Time-Harmonic Optical Flow with Applications in Elastography

TL;DR

This paper introduces mathematical models for reconstructing optical flow in time-harmonic elastography, leveraging Fourier analysis to simplify multi-frame optical flow estimation, and demonstrates their effectiveness with synthetic and real data.

Contribution

It presents three novel variational optical flow models specifically designed for time-harmonic elastography, utilizing Fourier transform techniques for efficient minimization.

Findings

Models successfully reconstruct velocity fields in synthetic data.

Application to real-world elastography data shows improved flow estimation.

Fourier-based approach simplifies multi-frame optical flow analysis.

Abstract

In this paper, we propose mathematical models for reconstructing the optical flow in time-harmonic elastography. In this image acquisition technique, the object undergoes a special time-harmonic oscillation with known frequency so that only the spatially varying amplitude of the velocity field has to be determined. This allows for a simpler multi-frame optical flow analysis using Fourier analytic tools in time. We propose three variational optical flow models and show how their minimization can be tackled via Fourier transform in time. Numerical examples with synthetic as well as real-world data demonstrate the benefits of our approach. Keywords: optical flow, elastography, Fourier transform, iteratively reweighted least squares, Horn--Schunck method