Re: Accurate edge detection?

On Jul 26, 11:55 pm, Andrew_M <m...@[EMAIL PROTECTED]
> wrote:
> > > probably true, but doesn't this still simply assert that the maximum
> > > slope/gradient of the real physical edge image corresponds to the
true
> > > edge location?
>
> > It is not an assertion; it is a proof, under certain assumptions.
>
> Not true. Simple samples like Fraunghofer's diffraction, have no such
> a property.

I was not talking about real images. I was talking about an idealized
mathematical situation, as I made clear. In this situation, it was a
theorem. Evidently theorems do not apply to real images or
electromagnetic fields since these are not mathematical entities.
There are simple approximations in which the overall effect of the
optics is roughly linear in the energy field, in particular when
interference is not an issue. As you correctly point out, however,
when there is diffraction, there is no linearity, although again, in a
simple approximation, the spatially varying part of the energy density
incident on the camera lens close to the edge position is a linear
function of the edge characteristic function.

> True edge location is a thing, what has a meaning only for
> some sort of images. But, if you have a grayscale image, you may have
> no such things as an edge at all. Unfocused photo, for example.

I am well aware of the properties of images. Edge position refers to
edge position *in space*, not in the image, where it may be
arbitrarily defined. In general, the problem is well-posed as follows:
given the image, estimate the edge position *in space*. This still
assumes that the edge can be summarized by a single 'position'
parameter, but for a straight knife edge this is reasonable.

illywhacker;