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 be
> > 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
course,
> > 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 bench
> > 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
this
> > 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. Let's start with Fresnel
diffraction for just a perfect knife edge and screen using
monochromatic, coherent, nearly perfectly collimated light. This 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.
-
- -
-
- - - -
- -
- - - -
- - -
-- -
--
--
----
=3D=3D=3D> true 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. Then 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
|
