1D Function into 2D Function Interpolation
in [Matlab]
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From: Royi Avital on 28 Mar 2010 20:42 Hello. I have a 1D function which I want to interpolate into 2D function. I know the function should have "Polar Symmetry". Hence I use the following code: Assuming the 1D function is LSF of the length 15. [x, y] = meshgrid([-7:7]); r = sqrt(x.^2 + y.^2); PSF = interp1([-7:7], LSF, r(:)); % Sometimes using 'spline' option, same results. PSF = reshape(PSF, [7, 7]); I have few problems: 1. Got some overshoot at the edges. 2. Can't enforce some assumptions (Monotonic, Non Negative). Is there a better Interpolation method for those circumstances? I couldn't find "Lanczos" based interpolation I can use the same way as interp1 (For a certain vector of points, in "imresize" you can only set the length). Is there such function anywhere? Has anyone encountered a function which allows enforcing some assumptions (Monotonically Decreasing, Non Negative, etc..). Thanks.
From: Matt J on 28 Mar 2010 23:13 "Royi Avital" <RoyiREMOVEAvital(a)yahoo.com> wrote in message <hoot0q$4bp$1(a)fred.mathworks.com>... > Hello. > I have a 1D function which I want to interpolate into 2D function. > I know the function should have "Polar Symmetry". > Hence I use the following code: > Assuming the 1D function is LSF of the length 15. > > [x, y] = meshgrid([-7:7]); > r = sqrt(x.^2 + y.^2); > PSF = interp1([-7:7], LSF, r(:)); % Sometimes using 'spline' option, same results. > > PSF = reshape(PSF, [7, 7]); > > I have few problems: > 1. Got some overshoot at the edges. > 2. Can't enforce some assumptions (Monotonic, Non Negative). ================ Linear interpolation should satisfy all these properties.
From: Bruno Luong on 29 Mar 2010 02:48 "Royi Avital" <RoyiREMOVEAvital(a)yahoo.com> wrote in message <hoot0q$4bp$1(a)fred.mathworks.com>... > Hello. > I have a 1D function which I want to interpolate into 2D function. > I know the function should have "Polar Symmetry". > Hence I use the following code: > Assuming the 1D function is LSF of the length 15. > > [x, y] = meshgrid([-7:7]); > r = sqrt(x.^2 + y.^2); > PSF = interp1([-7:7], LSF, r(:)); % Sometimes using 'spline' option, same results. > > PSF = reshape(PSF, [7, 7]); > > I have few problems: > 1. Got some overshoot at the edges. > 2. Can't enforce some assumptions (Monotonic, Non Negative). > > Is there a better Interpolation method for those circumstances? Perhaps John's SLM http://www.mathworks.com/matlabcentral/fileexchange/24443-slm-shape-language-modeling Bruno
From: Royi Avital on 29 Mar 2010 09:49 "Matt J " <mattjacREMOVE(a)THISieee.spam> wrote in message <hop5s0$a8j$1(a)fred.mathworks.com>... > "Royi Avital" <RoyiREMOVEAvital(a)yahoo.com> wrote in message <hoot0q$4bp$1(a)fred.mathworks.com>... > > Hello. > > I have a 1D function which I want to interpolate into 2D function. > > I know the function should have "Polar Symmetry". > > Hence I use the following code: > > Assuming the 1D function is LSF of the length 15. > > > > [x, y] = meshgrid([-7:7]); > > r = sqrt(x.^2 + y.^2); > > PSF = interp1([-7:7], LSF, r(:)); % Sometimes using 'spline' option, same results. > > > > PSF = reshape(PSF, [7, 7]); > > > > I have few problems: > > 1. Got some overshoot at the edges. > > 2. Can't enforce some assumptions (Monotonic, Non Negative). > ================ > > Linear interpolation should satisfy all these properties. No it doesn't. I'll show you. Let's create a 2d Gaussian Kernel: h = fspecial('gauss', 15, 3); Now let's take a 1D profile of it: LSF = h(8, :); Let's apply the linear algorithms: [x, y] = meshgrid([-7:7]); r = sqrt(x.^2 + y.^2); PSF = interp1([-7:7], LSF, r(:)); PSF = reshape(PSF, [7, 7]); The results (Added "Spline" and 'Pchip"): http://i43.tinypic.com/auxyxi.png As you can see at the edges there's "Overshoot" (Especially in "Spline"). The linear method gets negative values and changes the form. Thanks.
From: Royi Avital on 29 Mar 2010 09:59
"Bruno Luong" <b.luong(a)fogale.findmycountry> wrote in message <hopif2$fpa$1(a)fred.mathworks.com>... > "Royi Avital" <RoyiREMOVEAvital(a)yahoo.com> wrote in message <hoot0q$4bp$1(a)fred.mathworks.com>... > > Hello. > > I have a 1D function which I want to interpolate into 2D function. > > I know the function should have "Polar Symmetry". > > Hence I use the following code: > > Assuming the 1D function is LSF of the length 15. > > > > [x, y] = meshgrid([-7:7]); > > r = sqrt(x.^2 + y.^2); > > PSF = interp1([-7:7], LSF, r(:)); % Sometimes using 'spline' option, same results. > > > > PSF = reshape(PSF, [7, 7]); > > > > I have few problems: > > 1. Got some overshoot at the edges. > > 2. Can't enforce some assumptions (Monotonic, Non Negative). > > > > Is there a better Interpolation method for those circumstances? > > Perhaps John's SLM > http://www.mathworks.com/matlabcentral/fileexchange/24443-slm-shape-language-modeling > > Bruno It seems great but one thing, it seems to fit a plot to random points not to interpolate and extrapolate. Is there an option using is the same way I use interp1? Thanks. |