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

Most previous studies on lossless image compression have focused on improving preprocessing functions to reduce the redundancy of pixel values in real images. However, we assumed stochastic generative models directly on pixel values and focused on achieving the theoretical limit of the assumed model...

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Published inEntropy (Basel, Switzerland) Vol. 24; no. 8; p. 1152
Main Authors Nakahara, Yuta, Matsushima, Toshiyasu
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.08.2022
MDPI
Subjects
Algorithms
Analysis
Bayes code
Criteria
Decision theory
Image compression
Image segmentation
Information theory
lossless image compression
Mathematical analysis
Optimization
Pixels
Polynomials
Probability distribution
quadtree
Random variables
Redundancy
stochastic generative model
Stochastic models
Vermont
Online AccessGet full text
ISSN1099-4300
1099-4300
DOI10.3390/e24081152

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Summary:Most previous studies on lossless image compression have focused on improving preprocessing functions to reduce the redundancy of pixel values in real images. However, we assumed stochastic generative models directly on pixel values and focused on achieving the theoretical limit of the assumed models. In this study, we proposed a stochastic model based on improper quadtrees. We theoretically derive the optimal code for the proposed model under the Bayes criterion. In general, Bayes-optimal codes require an exponential order of calculation with respect to the data lengths. However, we propose an algorithm that takes a polynomial order of calculation without losing optimality by assuming a novel prior distribution.
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This paper is an extended version of our paper published in Nakahara, Y.; Matsushima, T. Stochastic Model of Block Segmentation Based on Improper Quadtree and Optimal Code under the Bayes Criterion. In Proceedings of the 2022 Data Compression Conference (DCC), Snowbird, UT, USA, 22–25 March 2022; pp. 153–162.
ISSN:1099-4300
1099-4300
DOI:10.3390/e24081152