将1D高斯内插到2D高斯分布

Question

假设我有一维高斯函数.它的长度是600.

我想将其插值为600 X 600的2D高斯.

这是我写的代码(OTFx是高斯函数,OTF - 2d插值函数):

[x, y] = meshgrid([-300:299], [-300:299]);
r = sqrt((x .^ 2) + (y .^ 2));

OTF = interp1([-300:299], OTFx, r(:), 'spline');
OTF = reshape(OTF, [600, 600]);

问题是我最后得到了Overshoot: alt text http://i39.tinypic.com/259et0g.png

我该怎样预防呢？是否有更好的单调递减函数插值算法？

Answer 1

编辑:根据您的澄清,很明显发生了什么.您正在尝试插入超出可用数据范围的函数 - 即您将从插值到外推.样条曲线将导致您观察到的过冲.解决方案只是确保您的1D函数在区间[min(r),max(r)]中具有值.请注意,在原始数据中,max(r)约为424,而要插值的函数在[-300,299]范围内定义

% Simulated overshoot, see left figure:
x1d = [-300:299];
[x,y]=meshgrid(x1d,x1d);
r = sqrt(x.^2+y.^2);
gsn1d = exp(-x1d.^2/500);
lowpass = @(x)(x1d > -x & x1d < x);
gsn1dcutoff = ifft(fftshift(lowpass(10).*fftshift(fft(gsn1d))));
plot(gsn1dcutoff)
OTF2d = reshape(interp1(x1d,gsn1dcutoff,r(:),'spline'),[length(x1d),length(x1d)]);
mesh(OTF2d)

% Quick and dirty fix, see right figure:
x1dExtended = linspace(min(x1d*sqrt(2)),max(x1d*sqrt(2)),ceil(length(x1d)*sqrt(2)));
gsn1dE = exp(-x1dExtended.^2/500);
% ^^^ note that this has 600*sqrt(2) points and is defined on the diagonal of your square.   Now we can low-pass filter in the freq. domain to add ripple in space domain:
lowpass = @(x)(x1dExtended > -x & x1dExtended < x);
gsn1dcutoff = -real(ifft(fftshift(lowpass(10).*fftshift(fft(gsn1dE)))));
plot(gsn1dcutoff)
OTF2d = reshape(interp1(x1dExtended,gsn1dcutoff,r(:),'spline'),[length(x1d),length(x1d)]);
mesh(OTF2d)

替代文字http://img54.imageshack.us/img54/8255/clipboard01vz.png