From: jchd@worldnet.net (Jean-Christophe Deschamps)
Newsgroups: sci.math
Subject: Re: Hoff transform. What is it ? It is a typo, sorry. Hough is what I ment.
Date: Thu, 14 Sep 1995 22:43:20 GMT

On 14 Sep 1995 16:23:05 GMT, lenson <lenson@pci.on.ca> wrote:

> Typo. I ment Hough.
Nobody's perfect :-))

Guess: you could have more success in a group like
comp.graphics.algorithms.

Hough transforms are used to change the mode of representation of a
data set in order to ease detection of specific geometric forms. For
instance, you may want to use a Hough transform to detect ellipses of
a specified diameter (red corpuscules) in a numeric micro-photograph
of a drop of blood.

Hough transforms always use some parametric representation, chosen to
characterize the pattern you are detecting. Accumulation in the
parameter space must correspond to detected patterns in the data set.

For instance, the polar representation of lines is used in the case of
line detection. Lines (sets of roughly aligned points) in the data set
show up as concurrent sinusoids in the parameter space. Suitable
summations allows you to detect convergent lines in the data set, or
lines // to the axes, a.s.o.


There is an abundant litterature about Hough fransforms, thus
crosscheck these references with others':

Hough P.V.C.
  "Method and means for recognizing complex patterns"
  US Patent #3069654, 1962.

Duda R.O., Hart P.E.
  "Use of the Hough transform to detect lines and curves in pictures"
  Comm. of ACM, 15(1), 1972, pp. 11-15

Illingworts J., Kittler J.
  "A survey of the Hough transform"
  CVGIP, 44, 1988, pp. 87-116

Maitre H.
  "Un panorama sur la transformation de Hough"
  Traitement du signal, 2(4), 1985, pp. 305-317
  (in french)

Maitre H.
  "Contribution to the prediction of preformances of the Hough
transform"
  IEEE trans. on PAMI, 8(5), September 1986, pp. 669-674


Hough transforms for detecting circles and ellipses:

Davies E.R.
  "A modified Hough scheme for general circle location"
  Pattern Recognition Letters, 7, 1988, pp. 37-43

Tsuji S., Matsumoto F.
  "Detection of ellipses by a modified Hough Transformation"
  IEEE trans. on Computers, 27(8), 1978, pp. 777-781

Martin P.
  "Reconnaissance de partition musicales et reseaux de neurones"
  7eme congres RFIA, AFCET-INRIA ed., Paris, 1989, pp. 217-228
  (in french)


Discrete Hough transform:

Lopez Krahe J., Vilata R.
  "Transformation de Hough discrete et bornee. Application a la
detection de primitives rectangulaires"
  Proc. of MARI 87, Cesta ed., 2, Paris, March 1978, pp. 36-41
  (in french)


For more information on parametric representation and parameter peaks:

Slansky J.
  "On the Hough technique for curve detection"
  IEEE trans. on Computers, 27, October 1978, pp. 923-926

O'Gorman L., Sanderson A.C.
  "The converging squares algorithm: an efficient method for locating
peaks in multidimensions"
  IEEE trans. on PAMI, 6(3), 1984, pp.280-288


Hope this helps.

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