Assessing the possibility of using the method of image decomposition based on topological features to reduce entropy during image compression

The rapid increase in the volume of visual information on the internet stimulates the improvement and search for new approaches to solving the problem of image compression. One of the important characteristics in the field of image processing, in particular in matters of compression, is entropy. The work explores the possibility of using the method of image decomposition based on topological features to reduce entropy in order to further compress the image while maintaining high quality. Topological decomposition involves decomposing an image into components each of which reflects a separate element in the image. Topological decomposition allows us to group global structures and their details into separate matrices of special types. To reduce entropy, it is proposed to remove some detail components and restore the image. A distinctive feature of the proposed approach is that it does not distort the entire image, but only some areas. The proposed method is tested in a practical compression problem using the entropy-dependent RLE algorithm. The results showed that topological decomposition is good at reducing entropy, which will allow us to use the preprocessed image for compression. PSNR, SSIM, MSE, NRM indices are used to assess image quality. When compared with the wavelet transform, the proposed approach is competitive in terms of image quality assessment at a comparable compression ratio, and exceeds it for a certain class of images with slightly noisy long objects. The results open up opportunities for further study of topological decomposition in image compression with potentially greater efficiency and less distortion.

1. Doan Tien Ban, Tropchenko A.A. Fast in-frame coding algorithm for HEVC based on probability of mode selection. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2020, vol. 20, no. 1, pp. 74–81. (in Russian). https://doi.org/10.17586/2226-1494-2020-20-1-74-81
2. Said A. Machine learning for media compression: challenges and opportunities. APSIPA Transactions on Signal and Information Processing, 2018, vol. 7, no. 1, pp. e8. https://doi.org/10.1017/ATSIP.2018.12
3. Soler M., Plainchault M., Conche B., Tierny J. Topologically controlled lossy compression. Proc. of the IEEE Pacific Visualization Symposium (PacificVis), 2018, pp. 46–55. https://doi.org/10.1109/pacificvis.2018.00015
4. Ma H., Liu D., Yan N., Li H., Wu F. End-to-end optimized versatile image compression with wavelet-like transform. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2022, vol. 44, no. 3, pp. 1247–1263. https://doi.org/10.1109/TPAMI.2020.3026003
5. Yang X., Gong J., Wu L., Yang Z., Shi Y., Nie F.Reference-free low-light image enhancement by associating hierarchical wavelet representations. Expert Systems with Applications, 2023, vol. 213, pp. 118920. https://doi.org/10.1016/j.eswa.2022.118920
6. Sai S.V., Zinkevich A.V., Fomina E.S. Comparison of discrete cosine and wavelet transforms in RAW image compression systems. Computer Optics, 2022, vol. 46, no. 6, pp. 929–938. (in Russian). https://doi.org/10.18287/2412-6179-CO-1094
7. Dvornikov S.V., Dvornikov S.S., Ustinov A.A. Analysis of the correlation properties of the wavelet transform coefficients of typical images. Informatics and Automation, 2022, vol. 21, no. 5, pp. 983–1015. (in Russian). https://doi.org/10.15622/ia.21.5.6
8. Mun H., Yoon G.J., Song J., Yoon S.M. Scalable image decomposition. Neural Computing and Applications, 2021, vol. 33, no. 4, pp. 9137–9151. https://doi.org/10.1007/s00521-020-05677-x
9. Luzhkov Yu.V., Tropchenko A. Yu. Analysis of algorithms of the lossy compression based on the space signal decomposition. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2008, vol. 8, no. 13, pp. 37–42. (in Russian)
10. Zhou J., Ben J., Wang R., Zheng M., Du L. Lattice quad-tree indexing algorithm for a hexagonal discrete global grid system. ISPRS International Journal of Geo-Information, 2020, vol. 9, no. 2, pp. 83. https://doi.org/10.3390/ijgi9020083
11. Jagadeesh P., Nagabhushan P., Kumar R.P. A novel image scrambling technique based on information entropy and quad tree decomposition. International Journal of Computer Science Issues, 2013, vol. 10, no. 2, pp. 285–294.
12. Li Z., Snavely N. Learning intrinsic image decomposition from watching the world. Proc. of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2018, pp. 9039–9048. https://doi.org/10.1109/CVPR.2018.00942
13. Kizilkaya A., Elbi M.D. A fast approach of implementing the fourier decomposition method for nonlinear and non-stationary time series analysis. Signal Processing, 2022, vol. 206, pp. 108916. https://doi.org/10.1016/j.sigpro.2022.108916
14. Eremeev S.V., Abakumov A.V., Andrianov D.E., Titov D.V. Image decomposition method by topological features. Computer Optics, 2022, vol. 46, no. 6, pp. 939–947. (in Russian). https://doi.org/10.18287/2412-6179-CO-1080
15. Eremeev S.V., Abakumov A.V., Andrianov D.E., Shirabakina T.A. Vectorization method of satellite images based on their decomposition by topological features. Informatics and Automation, 2023, vol. 22, no. 1, pp. 110–145. (in Russian). https://doi.org/10.15622/ia.22.1.5
16. Xin G., Fan P. Soft compression for lossless image coding based on shape recognition. Entropy, 2021, vol. 23, no. 12, pp. 1680. https://doi.org/10.3390/e23121680
17. Kamble V., Bhurchandi K.M. No-reference image quality assessment algorithms: A survey. Optik, 2015, vol. 126, no. 11–12,pp. 1090–1097. https://doi.org/10.1016/j.ijleo.2015.02.093
18. Saha A., Jonathan Wu Q.M. Full-reference image quality assessment by combining global and local distortion measures. Signal Processing, 2016, vol. 128, pp. 186–197. https://doi.org/10.1016/j.sigpro.2016.03.026
19. Ibrahim R.A., Youssef S.M., Elkaffas S.M. An enhanced fractal image compression integrating quantized quadtrees and entropy coding. Proc. of the 11^th International Conference on Innovations in Information Technology (IIT), 2015, pp. 190–195. https://doi.org/10.1109/INNOVATIONS.2015.7381538
20. Lee J., Gong Q., Choi J.Y., Banerjee T., Klasky S., Ranka S., Rangarajan A. Error-bounded learned scientific data compression with preservation of derived quantities. Applied Sciences, 2022, vol. 12, no. 13, pp. 6718. https://doi.org/10.3390/app12136718

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License