Hello, I'm currently studying a Deriche filter. I've managed to create python program for derivative smoothing from this article [1]. As I understand, Deriche used one α for smoothing in both directions - X and Y, so this filter seems to me isotrophic. Is it correct way to use two alphas − α_x and α_y to add anistrophy?
Can someone please explain me the relaion between α in Deriche filter and σ in Gaussian filter? In [1] i found an equation picture, but i do not understand the symbol П. Is it π? To my mind, it's not, because in the article they took α = 0.14 and σ = 10. From these values П = 625/19≈3.1887755.
Thank you.
[1]: Deriche, R. (1990). Fast algorithms for low-level vision. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(1), 78–87. doi:10.1109/34.41386
Dear Dr Timur: Denoising image is considered as a very important pretreatment and a basic operation for meaningful analysis of acquired image. For more on this have a look at :
Article Isotropic and anisotropic filtering techniques for image den...
and
Conference Paper Fast Anisotropic Gauss Filtering
Regards--
These (separable) exponential filters are not isotropic like a (separable) Gaussian filter, even when the same alpha coefficient is used in the x and y directions. This is a unique property of Gaussian filters. By 'isotropic', I mean rotationally invariant. When you apply the low-pass exponential filter in 2D you can see the ridges along the x and y axes, but the Gaussian filter has perfect rotational symmetry. (Or near perfect if discretization and truncation are considered.)
The (non-recursive, FIR) Gaussian filter is parameterized using sigma, which is a standard deviation for an impulse response of h[m] = exp(-1/2*m^2/sigma^2)
The (recursive, IIR) exponential filter is parameterized using alpha for an impulse response h[m] = exp(-alpha*|m|), so 1/alpha could be interpreted as a standard deviation.
@ Ijaz Durrani Thank you for your answer and sorry for the long reply! Definitely will study these articles, thank you.
Aparna Sathya Murthy Thank you and sorry for long reply. I will use two alphas to create anistrophic filter!
You said that Deriche filter is a high pass filter, but Hale in [2] confirm it's a low pass filter.
[2] https://inside.mines.edu/~dhale/papers/Hale06RecursiveGaussianFilters.pdf
Hugh Lachlan Kennedy Thank you and sorry for long reply! Can you please give some more explanations about sigma = 1 / alpha? Because i do not understand how you get this equation from h[m] = exp(-1/2*m^2/sigma^2) and h[m] = exp(-alpha*|m|).
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