A Stochastic Model for Block Segmentation of Images Based on the Quadtree and the Bayes Code for It

Area of Science:

• Information Theory
• Computer Vision
• Image Processing

Background:

• Lossless compression typically assumes an explicit stochastic generative model.
• Implicit models in image compression hinder analysis of code length vs. entropy.
• Existing methods struggle with images exhibiting non-stationarity across segments.

Purpose of the Study:

• To propose a novel stochastic generative model for lossless image compression.
• To address the challenge of analyzing code length and entropy in implicit models.
• To improve compression rates for images with non-stationary segments.

Main Methods:

• Redefining the implicit stochastic generative model for images.
• Utilizing a quadtree-based approach for variable block size segmentation.
• Constructing a Bayes code optimal for the proposed model.
• Developing an efficient polynomial-time algorithm for optimal calculation.

Main Results:

• The proposed quadtree-based model effectively represents variable block sizes.
• An efficient algorithm calculates the optimal Bayes code in polynomial time.
• The derived algorithm demonstrates a better average coding rate than JBIG.

Conclusions:

• The novel stochastic generative model overcomes limitations in implicit modeling for image compression.
• The efficient algorithm enables practical application of the optimal Bayes code.
• This approach offers improved lossless image compression performance.