We discuss the detection of a connected shape in a noisy image. Two types of image are considered: in the first a degraded outline of the shape is visible, while in the second the data are a corrupted version of the s...
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We discuss the detection of a connected shape in a noisy image. Two types of image are considered: in the first a degraded outline of the shape is visible, while in the second the data are a corrupted version of the shape itself. In the first type the shape is defined by a thin outline of pixels with records that are different from those at pixels inside and outside the shape, while in the second type the shape is defined by its edge and pixels inside and outside the shape have different records. Our motivation is the identification of cross-sectional head shapes in ultrasound images of human fetuses. We describe and discuss a new approach to detecting shapes in images of the first type that uses a specially designed filter function that iteratively identifies the outline pixels of the head. We then suggest a way based on the cascade algorithm introduced by Jubb and Jennison (1991) of improving and considerably increasing the speed of a method proposed by Storvik (1994) for detecting edges in images of the second type.
We give a characterization of the existence of compactly supported L(p)-solutions, 1 less than or equal to p < infinity, for the two-scale dilation equations. For the L(2)-case, the condition reduces to the determi...
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We give a characterization of the existence of compactly supported L(p)-solutions, 1 less than or equal to p < infinity, for the two-scale dilation equations. For the L(2)-case, the condition reduces to the determination of the spectral radius of a certain matrix in terms of the coefficients, which can be calculated through a finite step algorithm. For the other cases, we implement the characterization by the four-coefficient dilation equation and obtain some simple sufficient conditions for the existence of the solutions. The results are compared with known ones.
Because multiresolution analyses and wavelet bases are generated by translating and dilating scaling and wavelet functions, these functions must satisfy some special equations involving Toeplitz and Toeplitz-like oper...
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ISBN:
(纸本)0819418447
Because multiresolution analyses and wavelet bases are generated by translating and dilating scaling and wavelet functions, these functions must satisfy some special equations involving Toeplitz and Toeplitz-like operations. These relations can be exploited when such functions are to be constructed or their properties are studied. In the case of multiwavelets, where more than one scaling functions generate the multiresolution analysis, the corresponding operators are block Toeplitz-like. We discuss here some basic properties of these operators and compare them to the classical case of one scaling function. Using these observations we study the convergence of the cascade algorithm and derive sufficient conditions for existence of solution to a two-scale dilation equation.
The cascade algorithm that is used for extended surface analysis depends on a new parameterization called the thermal transmission matrix to represent a single fin. This thermal transmission matrix, which is intended ...
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The cascade algorithm that is used for extended surface analysis depends on a new parameterization called the thermal transmission matrix to represent a single fin. This thermal transmission matrix, which is intended to replace the more familiar fin efficiency as a design and analysis parameterization, is a linear transformation that maps conditions of heat flow and temperature at the fin tip to heat flow and temperature conditions at the fin base. The cascade algorithm was derived by resorting to an analogy between a fin and the electrical transmission line. The cascade algorithm permits a fin to be subdivided into many subfins each having a thermal transmission matrix and then the individual transmission matrices for each of the subfins can be used, via a simple matrix product to form an overall equivalent thermal transmission matrix for the entire fin. This thesis develops a thermal transmission matrix for the radiating rectangular, trapezoidal, and triangular fins both for the free space and non-free space environments. Test cases have been run and their solutions exactly match those contained in the literature. The thesis concludes with optimization studies for each profile considered where it is observed that simple algebraic equations can be employed to describe the optimum geometry.
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