ImageIntegration LinearFitClipping slope

[georg.viehoever]

Hi,

ImageIntegration LinearFitClipping generates a slope map. The documentation http://pixinsight.com/doc/tools/ImageIntegration/ImageIntegration.html#usage_008 suggests that the slope map might be useful for identifying problems in the image. In my opinion, in its current form it mainly visualizes the fact that high intensity areas have higher absolute noise. This is because the variance of the Poisson distribution (that characterizes the statistical process producing an image in a CCD) is identical to its mean value http://en.wikipedia.org/wiki/Poisson_distribution#Poisson_noise_and_characterizing_small_occurrences.

I think the slope map would be more useful if it was normalized for the expected variation by dividing the current value by sqrt(integrated value). To verify this, I did a simulation (I will post this later), and I made an experiment in PI, see screenshot:
- top left: Integration result
- top right: slope map
- bottom left: slope map, modified in PixelMatg with expression $T/sqrt(integration). The nebula structures (except for the core) disappear. Stars and cores don't disappear, most likely because the linearity of $T/sqrt(integration) probably is not valid for large intensities.

Just a proposal.
Georg

Edit: Adding screenshot

[Juan Conejero]

Hi Georg,

Interesting idea. Let me make some experiments with the test data that I have and I'll comment on this.

[georg.viehoever]

Juan,

In addition to the small experiment, I did some simulations in R. To simulate the stacking of 40 images, I created random pixel stacks with 40 pixels each, with Poisson noise+5% uniformly distributed impulse noise (simulating airplanes etc.), and did this for different mean values (lambda parameter of the poisson distribution). I did it 100 times for each mean value, and computed slope as described in your documentation. The first attached plot shows the slope values found (as a box plot http://en.wikipedia.org/wiki/Box_plot), with the mean on the x-axis, and slope on y. The second plot shows the same, only here slope is divided by sqrt(mean).

I will make the simulation source code available  later today.

Georg

PS: the attached graphs were created with

Code: [Select]

boxplot(slope/mean~mean,data=r.lin)
boxplot(slope/sqrt(mean)~mean,data=r.lin)