More Image Sharpness

ImageMagick has FFT build into it! You just use the appropriate command line options in ImageMagic's Convert application.  I found ImageMagick's FFT documentation really helpful in understanding 2d FFTs of images. I just takes two command lines. The first performs the FFT and creates a magnitude and a phase plot.

convert ohelo.png -fft fft_ohelo.png

The phase plot's not really useful to us, so we'll just take the magnitude plot, which is the one that has a -0 appended to its name. Because it's plotted on a linear scale, it doesn't look like much - almost entirely black. But if we auto-scale it, and plot logarithmically, a pattern emerges.

convert fft_ohelo-0.png -auto-level -evaluate log 10000000 fft_ohelo_10000000.png

You may have to play around with the log scaling. It took me several tries to get something usable.

Here is the set of test images:

Straight Out of the Camera

5 Pixel Blur

25 Pixel Blur

 It's hard to tell the difference between the original and the 5 pixel blur, but look at the FFTs.

Straight Out of the Camera

5 Pixel Blur

25 Pixel Blur

The white areas farther from the center have the highest spatial frequencies and therefore are the sharpest. Blurring the image filters those out and results in a smaller circle. I'm not sure I understand the horizontal and vertical artifacts, but I think that may have something to do with the rectangular arrangement of the pixels.

To make this more quantifiable, I next plan to use ImageMagic's Sample option to grab radial lines at 5 degree increments between 5 and 85 degrees. Because of the symmetry of the quadrants, it's only necessary to sample from one of them.  I'll then average the samples and plot them on an X-Y axis.

Also, to make this real, I need to take the pictures with two different cameras or lenses. I think the subject should be something natural like leaves because man-made objects in some examples I've seen tend to have strong diagonal artifacts.

A later post will explore some of these refinements and possibly add some Ruby automation to the process.