This week I have tried to rewrite some of my C sharpness estimation code from a couple years ago in Python. Click here for a description and examples of how that code worked (section 2: 'selecting images'). One difference between then and now is that then the sharpness was estimated from a cloud-only subdisk extracted from aligned and preprocessed images and then run through a 2d Blackman filter before performing the FFT. Now, the estimate will need to be performed on raw images, full-frame. Hopefully it will work nearly as well.
I'm writing a Python program called 'sharpness.py' that reads either a single FITS image or a folder of images. If a single image, there is also an option to use PyQt to display the image and several intermediate results. Here is an example of reading an image (1041 on 7/13/04), taking the log(abs(fft)^2), and plotting the result wrt radial distance from the center of the transform:
Here is the radius of the transform and a plot of log(abs(fft)^2) x radius:
Here is the same thing plotting every 8th sample, and then a distribution made from 32 bins of the normalized average coefficients for spacial frequencies from 0 - 256 cycles/image (Nyquist limit):
Here is a printout of the distribution:
Min radius Max radius Max wavelength Min wavelength Count Score ---------- ---------- -------------- -------------- ----- ----- 0.00000000 8.00000000 512.00000000 64.00000000 197 0.04307483 8.00000000 16.00000000 64.00000000 32.00000000 604 0.04029211 16.00000000 24.00000000 32.00000000 21.33333333 1000 0.03865690 24.00000000 32.00000000 21.33333333 16.00000000 1420 0.03746054 32.00000000 40.00000000 16.00000000 12.80000000 1820 0.03648501 40.00000000 48.00000000 12.80000000 10.66666667 2200 0.03562503 48.00000000 56.00000000 10.66666667 9.14285714 2636 0.03479370 56.00000000 64.00000000 9.14285714 8.00000000 3012 0.03402480 64.00000000 72.00000000 8.00000000 7.11111111 3392 0.03327356 72.00000000 80.00000000 7.11111111 6.40000000 3844 0.03253255 80.00000000 88.00000000 6.40000000 5.81818182 4244 0.03177532 88.00000000 96.00000000 5.81818182 5.33333333 4608 0.03104300 96.00000000 104.00000000 5.33333333 4.92307692 5036 0.03043207 104.00000000 112.00000000 4.92307692 4.57142857 5444 0.02991078 112.00000000 120.00000000 4.57142857 4.26666667 5848 0.02935766 120.00000000 128.00000000 4.26666667 4.00000000 6220 0.02908197 128.00000000 136.00000000 4.00000000 3.76470588 6660 0.02881528 136.00000000 144.00000000 3.76470588 3.55555556 7024 0.02866269 144.00000000 152.00000000 3.55555556 3.36842105 7436 0.02849598 152.00000000 160.00000000 3.36842105 3.20000000 7852 0.02832412 160.00000000 168.00000000 3.20000000 3.04761905 8264 0.02829784 168.00000000 176.00000000 3.04761905 2.90909091 8644 0.02823004 176.00000000 184.00000000 2.90909091 2.78260870 9084 0.02807906 184.00000000 192.00000000 2.78260870 2.66666667 9432 0.02800991 192.00000000 200.00000000 2.66666667 2.56000000 9852 0.02806763 200.00000000 208.00000000 2.56000000 2.46153846 10268 0.02812096 208.00000000 216.00000000 2.46153846 2.37037037 10640 0.02807495 216.00000000 224.00000000 2.37037037 2.28571429 11084 0.02808236 224.00000000 232.00000000 2.28571429 2.20689655 11468 0.02813657 232.00000000 240.00000000 2.20689655 2.13333333 11880 0.02808763 240.00000000 248.00000000 2.13333333 2.06451613 12300 0.02825625 248.00000000 256.00000000 2.06451613 2.00000000 12658 0.02843890
Here is the same thing for a blurrier image (3540 on 7/13/04):
