Re: Accurate edge detection?

> Hmm. I appear to have offended you. =A0If it was because I had not yet
> acknowledged your reply to my query, I apologize. =A0I was, in fact,
> digesting your comments as well as the two references you provided. I
> was also reading what I found upon looking up "edge interpolation" as
> you suggested. =A0In the meantime, Andrew offered a suggestion that I
> was more easily and quickly able to address, which included my
> referring back to, and quoting my original post. You may have
> interpreted that as my ignoring your suggestions.
>
> Regarding your references, I believe I can see the point(s) you are
> making, but I also don't see the relavence to the *physics* of
> correlating the image of an edge to the location of the real edge. We
> might be talking past each other here, much as the Americans and Brits
> are separated by a common language. :-)
>
> Let's ignore pixels for a moment, and pretend we can sample the image
> of a back lit knife edge with infinite resolution, casting God's eye
> upon the screen on which the light eventualy falls. Are you familiar
> with Fresnel diffraction at an edge? When one looks at a plot of
> intensity of the light around the "shadow" zone, one sees there is
> light in the region that would otherwise be forbidden if there was no
> diffraction. =A0One also sees that "past" the edge, the light intensity
> climbs, reaches a peak, then oscillates in a decaying fa****on,
> eventually reaching a uniform intensity.
>
> If you look closely at this plot, we see that the point on the light
> intensity curve that in fact corresponds to the true location of the
> knife edge is of an increasing slope, but is neither the maximum slope
> (gradient), nor an inflection point, nor, generally speaking, is it
> midway between the minimum light level and the average high light
> level, much less the peak. =A0Thus, edge finding techniques that depend
> in some fa****on on maximum slope or gradient (Sobel, Canny ,etc.) or
> 50% threshold level, would not find the point on this edge image that
> corresponds to the position of the true physical edge. Of course this
> is just a start. =A0The edge image is further complicated by the many
> other phenomena that occur when using lenses to place the image onto a
> pixel detector.
>

Well, that' just same thing what me (and Mr. Aruzinsky too) trying to
explain. He is telling same thing as me, may be using slightly
different words. What d'you get as a result of diffraction is in fact
a convolution, what could be described by an linear transform. This
transform is not revertible, so the main trick is to find such a
source image, which after this transform will be like your scanned
photo. It is not a simple tecnique, known as "regularization". Using
simple words, you must to predetermine class of possible source
images. For example, two color images with more or less smooth edges.
Sample is the text- you have a photo of a page of some book, obtained
with low resolution camera (BTW, it might be done using long waves-
and diffraction will make nice mess from the source text) and trying
to restore hardly visible letters. But you know, that this page
contents not a random set of colored dots, and this fact can be an aid
for you. It'llbe too long story to explain this technique, and I'n
afraid I cannot name you Englich publi****ng concerning this method.
Can you make set of photos of some test objects with known structure?
Using them you may to get an idea about what transform occures with
your objects and use this info to restore them