A set of simultaneous quadratic equations with unknown coefficients is considered. The motivation for studying the equations is presented. Indeterminacy and identifiability are considered. A main lemma and three theor...
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A set of simultaneous quadratic equations with unknown coefficients is considered. The motivation for studying the equations is presented. Indeterminacy and identifiability are considered. A main lemma and three theorems are presented. A comparison with the well-known simultaneous diagonalization problem is given.< >
In this paper we present some enlightening results to show why and how stability assessment for Linear Time-Varying (LTV) systems based solely on the location of the "frozen-time eigenvalues (FTE)" fails to ...
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The authors present a surface triangulation technique for surface description at different levels of resolution in a range image. A step discontinuity constrained 2-1/2-D triangulation of all points is first computed....
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The authors present a surface triangulation technique for surface description at different levels of resolution in a range image. A step discontinuity constrained 2-1/2-D triangulation of all points is first computed. A sequential optimization process then removes, at each iteration. the point that minimizes the local retriangulation approximation error caused by its removal. The iterative process can stop at any time to obtain a desired level of approximation error.< >
Presents a method to compute the inter-frame transformation between two range image views of complex multi-part objects. No exact feature matching is attempted and no initial approximate transformation is provided. Th...
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Presents a method to compute the inter-frame transformation between two range image views of complex multi-part objects. No exact feature matching is attempted and no initial approximate transformation is provided. The method is naturally decomposed into two stages of initial estimation and final refinement of the transformation. A hierarchical triangulation-based surface representation provides an efficient way to select the control points at which the alignment of the two surfaces is to be evaluated. This representation also permits the selection of a manageable number of initial transformations among which at least one is to be in the parametric neighborhood of the actual transformation. Experimental results show that the computed transformation between two views of a complex multi-part object may provide angles of rotation within a fraction of a degree of the actual ones.< >
The authors develop an empirical measure for the selection of the Gaussian filter that is commonly used for edge enhancement. The measure is based totally on the image at hand. Edge enhancement by a Gaussian filter ha...
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The authors develop an empirical measure for the selection of the Gaussian filter that is commonly used for edge enhancement. The measure is based totally on the image at hand. Edge enhancement by a Gaussian filter has two distinct advantages: (1) the filter is fully described by a single parameter, the standard deviation sigma ; (2) the two-dimensional filter is separable and can be easily implemented. The filter's spatial support is a function of sigma . This support is normally in the range of +or-3.5 sigma . An empirical measure is described for the selection of the Gaussian filter's spatial support using the power spectrum density of the input image. Classic Fourier analysis is used to obtain a measure for the spatial support of the Gaussian filter given a particular image. Experimental results suggest that this measure can be used as an aid in deciding the Gaussian filter's spatial support needed to enhance the edges.< >
A new layered representation of images is proposed using, what one may call, vector wavelets defined by generalized Hermite polynomials. This representation has some special properties: it is distinct from and superio...
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A new layered representation of images is proposed using, what one may call, vector wavelets defined by generalized Hermite polynomials. This representation has some special properties: it is distinct from and superior to the other wavelet schemes of the literature; it is stable; it transforms the image into matrices of coefficients in the same manner as the standard transforms (Fourier, Hadamard and others), but at the specified 'scales'; the zero-crossings of the signal at various scales can be directly obtained from the coefficients; and the size of the resolution cell in the 'phase-space' is variable even at a specified scale, depending on the image being analysed. This representation has been successfully applied to different types of images, both synthetic and natural.< >
An edge detection technique that optimizes edge localization while providing edge continuity and edge thinning is introduced. The solution is obtained by annealing a mean field neural network, providing inexpensive so...
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An edge detection technique that optimizes edge localization while providing edge continuity and edge thinning is introduced. The solution is obtained by annealing a mean field neural network, providing inexpensive solutions with high parameter insensitivity. Anisotropic diffusion is used to provide localized edge data through the scale-space. analysis of network parameters, diffusion parameters, network convergence, and scale-space equivalence is provided. Results are shown for real image data and compared with the results of other important edge detection schemes.< >
A mathematical framework for the solution of statistical inference problems on a class of random sets is proposed. It is based on a new definition of expected pattern. The least-mean-difference estimator (restoration ...
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A mathematical framework for the solution of statistical inference problems on a class of random sets is proposed. It is based on a new definition of expected pattern. The least-mean-difference estimator (restoration filter) is proved, under certain conditions, to be equivalent to the minimization of the measure of size (area) of the set-difference between the original pattern and the expected pattern of the estimated (restored) pattern. Consequently, it is proved that, under certain conditions, if the estimator (restoration filter) is unbiased, then it is the least mean difference estimator (restoration filter).< >
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