Re: Accurate edge detection?

aruzinsky wrote:
> On Jul 23, 3:16 am, Martin Brown <|||newspam...@[EMAIL PROTECTED]
>
> wrote:
>> aruzinsky wrote:

>>> I was suggesting that, but I am not knowledgeable of every possible
>>> optical effect.  Name one optical effect that can't be represented by
>>> a linear transformation.

>> The most common ones that break modern deconvolution codes are a point
>> spread function that is not position invariant.
>> The is the imaging
>> system has off axis abberations (most real diffraction limited optics
>> suffer some degradation as you go off axis).
> 
> That is still a linear transformation, as I previously mentioned for

You are using "linear" in a way that is non-standard in the image 
processing community. The conventional definition is that in a linear 
transform the measured image is the strict convolution of a position 
invarinant point spread function and an unknown target image.

Edge effects on modern optical scopes produce some level of coma so that 
the stars images are not circularly symmetric off axis.

         v
	
 >	.	<

	^

Typically they develop gull wings as you go significantly off axis.

> the case of the bad Hubble telescope lens.  And, that problem was
> tractable.  In fact, many common deconvolution methods work directly
> in the spatial domain (no FFTs allowed) can be modified for this
> problem.

The most powerful ones almost invariably work in the Fourier domain. You 
need a fairly compact psf to work in the spatial domain and still get 
acceptable performance. Diffraction limited cicular telescope optics 
ring from unresolved stars with a characteristic Airey rings pattern. 
Off axis it becomes more messy.

Hubble researchers found the residual spatial variation of the psf a 
real problem in high dynamic range images.

http://adsabs.harvard.edu/abs/1994SPIE.2198.1349H

There is a solution but it involves a lot more computation
> 
>> And the real killer in the general photography situation is depth of
>> field. You can model the psf for a given subject distance, but when
>> different parts of the same image are all at different unknown
distances
>> you have a pretty much intractable problem. Or one that is only
>> resolvable with binocular pairs of images and insane amounts of
>> computing power.
> 
> It might be killer intractable, but I think it is linear.

Again you are using linear in a nonstandard way. It is linear in the 
sense that each pixel is the result of summation of the scene blurred 
with an appropriate psf for the object distance in every direction.

But that is not what is normally meant when linear is used in the 
context of image processing. The meaning is usually taken to be:

D = P * T

Where D is measured data, * is convolution,
P is a spatially invariant psf and T is the target image.
> 
>> If the OP wants specifically to find sharp edges with the utmost
>> precision and doesn't care about the computational cost then one of the
>> Bayesian methods using all available prior knowledge will probably give
>> the optimum result. This reference is a bit old but is a start:
>>
>> http://adsabs.harvard.edu/abs/1980ITAC...25...36M
>>
>> There seem to be few papers on this application which suggests to me
>> that it doesn't work well enough to be worth the computational cost.
>>
>> Regards,
>> Martin Brown
>> ** Posted fromhttp://www.teranews.com**-
Hide quoted text -
>>
>> - Show quoted text -
> 
> Don't forget that "optimal result" is with respect to some statistical
> cost function and some individual cases of estimated edge location can
> be grossly inaccurate.

The question that you ask of the data determines the answer that you 
get. If you ask the wrong question then all bets are off.

Regards,
Martin Brown
** Posted from http://www.teranews.com
**