理想的低通过过滤器将把所有空间频率维持在名义空间频率以下,并移除所有空间频率。 不幸的是,一个真正的理想的低通过过滤器有无限的支持(即拥有无限大的非零空间延伸 ) 。 即使一个实际近似于理想的低通过过滤器也有巨大的空间支持。
另一方面,Gaussian在过滤频率方面并不理想。 空间域的Gaussian在空间频域中被证明是Gaussian。 也就是说, 它不会产生非常尖锐的空间频率选择性。 不过, 过滤器的空间支持很小。 人们为此使用Gaussian过滤器, 因为这些过滤器比较方便。 与 Gaussian 进行过滤时, 与理想的低传过滤器相比, 通常看上去“ 自然 ”, 而理想的低传过滤器则能产生响铃的文物 。
Lanczos过滤器(窗口的罪过过滤器)也是另一种选择,因为它的空间支持很小,而且比高斯人更接近理想的过滤器。
然而,这对您的形象更好,这在很大程度上取决于您想要做什么。 虽然背后有重要的理论,但在图像处理中,这样的定性选择在很大程度上是一种艺术。
The type of filter you are looking for is ideally nonlinear: smoothing in areas without large-scale gradients (edges), and little smoothing close to edges to be preserved.
以下是两个备选方案:
The Kuwahara filter: http://homepage.tudelft.nl/e3q6n/publications/1999/PAA99DRBDPVLV/PAA99DRBDPVLV.pdf
Enhanced shortening flow (Figure 8) in: http://www.cs.jhu.edu/~misha/Fall07/Papers/intro-to-scalespace.pdf
In the second filter (Enhanced shortening flow), you can vary the scale parameter and the nonlinear function, h(Lw) on page 17. Thus, more trimming possibilities.
Ideally, the filter is completely isotropic (same frequency effect on each possible angle).
迈克尔·迈克尔
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