Min radius Max radius Max wavelength Min wavelength Count Score ---------- ---------- -------------- -------------- ----- ----- 0.00000000 8.00000000 512.00000000 64.00000000 197 0.04398423 8.00000000 16.00000000 64.00000000 32.00000000 604 0.04117782 16.00000000 24.00000000 32.00000000 21.33333333 1000 0.03929861 24.00000000 32.00000000 21.33333333 16.00000000 1420 0.03772854 32.00000000 40.00000000 16.00000000 12.80000000 1820 0.03641676 40.00000000 48.00000000 12.80000000 10.66666667 2200 0.03509932 48.00000000 56.00000000 10.66666667 9.14285714 2636 0.03386101 56.00000000 64.00000000 9.14285714 8.00000000 3012 0.03270312 64.00000000 72.00000000 8.00000000 7.11111111 3392 0.03153483 72.00000000 80.00000000 7.11111111 6.40000000 3844 0.03065055 80.00000000 88.00000000 6.40000000 5.81818182 4244 0.03022037 88.00000000 96.00000000 5.81818182 5.33333333 4608 0.02984994 96.00000000 104.00000000 5.33333333 4.92307692 5036 0.02962684 104.00000000 112.00000000 4.92307692 4.57142857 5444 0.02948804 112.00000000 120.00000000 4.57142857 4.26666667 5848 0.02931253 120.00000000 128.00000000 4.26666667 4.00000000 6220 0.02923771 128.00000000 136.00000000 4.00000000 3.76470588 6660 0.02905015 136.00000000 144.00000000 3.76470588 3.55555556 7024 0.02897174 144.00000000 152.00000000 3.55555556 3.36842105 7436 0.02886230 152.00000000 160.00000000 3.36842105 3.20000000 7852 0.02878383 160.00000000 168.00000000 3.20000000 3.04761905 8264 0.02869115 168.00000000 176.00000000 3.04761905 2.90909091 8644 0.02872059 176.00000000 184.00000000 2.90909091 2.78260870 9084 0.02867005 184.00000000 192.00000000 2.78260870 2.66666667 9432 0.02859581 192.00000000 200.00000000 2.66666667 2.56000000 9852 0.02855485 200.00000000 208.00000000 2.56000000 2.46153846 10268 0.02855297 208.00000000 216.00000000 2.46153846 2.37037037 10640 0.02850872 216.00000000 224.00000000 2.37037037 2.28571429 11084 0.02853153 224.00000000 232.00000000 2.28571429 2.20689655 11468 0.02866671 232.00000000 240.00000000 2.20689655 2.13333333 11880 0.02877451 240.00000000 248.00000000 2.13333333 2.06451613 12300 0.02892382 248.00000000 256.00000000 2.06451613 2.00000000 12658 0.02895105
Side-by-side:
Not too different. However, if instead of log(abs(fft)^2) one calculates just abs(fft)^2 and then computes the distribution of the normalized total (not average) coefficients at each radius, there is a difference in the percentage of energy in each frequency band of the image:
Min radius Max radius Max wavelength Min wavelength Count Score
---------- ---------- -------------- -------------- ----- -----
0.00000000 8.00000000 512.00000000 64.00000000 197 0.73503861
8.00000000 16.00000000 64.00000000 32.00000000 604 0.13970486
16.00000000 24.00000000 32.00000000 21.33333333 1000 0.05148516
24.00000000 32.00000000 21.33333333 16.00000000 1420 0.02524016
32.00000000 40.00000000 16.00000000 12.80000000 1820 0.01383987
40.00000000 48.00000000 12.80000000 10.66666667 2200 0.00826908
48.00000000 56.00000000 10.66666667 9.14285714 2636 0.00517407
56.00000000 64.00000000 9.14285714 8.00000000 3012 0.00347442
64.00000000 72.00000000 8.00000000 7.11111111 3392 0.00243512
72.00000000 80.00000000 7.11111111 6.40000000 3844 0.00169278
80.00000000 88.00000000 6.40000000 5.81818182 4244 0.00116907
88.00000000 96.00000000 5.81818182 5.33333333 4608 0.00091015
96.00000000 104.00000000 5.33333333 4.92307692 5036 0.00074590
104.00000000 112.00000000 4.92307692 4.57142857 5444 0.00057999
112.00000000 120.00000000 4.57142857 4.26666667 5848 0.00044773
120.00000000 128.00000000 4.26666667 4.00000000 6220 0.00039566
128.00000000 136.00000000 4.00000000 3.76470588 6660 0.00034138
136.00000000 144.00000000 3.76470588 3.55555556 7024 0.00029665
144.00000000 152.00000000 3.55555556 3.36842105 7436 0.00025688
152.00000000 160.00000000 3.36842105 3.20000000 7852 0.00021864
160.00000000 168.00000000 3.20000000 3.04761905 8264 0.00020143
168.00000000 176.00000000 3.04761905 2.90909091 8644 0.00019260
176.00000000 184.00000000 2.90909091 2.78260870 9084 0.00017961
184.00000000 192.00000000 2.78260870 2.66666667 9432 0.00018821
192.00000000 200.00000000 2.66666667 2.56000000 9852 0.00018359
200.00000000 208.00000000 2.56000000 2.46153846 10268 0.00019149
208.00000000 216.00000000 2.46153846 2.37037037 10640 0.00019281
216.00000000 224.00000000 2.37037037 2.28571429 11084 0.00022811
