The estimation of the intermediary stages of image evolution with given initial and terminal states

Reference: Jihun Han, Yoonsang Lee, Anne Gelb, Learning in-between imagery dynamics via physical latent spaces, SIAM Journal on Scientific Computing, 46 (5), C608-C632, 2024

Abstarct

We present a framework designed to learn the underlying dynamics between two images observed at consecutive time steps. The complex nature of image data and the lack of temporal information pose significant challenges in capturing the unique evolving patterns. Our proposed method focuses on estimating the intermediary stages of image evolution, allowing for interpretability through latent dynamics while preserving spatial correlations with the image. By incorporating a latent variable that follows a physical model expressed in partial differential equations (PDEs), our approach ensures the interpretability of the learned model and provides insight into corresponding image dynamics. We demonstrate the robustness and effectiveness of our learning framework through a series of numerical tests using geoscientific imagery data.