Re: Accurate edge detection?

On Jul 17, 11:54=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.)
>
>
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> 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

The information you seek mostly resides within the more general topic
of image interpolation/enlargement and not edge detection.

Google "edge interpolation" .

Also,

http://www.cs.huji.ac.il/~raananf/projects/upsampling/upsampling.html

http://www.general-cathexis.com/subpixel%20edge%20localization%20and%20inte=
rpolation.pdf

I uploaded the last for your benefit only and will delete it in 2
days.

Generally speaking, the influence of optics, sensor size and shape,
demosaicing, and size reduction can be represented by an undetermined
linear transformation Ax =3D y.  You determine enlarged image x' (with
sharp edges) such that Ax' =3D y subject to regularity constraints which
incor****ate a priori knowledge of natural images.