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