224.00000000 232.00000000 2.28571429 2.20689655 11468 0.00029883
232.00000000 240.00000000 2.20689655 2.13333333 11880 0.00042021
240.00000000 248.00000000 2.13333333 2.06451613 12300 0.00082809
248.00000000 256.00000000 2.06451613 2.00000000 12658 0.00517882
0.00000000 8.00000000 512.00000000 64.00000000 197 0.81966587
8.00000000 16.00000000 64.00000000 32.00000000 604 0.10535610
16.00000000 24.00000000 32.00000000 21.33333333 1000 0.03608526
24.00000000 32.00000000 21.33333333 16.00000000 1420 0.01417297
32.00000000 40.00000000 16.00000000 12.80000000 1820 0.00664905
40.00000000 48.00000000 12.80000000 10.66666667 2200 0.00330262
48.00000000 56.00000000 10.66666667 9.14285714 2636 0.00181718
56.00000000 64.00000000 9.14285714 8.00000000 3012 0.00112734
64.00000000 72.00000000 8.00000000 7.11111111 3392 0.00084038
72.00000000 80.00000000 7.11111111 6.40000000 3844 0.00062928
80.00000000 88.00000000 6.40000000 5.81818182 4244 0.00053931
88.00000000 96.00000000 5.81818182 5.33333333 4608 0.00040022
96.00000000 104.00000000 5.33333333 4.92307692 5036 0.00029603
104.00000000 112.00000000 4.92307692 4.57142857 5444 0.00025086
112.00000000 120.00000000 4.57142857 4.26666667 5848 0.00023486
120.00000000 128.00000000 4.26666667 4.00000000 6220 0.00018879
128.00000000 136.00000000 4.00000000 3.76470588 6660 0.00017594
136.00000000 144.00000000 3.76470588 3.55555556 7024 0.00016599
144.00000000 152.00000000 3.55555556 3.36842105 7436 0.00016438
152.00000000 160.00000000 3.36842105 3.20000000 7852 0.00017701
160.00000000 168.00000000 3.20000000 3.04761905 8264 0.00018789
168.00000000 176.00000000 3.04761905 2.90909091 8644 0.00019037
176.00000000 184.00000000 2.90909091 2.78260870 9084 0.00019563
184.00000000 192.00000000 2.78260870 2.66666667 9432 0.00022959
192.00000000 200.00000000 2.66666667 2.56000000 9852 0.00025868
200.00000000 208.00000000 2.56000000 2.46153846 10268 0.00023637
208.00000000 216.00000000 2.46153846 2.37037037 10640 0.00022866
216.00000000 224.00000000 2.37037037 2.28571429 11084 0.00023924
224.00000000 232.00000000 2.28571429 2.20689655 11468 0.00028155
232.00000000 240.00000000 2.20689655 2.13333333 11880 0.00039331
240.00000000 248.00000000 2.13333333 2.06451613 12300 0.00075834
248.00000000 256.00000000 2.06451613 2.00000000 12658 0.00456096
For example, compare the percent energy in the bands ending at wavelengths of 64 pixels, 32, 16, 8, 4, and 2:
64: 0.73503861 0.81966587 32: 0.13970486 0.10535610 16: 0.02524016 0.01417297 8: 0.00347442 0.00112734 4: 0.00039566 0.00018879 2: 0.00517882 0.00456096
In particular, the sharper image has less energy in the 512-64 pixel band, and more energy in the bands ending at 16, 8, 4, and 2 pixels. If one also sums these bands by 'octave', the results are more striking:
512-64: 0.73503861 0.81966587 64-32: 0.13970486 0.10535610 32-16: 0.07672532 0.05025823 16-8: 0.03075745 0.01289619 8-4: 0.00837640 0.00337972 4-2: 0.00939736 0.00844389
These results suggest that the 16-8 pixel and 8-4 pixel bands might be good indications of relative image sharpness. Obviously, the two images selected above are very different visually. But does this numerical difference also hold for 2 images closer together in apparent sharpness? Here are the reuslts from 2 images closer in apparent sharpness (1230 and 1236 on 7/13/04):
512-64: 0.74809618 0.75003314 64-32: 0.12485443 0.12263589 32-16: 0.07275120 0.07601406 16-8: 0.03456287 0.03279663 8-4: 0.00993453 0.00890008 4-2: 0.00980079 0.00962019
Again, the 16-8 pixel and 8-4 pixel bands are consistent with the visual evaluation. I still need to test this program a bit more, and then set it up to run on a whole folder of files. I expect the calculation to take a few seconds per image, and the program syntax to be:
> [python] sharpness.py directory [> output-file]
I might have this ready for you to test tomorrow or Sunday.
İSky Coyote 2007