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How to put probabilities on homographies.

Evgeni Begelfor1, Michael Werman

  • 1Computer Science Department, The Hebrew University of Jerusalem, Israel 91904. aristo@cs.huji.ac.il

IEEE Transactions on Pattern Analysis and Machine Intelligence
|October 22, 2005
PubMed
Summary

We introduce new "normal" distributions for matrix groups, enabling parameter estimation and mean calculation. This method enhances object recognition using planar projective homographies.

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Area of Science:

  • Matrix group theory
  • Probability distributions
  • Computer vision

Background:

  • "Normal" distributions are fundamental in statistics but challenging to define over matrix groups.
  • Estimating parameters for distributions on abstract mathematical structures requires specialized methods.

Purpose of the Study:

  • To introduce a novel family of "normal" distributions defined over matrix groups.
  • To develop a straightforward method for estimating the parameters of these distributions.
  • To demonstrate the practical application of these distributions in improving object recognition.

Main Methods:

  • Development of a new class of probability distributions on matrix groups.
  • Formulation of a parameter estimation technique for these distributions.
  • Application of the proposed distributions to planar projective homographies.

Main Results:

  • A method for calculating the mean of elements within a matrix group distribution is presented.
  • The application to planar projective homographies shows improved object recognition capabilities.
  • The defined priors contribute to more robust feature matching and scene understanding.

Conclusions:

  • The proposed "normal" distributions and estimation methods offer a powerful tool for analyzing data in matrix groups.
  • This approach provides a statistically sound way to incorporate prior knowledge in computer vision tasks.
  • The demonstrated improvements in object recognition highlight the practical utility of this novel distribution family.

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