ZERO-CROSSING BOUNDARY OF LAPLACE-GAUSSIAN FILTERED IMAGE AND ITS FRACTAL DIMENSION
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摘要: 本文考察了用拉普拉斯—高斯滤波器对遥感图象过零边界的计算方法.给出了直接从遥感图象边界转换成过零边界的稳函数.分析可看到,从遥感图象边界化算出过零边界是局地性决定的方式,得到的过零边界相对于原遥感图象边界的偏差主要取决于图象尺度、边界的局地曲率半径和所用高斯函数的尺度常数.证明拉普拉斯—高斯滤波过零边界法在图象尺度和曲率半径都大于高斯尺度常数10倍以上时,是获得遥感图象边界的精确方法.Abstract: The method of calculation of zero-crossing boundary of an observed image using replace-Gaussian filter is examined. It is shown that the determination of the zero-crossing boundary by the observed boundary is of local fashion. The deviation of the zer0-crossing boundary from the observed boundary depends mainly on the size scale L of the image, the local curvature radius ρ of the boundary, and the size constant of the Gaussian function, The deviation is smaller for smaller and large L and ρ. There are four critical values to characterize the features of the influence of σon the deviation of zero-crossing boundary from the observed boundary:wipe-out value (σ/L = 1/3), fractal value (σ/L = 1/ 10), exaggeration value (σ/L = 1/3), and deviation-free value (σ/L = 1/10). If σ/L is large than wipe-out value, the image will be wiped out by the filter and no zero-crossing boundary exists. When σ/L is less than the wipe-out value a zero-crossing boundary exists and can be obtained directly from the observed boundary. For σ/L less than the fractal value, zero-crossing boundary will faithfully thee the observed boundary and fractal dimension of the boundary curve can also be calculated. If σ/ρ is around the exaggeration value, the zero-crossing boundary will exaggerate the fluctuations in the observed boundary curve.If σ/p is less than the deviation-free value, the deviation of zero-crossing boundary from the observed boundary is not discernible. Therefore replace-Gaussian flited zero-crossing is an accurate method to locate homogeneous image boundary which the size and curvature radius are larger than 10σ.
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Key words:
- Image processing /
- Zero-crossing boundary
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