-encoded line drawings. The recurrent vectors are encoded as their corresponding addresses in the codebook preceded by header bits. The encoding procedure and an efficient way to organize and label the vectors, which turns out to be somewhat similar to the generalized chain codes, are described in this paper.
It is shown how to construct G2-continuous spline with arcs of cubics. Each arc is a piece of the oval of a cubic and it is controlled locally by a triangle tangent to the arc at both endpoints. Formulas for mixed int...
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ISBN:
(纸本)0819410314
It is shown how to construct G2-continuous spline with arcs of cubics. Each arc is a piece of the oval of a cubic and it is controlled locally by a triangle tangent to the arc at both endpoints. Formulas for mixed interpolation of further points and tangents are given in terms of geometrically meaningful shape parameters. It is shown that under certain restrictions, the numerical values of the curvatures may be prescribed at the joints. Some new shape handles are developed for the local control of each arc of the spline. Intersection problems are easily handled. The main advantage of algebraic splines is that they are completely parametrization free.
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.
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