Hidden behind natural images: topological encoding and decoding by image vortices

Mei Ian SAM^1*, Hsiu-Hau LIN¹

¹Department of Physics, National Tsing Hua University, Hsinchu, Taiwan

* Presenter:Mei Ian SAM, email:funfunfunghisss@gmail.com

Medical image analysis is of crucial importance to detect abnormality, morbidness and precancerous conditions. To recognize these minor visual clues in the earliest stage, it is important to understand how images are encoded in human vision and how the visual codes are compressed and prioritized, just like the autoencoders in machine learning. Here we show that most 2D natural images can be compressed and encoded by topological vortex pairs near 1D boundaries. These topological codes can be decoded via the logarithmic potentials associated with vortices to reconstruct the original images with high fidelity. The compression achieved by the topological encoding/decoding reveals the hidden structures of natural images and enable us to identify the principal components for human vision. By projecting out these principal components in the images, the originally invisible can be unveiled and may serve as a powerful algorithm to detect precancerous conditions in medical images.

Keywords: Natural image statistic, Medical image analysis, Laplacian regularizer