# A Variational Model for Joint Motion Estimation and Image Reconstruction

arXiv: https://arxiv.org/abs/1607.03255 · HTML: https://mlsanity.com/paper/1607.03255/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jul 2016.

## Built on by (most cited first, 6 of 6)

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- [Enhancing Dynamic CT Image Reconstruction with Neural Fields and Optical Flow](https://mlsanity.com/paper/2406.01299/) (2024)
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- [Single-shot Tomography of Discrete Dynamic Objects](https://mlsanity.com/paper/2311.05269/) (2023)
- [DYRECT Computed Tomography: DYnamic Reconstruction of Events on a Continuous Timescale](https://mlsanity.com/paper/2412.00065/) (2024)

## Abstract (arXiv)

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.