Re: Accurate edge detection?

On Jul 20, 4:24=A0pm, aruzinsky <aruzin...@[EMAIL PROTECTED]
> wrote:
> On Jul 20, 2:24=A0pm, "Science.Medical.Imaging List"
>
>
>
>
>
> <pixel.to.l...@[EMAIL PROTECTED]
> wrote:
> > On Jul 19, 7:44=A0am, "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.- Hide quoted text -
>
> - Show quoted text -

Here are two optical effects that treat light non linearly:

Raman effect
Brillouin scattering

Here is one start:

http://en.wikipedia.org/wiki/Nonlinear_optics

Now an argument could be that these effects (or their kins) dont
usually affect many common image acquisition systems. But they do
affect some. And hence my statement: that some optical effects can
only be approximated with a linear transformation - they cannot be
truly represented using just linear transforms. Given above are the
examples.