用高斯·拉普拉斯·过零法计算遥感影像中不同类区域边界位置的精度

Calculation of Boundary between Regions of Different Classes in Remote Sensing Image by Gaussian Laplace Zerocrossing Method

高斯·拉普拉斯·过零法是目前计算机图像处理中普遍用来计算遥感影像中不同类区域的边界位置的方法。对该方法计算得到的边界位置的精度作了分析计算，结果表明，边界计算的精度取决于所用的高斯特征尺度σ和实际边界的形状，后者的影响是局地性的。在实际计算中可以忽略掉距离超过４σ的那些边界段的影响。

Gaussian Laplace Zerocrossing method is general accepted method to calculateboundary between regions of different classes in remote sensing image. Analytical calcula-tion of the accuracy of calculated boundary by the method is given, The existance of theboundary by zerocrossing method is shown first. It is then shown that the position of thecalculated boundary is determined by the summation of the contributions by all sections ofthe real boundaries. The most important contribution comes from the section where lo-cates one Gaussian scale away. The influence of those boundary sections with distances far-ther than four Gaussian scales is neglectable. It can therefore be said that the influence ofthe shape of the real boundary on the position of the calctilated boundary is of localfash-ion.If the line of a real boundary is longer than eight Garssian scales,the calculatedboundary in the middle will be identical with the real boundary. If the real boundary is convex, the calculated boundary will deviate out more convexlythan the real boundary. If the real bounday is concave,the calculated boundary will deviatein more concavely. The amotint of deviation depends upon local (within four Gaussianscales)curvature of the real boundary and the Gaussian scale. The larger the curvature,thesmaller the deviation. The larger the scale, the larger the deviation.Although the image is considered as a two dimensional functions in the Gaussian Laplace Zerocrossing method, for an image with constant intensities, we can also direct-1y transform the real boundary into calculated boundary. The formulas for the directtransformation is given in the paper.