A Variational Model for Joint Motion Estimation and Image Reconstruction

TL;DR

This paper introduces a variational model for simultaneously estimating motion and reconstructing image sequences, emphasizing a brightness constancy approach, with theoretical analysis, numerical solutions, and advantages over existing methods.

Contribution

The paper presents a new variational framework for joint motion estimation and image reconstruction, including rigorous existence proofs and efficient primal-dual algorithms.

Findings

Proved existence of minimizers in a suitable function space.

Developed primal-dual algorithms for numerical solution.

Demonstrated benefits over sequential methods in examples.

Abstract

The aim of this paper is to derive and analyze a variational model for the joint estimation of motion and reconstruction of image sequences, which is based on a time-continuous Eulerian motion model. The model can be set up in terms of the continuity equation or the brightness constancy equation. The analysis in this paper focuses on the latter for robust motion estimation on sequences of two-dimensional images. We rigorously prove the existence of a minimizer in a suitable function space setting. Moreover, we discuss the numerical solution of the model based on primal-dual algorithms and investigate several examples. Finally, the benefits of our model compared to existing techniques, such as sequential image reconstruction and motion estimation, are shown.