Image Fusion An Application in Diffusion Maps

Abstract

This work addresses fusion across data sets representing the same monotonic process. A monotonic trajectory is strictly increasing or decreasing, which is advantageous for creating a unique, one-to-one mapping of the system state and some independent variable. In this instance, we observe the process against time to register images prior to fusion. Due to heterogeneous methods for collection and observation, data integration is of interest in order to improve reliability of information within overlapping regions while filling in complementary gaps from each input so that a final product is of greater use. The algorithm is carried out on artificially generated images for the sake of clearly demonstrating the method. Data is subsequently modified with missing information or distortions to emulate experimental situations. This framework incorporates a nonlinear dimensionality reduction technique, diffusion maps, to uncover the underlying trajectory across different data sets with respect to time and fills in information closest to points of interest. Presented is a solution that works in lower dimensional space to automatically temporally register images and integrate between data sets.