[comp.ai.neural-nets] matching sets of points in 2 space

ibarroda@csr (Ian Barrodale) (05/02/91)

             Point Set Matching
	     ------------------
	     (Barrodale Computing Services Ltd, May 1991).

Problem Definition: 
  We are given two sets of points in the plane. These points could represent
  two `simplified' images or output from some sensors. The first set
  contains M points. The second set is similar to the first set, except
  that some of the points from the first set are missing and some new
  points, not in the first set, are present. The second set contains N
  points. The positions of the points in the second set are, within a
  given tolerance, the same as common points in the first set. However,
  within this tolerance fairly large local distortions can occur.

  The problem has three parts:
    1. Find all the points in the first set which do not have a match in
    the second set.

    2. Find all points in the second set which do not have a match in
    the first set.

    3. For all points in the first set which have a common point in the
    second set find the correct match.

Questions:
  We are interested in hearing from anyone who has worked on the above
  problem or has worked on related problems. We are also interested in
  looking at the possibility of using artificial intelligence
  techniques, like neural networks, for solving the problem. The
  following is a list of questions that we have at this time:

  1. Should we try to emulate human vision in solving the above problem
  or use only simple geometric considerations?

  2. If the solution emulates human vision (i.e. does not directly use
  coordinate information), what type of feature or point relationships
  should it use?

  3. If the solution uses coordinate information, what type of geometric
  feature or geometric relationship would it be based on?

  4. Can the given data be transformed such that the problem becomes
  simpler? For example, can the problem be restate as the solution of
  two one dimensional comparisons?

  5. Can this problem be formulated such that it can be solved using a
  Hough transform approach?

  6. Can this problem be formulated such that it can be solved using a
  neural network approach?

  7. Can this problem be formulated such that it can be solved using
  genetic algorithms?

  8. What other types of approach may lead to a solution of the above
  problem.


Thank you.

Ian Barrodale.
ibarroda@csr.uvic.ca
(604) 721-2206
Suite 8 - 1560 Church Avenue, 
Victoria, B.C, 
Canada, V8P 2Hi

tmb@ai.mit.edu (Thomas M. Breuel) (05/04/91)

In-reply-to: ibarroda@csr's message of 2 May 91 15:44:47 GMT
Newsgroups: comp.ai.neural-nets, comp.ai, comp.ai.vision
Subject: Re: matching sets of points in 2 space
References: <ibarroda.673199087@csr>
Distribution: 
FCC: /homes/tmb/mail/nout
--text follows this line--
>		Point Set Matching
>		------------------
>		(Barrodale Computing Services Ltd, May 1991).
>
>  Problem Definition: 
>    We are given two sets of points in the plane. These points could represent
>    two `simplified' images or output from some sensors. The first set
>    contains M points. The second set is similar to the first set, except
>    that some of the points from the first set are missing and some new
>    points, not in the first set, are present. The second set contains N
>    points. The positions of the points in the second set are, within a
>    given tolerance, the same as common points in the first set. However,
>    within this tolerance fairly large local distortions can occur.
>
>    The problem has three parts:
>      1. Find all the points in the first set which do not have a match in
>      the second set.
>
>      2. Find all points in the second set which do not have a match in
>      the first set.
>
>      3. For all points in the first set which have a common point in the
>      second set find the correct match.
>
>  Questions:
>    We are interested in hearing from anyone who has worked on the above
>    problem or has worked on related problems. We are also interested in
>    looking at the possibility of using artificial intelligence
>    techniques, like neural networks, for solving the problem.

[since this question seems to come up from time-to-time, I'm posting
this response]

The following papers will give you a good start at the literature
(Eric Grimson's book has an extensive bibliography of the pre-1990
work on the subject; you should look there for other references):

   Alt H., Mehlhorn K., Wagener H., Welzl E., 1988, Congruence,
   Similarity, and Symmetries of Geometric Objects., Discrete and
   Computational Geometry.
   
   Baird H. S., 1985, Model-Based Image Matching Using Location, MIT
   Press, Cambridge, MA.
   
   Breuel T. M., 1991, An Efficient Correspondence Based Algorithm for 2D
   and 3D Model Based Recognition, In Proceedings IEEE Conf. on Computer
   Vision and Pattern Recognition.
   
   Cass T. A., 1990, Feature Matching for Object Localization in the
   Presence of Uncertainty, In Proceedings of the International
   Conference on Computer Vision, Osaka, Japan, IEEE, Washington, DC.
   
   Grimson E., 1990, Object Recognition by Computer, MIT Press,
   Cambridge, MA.

State-of-the-art algorithms running on a SparcStation can find optimal
solutions (either maximal size of match at given error or minimum
error at given size of match) to this kind of bounded error
recognition problem on the average in under a minute, for models
consisting of hundreds points of and images consisting of 1000-2000
unlabeled, oriented features.

rigoutso@VANZETTI.CS.NYU.EDU (Isidore Rigoutsos) (05/07/91)

In-reply-to: ibarroda@csr's message of 2 May 91 15:44:47 GMT

One could use geometric  constraints  to  solve  the  stated problem.   The  
geometric  hashing  method  takes  such  an approach.  The following are some
references:

               Hummel, R. and H. Wolfson.  ``Affine  Invariant  Match-
          ing''.  In  "Proceedings  of  the  Darpa Image Understanding
          Workshop, April 1988.

               Lamdan, Y. and H. Wolfson. ``Geometric Hashing: A  Gen-
          eral  and  Efficient  Model-Based  Recognition  Scheme''. In
          "Proceedings of the 2nd International Conference on Computer
          Vision, Ann Arbor, Michigan, June 1988.

               Rigoutsos,  I.  and  R.  Hummel.  ``Scalable   Parallel
          Geometric Hashing for Hypercube SIMD Architectures''. Techn-
          ical Report 553, Courant Institute of Mathematical Sciences,
          New York University.

               Rigoutsos, I. and R. Hummel. ``Scalable  Implementation
          of   Geometric  Hashing  on  the  Connection  Machine''.  In
          Proceedings "Workshop on Direction  in  Automated  CAD-Based
          Vision  Systems",   Maui,  Hawaii, June 1991. Also Technical
          Report 554, Courant Institute of Mathematical Sciences,  New
          York University.

               Rigoutsos, I. and R. Hummel. ``Robust Similarity/Affine
          Invariant  Matching in the Presence of Noise''. Submitted to
          8'th Israeli Conference on Artificial Intelligence and  Com-
          puter Vision. Tel-Aviv, 1991.


We currently have a working system on the Connection Machine. The database
contains 1024 models each consisting of 16 points. With scenes of 200 points
and one embedded model, one can achieve recognition times of ~10 seconds on a 
64-K model.  A new approach allows robust  recognition in the presence of high
levels of noise: assuming a Gaussian distributed positional error of standard
deviation sigma, robust recognition is achieved for values of sigma >= 3.5
pixels.


Isidore Rigoutsos


-- 
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sfb@NCoast.ORG (Stephen F. Bush) (05/09/91)

 
I am interested in any information/conferences/seminars on
AI applied to computer networking. I would imagine there
should be applications of expert systems, neural networks, and
genetic algorithms towards network network management.


Any information would be appreciated.


				Thank You,
				Steve Bush
				GE Information Systems