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

Citation Author(s):
Yuta Nakahara, Toshiyasu Matsushima
Submitted by:
Yuta Nakahara
Last updated:
21 March 2022 - 8:52pm
Document Type:
Presentation Slides
Yuta Nakahara

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 efficient algorithm that takes a polynomial order of calculation without losing optimality by assuming a novel prior distribution.

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