问题
I am building a pyramid of images. First I take a big picture and build a smaller one even smaller, etc. I use interpolation to reduce the image. And I need to understand at what interpolation there will be less lost information between images. This is what I mean by interpolation quality. I am looking at horizontal gradients. Please tell me how good this criterion is or if there is something better.
Blurred = imfilter(img, PSF);
Blurred = im2double(Blurred)
Blurred2 = imresize(Blurred, [300 300], "Method", "bicubic");
[x0,y0] = meshgrid(1:360,1:360);
[x, y] = meshgrid(1:1.2:360, 1:1.2:360);
Blurred3 = interp2(x0, y0, Blurred, x,y, "spline");
gradX = diff(Blurred,1,1);
gradY = diff(Blurred,1,2);
gradX2 = diff(Blurred2,1,1);
gradY2 = diff(Blurred2,1,2);
gradX3 = diff(Blurred3,1,1);
gradY3 = diff(Blurred3,1,2);
[h, cx]=imhist(gradX);
[h2, cx2]=imhist(gradX2);
[h3, cx3]=imhist(gradX3);
h=log10(h);
h2 = log10(h2);
h3 = log10(h3);
figure, plot(cx, h)
hold on
plot(cx2, h2);
plot(cx3, h3);
hold off
回答1:
You're using the finite difference approximation to the derivative. The units in gradX are intensity units/pixel, with "pixel" the distance between pixels (which is assumed to be 1). When you rescale your image, you increase the pixel size, but in the derivative you're still assuming the distance between pixels is 1. Thus, the values in gradX2 are larger than those in gradX. You'd have to normalize by the image width to correct for this effect.
But still, after normalization, I don't see how this is a measure of quality of the interpolation. The right question would be: how well can I reconstruct Blurred from Blurred2? I'm assuming here that Blurred has been blurred just sufficiently to avoid aliasing when resampling the image.
I would apply a 2nd round of interpolation to Blurred2 to recover an image of the same size as Blurred, then compare the two images using MSE or similar error measure.
来源：https://stackoverflow.com/questions/63801487/how-to-evaluate-the-quality-of-interpolation