通过使用对数图像处理的Asplund距离映射实现双面探测
Double-sided probing by map of Asplund's distances using Logarithmic Image Processing in the framework of Mathematical Morphology
AI总结：
本文在数学形态学框架下，利用对数图像处理的标量乘法建立数学形态学与探针与灰度函数之间Asplund距离映射的联系，并通过实例展示该方法在模式匹配中的应用。
摘要：
我们通过使用对数图像处理的标量乘法，建立了数学形态学与探针和灰度函数之间Asplund距离映射之间的联系。我们证明该映射是函数通过结构函数（即探针）进行膨胀和腐蚀的比值的对数。膨胀和腐蚀是将图像的格映射到正函数的格中的映射。使用平坦的结构元素，可以通过图像的膨胀和腐蚀来简化Asplund距离映射的表达，这些映射仍保留在图像的格中。我们通过一个使用非平坦结构函数的模式匹配示例来展示我们的方法。
英文摘要：
We establish the link between Mathematical Morphology and the map of Asplund's distances between a probe and a grey scale function, using the Logarithmic Image Processing scalar multiplication. We demonstrate that the map is the logarithm of the ratio between a dilation and an erosion of the function by a structuring function: the probe. The dilations and erosions are mappings from the lattice of the images into the lattice of the positive functions. Using a flat structuring element, the expression of the map of Asplund's distances can be simplified with a dilation and an erosion of the image; these mappings stays in the lattice of the images. We illustrate our approach by an example of pattern matching with a non-flat structuring function.
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