A stochastic model for block segmentation of images based on the quadtree and the bayes code for it

Yuta Nakahara*, Toshiyasu Matsushima

*この研究の対応する著者

研究成果: Article査読

抄録

In information theory, lossless compression of general data is based on an explicit assumption of a stochastic generative model on target data. However, in lossless image compression, researchers have mainly focused on the coding procedure that outputs the coded sequence from the input image, and the assumption of the stochastic generative model is implicit. In these studies, there is a difficulty in discussing the difference between the expected code length and the entropy of the stochastic generative model. We solve this difficulty for a class of images, in which they have non-stationarity among segments. In this paper, we propose a novel stochastic generative model of images by redefining the implicit stochastic generative model in a previous coding procedure. Our model is based on the quadtree so that it effectively represents the variable block size segmentation of images. Then, we construct the Bayes code optimal for the proposed stochastic generative model. It requires the summation of all possible quadtrees weighted by their posterior. In general, its computational cost increases exponentially for the image size. However, we introduce an efficient algorithm to calculate it in the polynomial order of the image size without loss of optimality. As a result, the derived algorithm has a better average coding rate than that of JBIG.

本文言語English
論文番号991
ジャーナルEntropy
23
8
DOI
出版ステータスPublished - 2021 8

ASJC Scopus subject areas

  • 情報システム
  • 数理物理学
  • 物理学および天文学(その他)
  • 電子工学および電気工学

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