Re: Mathematics of Hough Transform
From: Jonathan G Campbell (jg.campbell_at_ntlworld.com)
Date: 11/13/04
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Date: 13 Nov 2004 09:28:53 -0800
Tim Brauch <RnEeMwOs.pVoEst@tbrauch.cNOoSPAMm> wrote in message news:<Xns95A01C80D184Fwebmastertbrauchcom@216.148.227.77>...
> Thomas Deselaers <deselaers@informatik.rwth-aachen.de> wrote in
> news:ya1pt2jv7xn.fsf@deuterium.informatik.rwth-aachen.de:
>
> > Tim Brauch <RnEeMwOs.pVoEst@tbrauch.cNOoSPAMm> writes:
> >
> > Have a look at the book "Computer Vision -- A Modern Approach" by
> > Forsyth and Ponce. It is a well written introduction to many areas in
> > computer vision.
> >
> > t.
> >
The following may be the canonical references for the (line) Hough
transform:
R.O. Duda and P.E. Hart, Pattern Classification and Scene Analysis,
Wiley Interscience, 1973.
D.H. Ballard and C.M. Brown, Computer Vision, Prentice Hall, 1982.
(May include other curves, e.g. ellipse; I don't own the book.)
In any case, for straight lines, the math. is relatively simple.
Nothing someone with high-school math. couldn't cope with.
>
> Ah, I am taking a course in computer vision next semester. We are not
> using that text, but I will definitely look into it. And this brings me to
> another question or observation...
>
> I am approaching image processing from a math background. I have a BS and
> MA in math already, now working towards a Ph.D. in applied mathematics. I
> have taken computer science course, such as OOP and algorithm analysis. I
> really like image processing and it seems to be one of the few areas of
> math were you can honestly "see" results. However, one problem I have come
> across is that most texts seem to be written for the computer scientist and
> tend to gloss over the mathematics.
>
Since many computer science courses contain merely a semester of math.
and discrete math. at that, and since publisher know their audience,
it's hardly surprising that they contain a minimum of mathematics. But
I reckon that the originators of most image processing algorithms were
mathematicians, applied mathematicians, physicists or theoretical
electrical engineers (and the latter two would have covered the
equivalent of two years of honours level applied math.).
IMHO, you are very fortunate to be approaching image processing from
your direction, rather than from the opposite.
> Gonzalez and Woods' "Digital Image Processing" seems to be a nice place to
> start.
Yes, G & W good for Hough transform. The 1 2 3 4 5 example (Figure
10.20, 2nd ed.) is handy for a first test of your software
implementation.
But searching for other texts always puts me in TA section of the
> library, not the QA section. This is not a bad thing, but it is harder to
> convince my department of the value. As it is, the computer vision class
> next semester is being taught in the math department, but for the benefit
> of the electrical engineering and computer science departments.
>
> The reviews of "Computer Vision -- A Modern Approach" seem promising to me.
>
To me it seems to make some topics more difficult than necessary; but
maybe that's because my math. gets stretched.
Other books you should own:
A.K. Jain, Fundamentals of Digital Image Processing, Prentice Hall,
1989. Quite mathematical.
A. Rosenfeld and A. Kak, Digital Picture Processing, 2nd ed., 1982,
Academic Press, Volumes 1 and 2. Gives a proper mathematical basis for
the subject.
And maybe, for more recent developments. Sonka, Hlavac and Boyle,
Image Processing, Analysis, and Machine Vision, International Thompson
Press, 1999.
> I guess my question is whether there are many texts and papers written from
> the math point of view, or am I going to be fighting an uphill battle?
You mean an easy (but boring) flat battle surely ;-)
> It's more of a rhetorical question than anything else.
>
You should ensure that you have access to IEEE Trans Pattern Analysis
and Machine Intelligence, and IEEE Trans. Image Processing. IMHO they
are the key source of image processing research.
Incidentally, do a quick scan of an issue of each and place yourself
in the shoes of someone who has high-school math. + a semester or two
of discrete math. !
A good deal of the important research on Hough transforms was
published before people put articles online (before 1990). If you need
a start on a literature survey, in addition to Duda and Hart and
Ballard and Brown, authors Kittler and Illingworth are good starting
points. See Illingworth and Kittler, A Survey of the Hough Transform,
Computer Vision graphics and Image Processing, Vol. 44, pp. 87--116,
1988. Also V.F. Leavers, Which Hough Transform (173 references),
source unknown, 1992/3.
Best regards,
Jon C.
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