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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