为什么同一内核的多次打开/关闭不起作用? [英] Why multiple openings/closing with a same kernel does not have effect?

问题描述

我知道关门和开门的情况，但是我还有一个问题！根据冈萨雷斯(Gonzales)的数字图像处理，第三版"所述，打开/关闭的多次应用在您首次应用后没有任何效果！我不知道吗?有人可以帮忙吗?

解决方案

这是预期的行为，因为打开和关闭都是此处找到讨论.

在更直观的意义上，集合X上的开口是腐蚀，然后通过相同的结构化函数进行扩张.一旦完成第一次迭代，由于腐蚀和膨胀消除并在集合X中添加相同的"1"，则集合X不会更改.打开和关闭的乘积也是幂等运算-这非常有趣.另一方面，如果在每次迭代中都更改了用于打开/关闭的结构元素的半径，则将获得一个交替顺序滤镜，该滤镜产生图像的多尺度简化，从而产生一个

解决方案

This is expected behavior since openings and closings are idempotent operations. An operation is idempotent if, whenever it is applied twice to any value, it gives the same result as if it were applied once: f(f(x)) = f(x). Openings are operators on lattice L that are idempotent, increasing, and anti-extensive while closings are operators on L that are idempotent, increasing, and extensive. One can find a discussion on what is idempotence here.

In a more intuitive sense, an opening on set X is a erosion followed by dilation by the same structuring function. Once the first iteration is done the set X does not change since the erosion and dilation remove and add the same '1's in the set X. The product of opening and closing is also an idempotent operation - which is very interesting. One the other hand if at each iteration one changes the radius of the structuring element for the openings/closings, one would obtain an Alternated Sequential Filter, which produces multiscale simplification of the image, thus producing a scale-space.

I would refer you to the book by Jean Serra on mathematical morphology or better understanding.

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