Re: Accurate edge detection?

Martin Brown wrote:
> aruzinsky wrote:
>> On Jul 23, 3:16 am, Martin Brown <|||newspam...@[EMAIL PROTECTED]
>
>> wrote:
>>> aruzinsky wrote:
> 
>>>> I was suggesting that, but I am not knowledgeable of every possible
>>>> optical effect.  Name one optical effect that can't be represented by
>>>> a linear transformation.
> 
>>> The most common ones that break modern deconvolution codes are a point
>>> spread function that is not position invariant.
>>> The is the imaging
>>> system has off axis abberations (most real diffraction limited optics
>>> suffer some degradation as you go off axis).
>>
>> That is still a linear transformation, as I previously mentioned for
> 
> You are using "linear" in a way that is non-standard in the image 
> processing community. The conventional definition is that in a linear 
> transform the measured image is the strict convolution of a position 
> invarinant point spread function and an unknown target image.

I don't agree, Martin.  I suppose that the terminology convention you 
suggest may be the case for some backgrounds, but certainly not all.  I 
come to image processing from an undergraduate background in electrical 
engineering, followed by a course of graduate study in digital signal 
and image processing.  From undergraduate courses in signals and 
systems, communications, and control theory, through graduate courses in 
Fourier theory, signal processing, spectral analysis, etc., a crystal 
clear and consistent distinction was made between a linear system and a 
time-invariant (or ****ft-invariant) system.  Systems satisfying both 
properties were almost universally referred to as LTI (linear 
time-invariant) or LSI (linear ****ft-invariant) systems.  As students, 
our ability to correctly classify systems by both of these properties 
was frequently tested by homework assignments and exams.  :-)  And when 
I was an electrical engineer professor, I carefully taught the 
distinction myself.

Although I am not an expert in the image restoration research 
literature, I have the impression that the distinction between systems 
that are linear ****ft-varying and that are linear ****ft-invariant is 
very im****tant one in that field, not to be glossed over.

I do see the term "linear" used sometimes to describe LSI systems, 
typically in a discussion of spatial-domain convolution or 
frequency-domain multiplication.  It is usually clear from the context 
that "linear" is being used as shorthand for LSI, and I generally make 
that substitute mentally as I read.

---
Steve Eddins
http://blogs.mathworks.com/steve/