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.
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.
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.
A unified Eigenfilter approach is proposed for determining the mean-square-optimal coefficients of the McClellan transformation. The approach applies to all filter shapes without the use of prior knowledge of the prop...
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A unified Eigenfilter approach is proposed for determining the mean-square-optimal coefficients of the McClellan transformation. The approach applies to all filter shapes without the use of prior knowledge of the properties of the coefficients. Several design examples for arbitrarily shaped and oriented 2-D fan, elliptical, and diamond filters are given to demonstrate the results achieved with this method. Comparisons with other recently published methods are made to demonstrate the advantages of our method.
We describe the properties of algorithms based on methods of inhomogeneous diffusion and their application to image and video coding. Filtering by inhomogeneous diffusion has the desirable property of reducing noise a...
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We describe the properties of algorithms based on methods of inhomogeneous diffusion and their application to image and video coding. Filtering by inhomogeneous diffusion has the desirable property of reducing noise and other artifacts while preserving the image structure, maintaining or improving image quality. As a preprocessor, this filtering removes non-perceptible noise, leading to improved compression. As a postprocessor, it suppresses coding artifacts, such as the block impairments of DCT-based coders. Maintaining the basic structure of JPEG, MPEG, and other coders, we describe the improvements possible with inhomogeneous diffusion preprocessing and postprocessing.
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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Finite context models improve the performance of chain based encoders to the point that they become attractive, alternative models for binary image compression. The resulting code is within 4% of JBIG at 200 dpi and i...
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Finite context models improve the performance of chain based encoders to the point that they become attractive, alternative models for binary image compression. The resulting code is within 4% of JBIG at 200 dpi and is 9% more efficient at 400 dpi.
The design of a wavelet image coder can be divided into three parts: wavelet representation, quantization, and error-free encoding. We evaluate each of these parts individually and synthesize them into complete coders...
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The design of a wavelet image coder can be divided into three parts: wavelet representation, quantization, and error-free encoding. We evaluate each of these parts individually and synthesize them into complete coders. The evaluation is in the rate-distortion sense; two image quality metrics are used: a perception-based, quantitative picture quality scale (PQS) and the conventional distortion measure, peak signal-to-noise ratio (PSNR). Two representative wavelets, three quantizers, three encoders, and some combinations of these parts are comparatively evaluated. Our results provide an insight into the design issues of optimizing wavelet coders, as well as a good reference for application developers to choose from an increasingly large family of wavelet coders for their applications.
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