On Jul 18, 4:45=A0pm, slus...@[EMAIL PROTECTED]
wrote:
> On Jul 17, 4:14=A0pm, "Science.Medical.Imaging List"
>
>
>
>
>
> <pixel.to.l...@[EMAIL PROTECTED]
> wrote:
> > On Jul 17, 10:54=A0am, slus...@[EMAIL PROTECTED]
wrote:
>
> > > I originally posted the following on the sci.optics newsgroup
because
> > > it's more of an optical query. =A0Nevertheless, the folks here may
be
> > > more familiar with the available references and research that's been
> > > done. Please forgive my statement of some things that will no doubt
b=
e
> > > obvious to many here. =A0(BTW: I also have a description of the
> > > experiments we've performed for anyone interested.)
>
> > >
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D
> > > In the image processing community, there are discussions of edge
> > > detection techniques. =A0For a simple case, imagine an opaque knife
> > > edge
> > > with a uniform back light behind it. Further imagine there is a lens
> > > that images the knife edge onto a pixel detector of a camera.
>
> > > In general, the transition from dark to light at the detector is
some
> > > smoothly varying function, not a sharp jump. =A0Diffraction, of
cours=
e,
> > > limits the ultimate sharpness of the edge image -- diffraction at
the
> > > edge itself, and diffraction at the aperture of the lens.
> > > Aberrations
> > > of the lens will also contribute to this edge smoothing.
>
> > > The digital image as presented *by* the camera may take only a pixel
> > > or two to transition from dark to light, or it might take many more.
> > > Regardless, digitization and pixel size and other factors such as
MTF
> > > of the electronics themselves serve to mask the true edge function
>
> > > A very common starting point in the discussions and papers about
edge
> > > detection techniques is the assumption that the point at which the
> > > slope of the edge is maximum represents the "true" edge position.
> > > From then on, the various edge detection algorithms usually present
> > > different methods of more accurately calculating this maximum slope,
> > > especially in the face of optical and electronic noise, etc.
>
> > > Nevertheless, it seems to me that the assumption that the maximum
> > > slope represents the true edge is at least unmotivated (no matter
how
> > > "common sense" it feels) if not wrong. =A0I have in mind the
pictures
> > > of
> > > edge diffraction as produced by using Cornu's spiral. =A0The
location
> > > of
> > > the true edge, relative to the average intensity of the light area
> > > (smoothing out the diffraction oscillations), looks to be at a
> > > position of increasing slope as you go from dark to light, but NOT
> > > maximum. =A0Furthermore, the edge is less than the 50% point of peak
> > > light intensity. =A0(Another assumption sometimes made in image
> > > processing is that the 50% point of the dark to light transistion
> > > represents the edge.)
>
> > > 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? =A0We have done a couple of
benc=
h
> > > tests to suggest under the experimental conditions that the best
edge
> > > location is about 41% to 46% of the range of the dark to light
> > > transition. =A0We haven't yet completed our analysis regarding how
th=
is
> > > compares to the peak slope.
>
> > > This problem has to have been tackled successfully before, but so
far
> > > I've not found any good sources that address the optical issue, only
> > > software techniques.
>
> > > Thanks!
>
> > > Spencer
>
> > Good post!
>
> > With edge detection techniques that focus only on algorithmic aspects
> > of it, without a concern for how the image was acquired, your post
> > raises an im****tant point: an image analysis algorithm must know how
> > the image was acquired in the first place, and make use of that
> > information.
>
> > But again, if an image is provided with some representation of an
> > edge, along with all the givens of noise sources in hardware,
> > sampling, etc., but NOT given is its source or how it was acquired, a
> > computer program can at best (if ever) only mimic what human visual
> > system will do to mark the edge: 'it will only consider what is
> > *visible* in the image'.
>
> > So to me, it seems like there cannot be a general edge detection
> > method that will work on images acquired using all available methods
> > in all available conditions. Hence your pursuit to mark the 'correct'
> > or 'accurate' edge in a digital image, considering all the optical
> > phenomenon that may affect the process, may still depend on how the
> > image is acquired.
>
> > Or can it be generalized?
>
> > Good luck.
>
> > [http://groups.google.com/group/medicalimagingscience/web/smiviewer-
> > download-page]- Hide quoted text -
>
> > - Show quoted text -
>
> My guess is that generalizing the optical edge function for the real
> world would be an infinite project. =A0Let's start with Fresnel
> diffraction for just a perfect knife edge and screen using
> monochromatic, coherent, nearly perfectly collimated light. =A0This can
> be solved to show that the the intensity pattern at the screen looks
> something like this, with intensity vertical and x-position of the
> knife edge and screen being horizontal.
>
> =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0-
> =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0- =A0 =A0 =A0 -
> -
> =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0- =A0 =A0 =A0 =A0 =A0 =A0- =A0 =A0
=A0=
=A0 =A0 =A0 =A0- =A0 =A0 =A0 =A0 =A0-
> - =A0 =A0 -
> =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0- =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 - =A0 =
=A0 =A0 =A0- =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0-
> - =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0- =A0 =A0 =A0 -
> =A0 =A0 =A0 =A0 =A0 =A0 -- =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =
=A0-
> =A0 =A0 =A0 =A0 =A0--
> =A0 =A0 =A0 --
> ----
> =3D=3D=3D> =A0 =A0 =A0 =A0 =A0 =A0true knife edge
>
> Here we see that the maximum slop does not necessarily correspond to
> the true knife edge position, nor to the 50% point of the peak average
> light level. But this is for one case at one wavelength, with no
> imaging lens involved.
>
> For non-monocrhomatic, non-spatially coherent, non-collimated sources
> it gets *much* more complex. =A0Then you add a real lens, with it's own
> aberrations, and diffraction effects due to the aperture (possibly
> convolve the point spread function with the edge diffraction
> function?) at different f-numbers!
>
> Admittedly some of the effects may be small, and mostly ignorable.
> But, when one is trying to do robust and very accurate sub-pixel
> interpolation...
>
> Spencer- Hide quoted text -
>
> - Show quoted text -
Oops. Sorry about the bad "graphic". Let's see if fixed font works
better:
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=3D=3D=3D=3D> True knife edge
Spencer
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