Re: 2-D Butterworth lowpass filter?

*To*: mathgroup at smc.vnet.net*Subject*: [mg113829] Re: 2-D Butterworth lowpass filter?*From*: hadi motamedi <motamedi24 at gmail.com>*Date*: Sun, 14 Nov 2010 06:11:29 -0500 (EST)

On 11/12/10, Patrick Scheibe <pscheibe at trm.uni-leipzig.de> wrote: > Hi, > > using Gonzalez/Woods again (page 273, 3rd ed.) the transfer function is > given by > > d[u_, v_, p_, q_] := Sqrt[(u - p/2)^2 + (v - q/2)^2] > h[u_, v_, p_, q_, n_, d0_] := 1/(1 + (d[u, v, p, q]/d0)^(2 n)); > > I'm using a compiled version of it > > hc = Compile[{u, v, p, q, n, d0}, > 1/(1 + (Sqrt[(u - p/2)^2 + (v - q/2)^2]/d0)^(2 n))]; > hcompiled[u_?NumericQ, v_?NumericQ, p_?NumericQ, q_?NumericQ, > n_?NumericQ, d0_?NumericQ] := hc[u, v, p, q, n, d0] > > With this the plots on page 274 are > > Plot3D[hcompiled[u, v, 0, 0, 3, 3], {u, -15, 15}, {v, -15, 15}, > PlotRange -> All, PlotPoints -> 30] > Plot[Evaluate[h[u, 0, 0, 0, #, 5] & /@ Range[4]], {u, 0, 15}, > PlotStyle -> {Thick}, PlotRange -> All] > > And now (taking the CenteredFourier from Matthias) > > CenteredFourier[img_] := > Module[{data = ImageData[img], dim}, dim = Dimensions[data]; > Fourier[data*(-1)^Table[i + j, {i, First[dim]}, {j, Last[dim]}]]]; > > CenteredInverseFourier[F_] := Module[{dim}, dim = Dimensions[F]; > Image[Re[ > InverseFourier[F]*(-1)^ > Table[i + j, {i, First[dim]}, {j, Last[dim]}]]]]; > > ButterWorthFilter[img_, n_, d0_] := Module[{nx, ny, bw}, > {nx, ny} = ImageDimensions[img]; > bw = Table[hcompiled[u, v, nx, ny, n, d0], {v, 1, ny}, {u, 1, nx}]; > CenteredInverseFourier[bw*CenteredFourier[img]] > ] > > > And to test it you could try to create figure 4.45 of the book (please > check that there are no unwanted newlines in the link-strings when you > copy it to the notebook!) > > img = Import[ > "http://www.imageprocessingplace.com/downloads_V3/dip3e_downloads/\ > dip3e_book_images/DIP3E_CH04_Original_Images.zip", > "DIP3E_Original_Images_CH04/Fig0445(a)(characters_test_pattern).\ > tif"]; > GraphicsGrid@ > Partition[ > Flatten[{img, > ButterWorthFilter[img, 2, #] & /@ {10, 30, 60, 160, 460}}], 2] > > > I must admit that the images in the book are more blurred with the same > setting. > > Cheers > Patrick > Thank you very much for your help. I tried for your code but I didn't see the resulted filtered image. Can you please let me know how to display the resulted filtered image?