Analytical Image Models and Their Applications

  • Anuj Srivastava
  • Xiuwen Liu
  • Ulf Grenander
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2350)


In this paper, we study a family of analytical probability models for images within the spectral representation framework. First the input image is decomposed using a bank of filters, and probability models are imposed on the filter outputs (or spectral components). A two-parameter analytical form, called a Bessel K form, derived based on a generator model, is used to model the marginal probabilities of these spectral components. The Bessel K parameters can be estimated efficiently from the filtered images and extensive simulations using video, infrared, and range images have demonstrated Bessel K form’s fit to the observed histograms. The effectiveness of Bessel K forms is also demonstrated through texture modeling and synthesis. In contrast to numeric-based dimension reduction representations, which are derived purely based on numerical methods, the Bessel K representations are derived based on object representations and this enables us to establish relationships between the Bessel parameters and certain characteristics of the imaged objects. We have derived a pseudometric on the image space to quantify image similarities/differences using an analytical expression for L 2-metric on the set of Bessel K forms. We have applied the Bessel K representation to texture modeling and synthesis, clutter classification, pruning of hypotheses for object recognition, and object classification. Results show that Bessel K representation captures important image features, suggesting its role in building efficient image understanding paradigms and systems.


Image features spectral analysis Bessel K forms clutter classification object recognition 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Anuj Srivastava
    • 1
  • Xiuwen Liu
    • 2
  • Ulf Grenander
    • 3
  1. 1.Department of StatisticsFlorida State UniversityTallahassee
  2. 2.Department of Computer ScienceFlorida State UniversityTallahassee
  3. 3.Division of Applied MathematicsBrown UniversityProvidence

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