Re: Accurate edge detection?

aruzinsky wrote:
> On Jul 20, 2:24 pm, "Science.Medical.Imaging List"
> <pixel.to.l...@[EMAIL PROTECTED]
> wrote:
>> On Jul 19, 7:44 am, "aruzinsky" <aruzin...@[EMAIL PROTECTED]
>>
>> cathexis.com> wrote:
>>> For some reason, my Google Usenet ****tal is not automatically
producing
>>> quotes on my reply to your post therefore I have done it manually.
>>> "About the last part: are you sure most of the influence of 'optics,
>>> sensor size and shape,
>>> demosaicing, and size reduction' can be represented by a linear
>>> transformation on acquired values?
>>> I would think you meant not 'represented' but 'estimated'.
>>> I would be really interested in knowing about any existing (published)
>>> proofs in sup****t of your response."
>>> It is not a linear transformation on "acquired values," y, but on x
which
>>> represents
>>> a higher resolution discrete image that  approximates the continuous
>>> (infinite resolution) image falling on the sensors.  x' is an estimate
of
>>> x.  Depending on the estimation method, x' may or may not be a linear
>>> function of observations, y.  
>>> The matrix A represents convolution and decimation and is not
invertible.
>>> It is well known that most, if not all, optical effects are
convolutions, a
>>> linear transformation. Possibly the convolution kernel is a function
of
>>> spatial coordinate (as in the case of the bad Hubble telescope lens)
but
>>> it still can be represented by a linear transformation, A.  The effect
of
>>> pixel sensor size and shape is represented by continuous convolution
>>> followed by decimation which again can be incor****ated into A.  Some,
but
>>> not all cases of demosaicing are also linear transformations.
>>> --
>>> Message posted
usinghttp://www.talkaboutgraphics.com/group/sci.image.processing/
>>> More information athttp://www.talkaboutgraphics.com/faq.html
>> This makes more sense now. Your earlier post suggested (perhaps it was
>> the words) that all optical effects can be represented by a
>> combination of linear transformations. That was hard to understand. It
>> is more reasonable to say that 'some' of the optical effects can be
>> represented as linear transformations.- Hide quoted text -
>>
>> - Show quoted text -
> 
> 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).

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.

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
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