## Estimating image sharpness via cusp autocorrelation -- 2

**Summary**

Shown below are new autocorrelation analyses of the same image files from last time.
The differences are:

- I have reduced the cusp neighborhood (and autocorrelation size) to 21x21 pixels. Although
this is still larger than Eliot's request of 16x16, it appears to be small enough to better localize the
cusps (and speed up the calculations). A smaller square region cannot contain some of the blurrier cusps,
which already fill most of the 21x21 square.
- I have reduced the centroid-walking in the cusp-centering routine, so that more of the lower intensity
pixels at the tip are included, and less of the limb and terminator.
- I have plotted value vs. radius for all elements of the autocorrelation result, rather than just the
average wrt radius for all angles. This shows the distribution of scattered points in each result, and
allows one to see and characterize the differences between sharp and blurry cusps.

Here are the new results:

There appear to be 3 consistent distinctive differences between the autocorrelations of sharp and blurry cusps:

- The sharper cusps produce a much broader spread of points in the 2d clusters.
- The sharper cusps have 2 very distinct tails to the clusters, which come from the asymmetry of
the autocorrelation array at the corners.
- The blurrier cusps have narrower point spreads, closer tails, but have a convex envelope
of points at higher values for smaller radii due to the spread of the cusp.

These observations seem to be consistent with the idea of Fourier duality: narrower functions have wider Fourier
spectra and vice-versa.
Although any of these criteria might be used to estimate image sharpness, perhaps the simple area of the cluster
(or something like it) might provide a single real value that could be used to rank images (e.g. more area = higher
sharpness). So, I think the next step is for me to turn the autocorrelation scatter plots into a scalar function
(possibly by
binning values and calculating the range or standard deviation of each radius) to see if the resulting ranking
corresponds well with visual estimation of the image sharpness.

© Sky Coyote 2007.