Re: Accurate edge detection?

On Jul 23, 3:16=A0am, Martin Brown <|||newspam...@[EMAIL PROTECTED]
>
wrote:
> 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
produci=
ng
> >>> 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
w=
hich
> >>> represents
> >>> a higher resolution discrete image that =A0approximates the
continuou=
s
> >>> (infinite resolution) image falling on the sensors. =A0x' is an
estim=
ate of
> >>> x. =A0Depending on the estimation method, x' may or may not be a
line=
ar
> >>> function of observations, y. =A0
> >>> The matrix A represents convolution and decimation and is not
inverti=
ble.
> >>> It is well known that most, if not all, optical effects are
convoluti=
ons, 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. =A0The
eff=
ect of
> >>> pixel sensor size and shape is represented by continuous convolution
> >>> followed by decimation which again can be incor****ated into A.
=A0Som=
e, 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. =A0Name 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
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.

> 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.

> 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.