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Stochastic Model of Block Segmentation Based on Improper Quadtree and Optimal Code under the Bayes Criterion.

Yuta Nakahara1, Toshiyasu Matsushima2

  • 1Center for Data Science, Waseda University, 1-6-1 Nisniwaseda, Shinjuku-ku, Tokyo 169-8050, Japan.

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This study introduces a novel stochastic model for lossless image compression using improper quadtrees. Our method achieves theoretical limits with efficient polynomial-time computation, improving upon existing techniques.

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Area of Science:

  • Computer Science
  • Information Theory
  • Image Processing

Background:

  • Previous lossless image compression research primarily focused on preprocessing.
  • Stochastic generative models directly on pixel values offer a path to theoretical limits.

Purpose of the Study:

  • To propose a novel stochastic generative model for lossless image compression.
  • To achieve the theoretical compression limit for the proposed model.
  • To develop an efficient algorithm for optimal coding.

Main Methods:

  • Developed a stochastic model based on improper quadtrees.
  • Theoretically derived the Bayes-optimal code for the model.
  • Proposed a polynomial-time algorithm for optimal coding by assuming a novel prior distribution.

Main Results:

  • The proposed improper quadtree model enables achieving theoretical compression limits.
  • The developed algorithm computes Bayes-optimal codes in polynomial time, overcoming exponential complexity.
  • The novel prior distribution is key to the algorithm's efficiency and optimality.

Conclusions:

  • The improper quadtree model is a promising approach for advanced lossless image compression.
  • Efficient computation of Bayes-optimal codes is achievable, advancing the field.
  • This work sets a new benchmark for lossless image compression algorithms.