Thin-plate spline fitting is often applied to fitting smooth surfaces to a collection of data. However, discontinuities in the data are smoothed by this technique. This occurs because of several underlying assumptions...
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ISBN:
(纸本)081940747X
Thin-plate spline fitting is often applied to fitting smooth surfaces to a collection of data. However, discontinuities in the data are smoothed by this technique. This occurs because of several underlying assumptions of spline fitting that do not hold when discontinuities are present. The theory of robust statistics can be used to deal with these outliers. In this paper, we present one way to apply the theory of robust statistics to the problem of discontinuous surface fitting.
In this paper, we deal with the problem of associative memory synthesis via multivariate interpolation. We present an abstract yet simple formalism to address the possibility of detecting and eliminating redundant inp...
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ISBN:
(纸本)081940747X
In this paper, we deal with the problem of associative memory synthesis via multivariate interpolation. We present an abstract yet simple formalism to address the possibility of detecting and eliminating redundant input data from the set of exemplars. The remaining pairs are then stored in a way so as to introduce controlled redundancy by replication of the corresponding neurons. The redundancy is detected via orthogonalization carried out in a Reproducing Kernel Hilbert Space setting.
In this paper, we firstly construct a general Binary Subdivision Algorithm (BSA) for surfaces over uniform triangulations and then present a matrix approach of convergence analysis. In the analysis, the idea of "...
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Integer versions of subdivision and corner cutting algorithms of NURBS curves are presented here. The algorithms are used to render NURBS curves of any degree on a raster device by either computing a polygonal approxi...
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This paper describes the first results of a test implementation of the new multivariate B-splines as recently developed for quadratics and cubics. The surface scheme is based on blending functions and control points a...
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ISBN:
(纸本)081940747X
This paper describes the first results of a test implementation of the new multivariate B-splines as recently developed for quadratics and cubics. The surface scheme is based on blending functions and control points and allows us to model Ck-1-continuous piecewise polynomial surfaces of degree k over arbitrary triangulations of the parameter plane. The surface scheme exhibits both affine invariance and the convex hull property, and the control points can be used to manipulate the shape of the surface locally. Additional degrees of freedom in the underlying knot net allow for the modeling of discontinuities. Explicit formulas are given for the representation of polynomials and piecewise polynomials as linear combinations of B-splines.
The polyphase decomposition of a sequence is a useful tool in multirate signal processing such as in the design of computationally efficient decimators and interpolators, the design of analysis/synthesis filter banks,...
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ISBN:
(纸本)081940747X
The polyphase decomposition of a sequence is a useful tool in multirate signal processing such as in the design of computationally efficient decimators and interpolators, the design of analysis/synthesis filter banks, and the development of fast discrete transform algorithms. This paper reviews a recently introduced generalization of the polyphase decomposition concept and outlines some of its applications in the simplification of digital filtering algorithms such as the design and implementation of finite-impulse-response (FIR) digital filters, the design of decimators and interpolators, and discrete Fourier transform computations.
Detection of corners in an image is very useful in computervision and pattern recognition. The existing algorithms for corner detection seem to be insufficient in many situations. The corner detection algorithm propo...
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ISBN:
(纸本)081940747X
Detection of corners in an image is very useful in computervision and pattern recognition. The existing algorithms for corner detection seem to be insufficient in many situations. The corner detection algorithm proposed in this paper is based on spline-wavelet decompositions. Corner and edge detectors are constructed from the 2-D wavelet transform coefficients. A somewhat sophisticated thresholding technique is applied to remove noise and minor irregularities in the images. Noise can be further reduced if additional processing is applied to the component images at all resolutions. Information on the edges and corners is contained in the component images in all the octaves to facilitate precise localization. A real-time wavelet decomposition algorithm is developed for the corner and edge detectors. It is very efficient and requires very little memory, since most of the computations involve only simple moving average operations and sub-sampling.
Traditional techniques for computing offsets are local in nature and lack good criteria for eliminating possible self-intersections of the offset. Methods based on integrating differential equations and image processi...
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ISBN:
(纸本)081940747X
Traditional techniques for computing offsets are local in nature and lack good criteria for eliminating possible self-intersections of the offset. Methods based on integrating differential equations and image processing do not lack such criteria but seem to require constructing the solution in the ambient space, i.e., in one dimension larger than the offset. We investigate such methods.
This paper presents an image interpolation algorithm using the recently developed local cardinal interpolatory spline (LCIS). The procedures for constructing the LCIS basis are described for both univariate and bivari...
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ISBN:
(纸本)081940747X
This paper presents an image interpolation algorithm using the recently developed local cardinal interpolatory spline (LCIS). The procedures for constructing the LCIS basis are described for both univariate and bivariate cases. This new LCIS algorithm is very efficient and can be implemented easily. Without the need of a mapping procedure, this method is faster than any other polynomial interpolation approach. The C2 property of the LCIS also allows the gradient operator to be constructed for edge detection. Both image interpolation and edge detection algorithms are compared with existing methods in two different examples.
We present two algorithms to construct C1-smooth models of skeletal structures from CT/NMR voxel data. The boundary of the reconstructed models consists of a C1- continuous mesh of triangular algebraic surface patches...
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ISBN:
(纸本)081940747X
We present two algorithms to construct C1-smooth models of skeletal structures from CT/NMR voxel data. The boundary of the reconstructed models consists of a C1- continuous mesh of triangular algebraic surface patches. One algorithm first constructs C1-continuous piecewise conic contours on each of the CT/NMR data slices and then uses piecewise triangular algebraic surface patches to C1 interpolate the contours on adjacent slices. The other algorithm works directly in voxel space and replaces an initial C0 triangular facet approximation of the model with a highly compressed C1- continuous mesh of triangular algebraic surface patches. Both schemes are adaptive, yielding a higher density of patches in regions of higher curvature.
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