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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.15507 |
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| _version_ | 1866929672978169856 |
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| author | Melnyk, Oleh Quellmalz, Michael Steidl, Gabriele Jaitner, Noah Jordan, Jakob Sack, Ingolf |
| author_facet | Melnyk, Oleh Quellmalz, Michael Steidl, Gabriele Jaitner, Noah Jordan, Jakob Sack, Ingolf |
| contents | 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 |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_15507 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Time-Harmonic Optical Flow with Applications in Elastography Melnyk, Oleh Quellmalz, Michael Steidl, Gabriele Jaitner, Noah Jordan, Jakob Sack, Ingolf Numerical Analysis 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 |
| title | Time-Harmonic Optical Flow with Applications in Elastography |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2405.15507 |