On Jul 22, 11:59=A0am, aruzinsky <aruzin...@[EMAIL PROTECTED]
> wrote:
> On Jul 22, 8:04=A0am, slus...@[EMAIL PROTECTED]
wrote:
>
>
>
> > Thank you for your interest and offer to review some sample images.
> > Unfortunately, our concern is not on the software or algorithmic side,
> > but on the optical side. =A0As I mentioned in my original post:
>
> > "Does anyone have references they can point to (or their own
> > pesuasive
> > arguments) that describe where the true edge location should be
> > relative to the edge image function?"
>
> I already did. =A0What is wrong with you?
>
>
>
> > I also mentioned that I originally posted to sci.optics, then added
> > sci.image.processing because I thought the folks here might be more
> > aware of relavent references. =A0The (apparently) commonly held belief
> > that the maximum slope of the edge image, or the midpoint between the
> > maximum and minimum grey level values of the edge image corresponds to
> > the true edge location seems unmotivated or unsup****ted to me, even
> > though it "feels" like common sense. =A0
>
> That is an algorithm, albeit a really stupid one that is not common
> sense, so don't tell me that you are not interest in algorithms.
> Furthermore, that is not a commonly held belief, e.g., it is common
> knowledge that shock filters sharpen an edge around the inflection
> point (the inflection point is preserved) and nobody, I know of,
> pretends that shock filtering is deconvolution.
>
> > We have also performed bench
> > experiments that suggest that neither the max. slope nor the grey
> > level midpoint corresponds to the true edge, with errors being in the
> > range of 0.2 to 0.45 pixels in the experimental set up we used.
>
> I hope my tax money didn't fund that busy work.
>
> >=A0We
> > are continuing our own investigation, but I have to believe that
> > someone has already done this at some time and published their
> > results. =A0I'd love to find out that our own efforts at inventing the
> > wheel are unecessary. :-)
>
> I already gave you a reference to a relatively simple algorithm that
> might do better than 0.2 pixels. =A0 It would be foolish not to try it.
Hmm. I appear to have offended you. If it was because I had not yet
acknowledged your reply to my query, I apologize. I 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. In 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. One 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. Thus, 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. The edge image is further complicated by the many
other phenomena that occur when using lenses to place the image onto a
pixel detector.
My own readings found, in many cases, discussion of edge detection
schemes that do in fact start with the presumption that the maximum
slope or gradient of an edge image should in some way correspond to
the true location of the edge, but with no explanation of why the
author believes this to be so. My guess is that this is something
that is simply "understood" by those working in the field, and is
passed along from one person to another without question. It's
obvious that you hold no such belief, but at the level of my
investigation it *is* common.
As for time spent investigating this, rest assured that this is
strictly a capitalistic venture using private money, snide comments
not withstanding.
It may be of no interest to you, but others might find something
interesting. I'm cutting and pasting here a brief description of our
experiments that I also orignally posted on sci.optics:
Using a
chrome-on-glass bar target that is measured as 12.503mm long
+/-0.003mm, we grabbed images with a telecentric lens and red LED
collimated back light. We then used a micrometer stage to move the
target 12.503mm (again, with an error of +/-0.003mm) -- so that the
trailing edge at the new postion corresponds to the leading edge of
the original position. The direction of motion was perpendicular to
the lens optical axis to within 0.25 degrees. We then used various
edge detection methods, including the 2nd derivative of the edge with
a fit to a parabola, as well as the simple 50% local thresholding,
among others. What we found consistently through different positions
in the field of view and different new set-ups is that the trailing
edge appeared to fail to move far enough to coincide with the old
leading edge. The error range was ~0.2 to 0.45 pixels, or about
0.015mm to 0.034mm in real world units -- always considerably larger
than target and motion error, and alway in the same direction of
error.
Another way to interpret this result is that an object consistently
looks larger than it actually is. (If the bar target appears to be
12.523mm, and you move it 12.503mm, the trailing edge will fail to
"catch" the initial position of the leading edge.)
We've tried this with different lens f-numbers from F/45 to F/8 and
did not see an obvious trend that followed the aperture, but on this
front we've only made a small number of tests -- 4 at each f-number.
The errors average ~0.3pixels, with the standard deviation ~0.05.
I will also add that we have used two different cameras (AVT Stingray
145b and Sony XC-ST70) out of suspicion that a non-linear responsivity
could be the culprit. While differing slightly in detail, we saw
essentially the same result.
Spencer
|
