In many applications one is concerned with the approximation of functions from a finite set of given data sites with associated function values. We describe a construction of a hierarchy of triangulations which approx...
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In many applications one is concerned with the approximation of functions from a finite set of given data sites with associated function values. We describe a construction of a hierarchy of triangulations which approximate the given data at varying levels of detail. Intermediate triangulations can be associated with a particular level of the hierarchy by considering their approximation errors. This paper presents a new data-dependent triangulation scheme for multi-valued scattered data in the plane. We perform piecewise linear approximation based on data-dependent triangulations. Our scheme preserves edges (discontinuities) that might exist in a given data set by placing vertices close to edges. We start with a coarse, data-dependent triangulation of the convex hull of the given data sites and subdivide triangles until the error of the piecewise linear approximation implied by a triangulation is smaller than some tolerance.
In many applications one is concerned with techniques for visualizing data sets with real-time interaction. One technique for providing real-time performance is through the use of multiresolution techniques. These tec...
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In many applications one is concerned with techniques for visualizing data sets with real-time interaction. One technique for providing real-time performance is through the use of multiresolution techniques. These techniques provide multiple representations of a data set at different levels of detail. The idea is to select a level of detail that can be rendered within the user's time constraints. We discuss a mechanism which renders finer-detailed representations where the data set has a high frequency, and coarser representations where the data set has lower frequency. We present a new technique for storing curvilinear data sets within a quadtree representation and discuss two rendering schemes: an anti-aliasing scheme and a scheme for maintaining a specified frame rate.
We present a highly efficient, automatic method for the generation of hierarchical surface triangulations. Given a set of scattered points in three-dimensional space, without known connectivity information, our method...
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We present a highly efficient, automatic method for the generation of hierarchical surface triangulations. Given a set of scattered points in three-dimensional space, without known connectivity information, our method reconstructs a valid triangulated surface model in a two-step procedure. First, we apply clustering to the set of given points and identify point subsets in locally nearly planar regions. Second, we construct a surface triangulation from the output of the clustering step. The output of the clustering step is a set of 2-manifold tiles, which locally approximate the underlying, unknown surface. We construct the triangulation of the entire surface by triangulating the individual tiles and triangulating the gaps between the tiles. Since we apply point clustering in a hierarchical fashion we can generate model hierarchies by triangulating various levels resulting from the hierarchical clustering step.
We present two applications of wavelet and related techniques to problems arising in medical imaging. Both make considerable use of the edge detection and classification properties of wavelet-type representations. Fir...
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This paper presents a method to preprocess an image so that when segmented it yields a partitioning in which textured regions are approximated with a substantially reduced number of uniform regions (which is desirable...
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This paper presents a method to preprocess an image so that when segmented it yields a partitioning in which textured regions are approximated with a substantially reduced number of uniform regions (which is desirable...
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This paper presents a method to preprocess an image so that when segmented it yields a partitioning in which textured regions are approximated with a substantially reduced number of uniform regions (which is desirable for the coding). The segmentation method used to form this representation combines a Gaussian texture model and Gibbs-Markov contour model in order to find regions with boundaries which correspond closely to the objects in the image. Given the image segmentation, an approximation to the original image is generated by filling each region with its mean value. If higher quality reconstruction is desired, the quantized approximation error is also encoded. In order to exploit the reduced sensitivity of the human visual system to the error around edges (visual masking), the error is quantized using three nonlinear quantizers corresponding to the smoothly varying, textured, and remaining areas of the image, respectively.< >
A maximum likelihood estimation (MLE) method is used to estimate the fractal dimension of a number of natural texture images with and without the presence of noise. An additional texture measure which can be linked to...
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A maximum likelihood estimation (MLE) method is used to estimate the fractal dimension of a number of natural texture images with and without the presence of noise. An additional texture measure which can be linked to the lacunarity measure is used to characterize natural textures since fractal dimension alone cannot totally characterize texture images. Segmentation of natural textures is successfully achieved by a k-means clustering algorithm using fractal dimension and the additional measure as representative features.< >
We investigate the performance of selected texture models for the purpose of land use classification. The texture models are evaluated based on the resulting classification error rates. Three classes of texture models...
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