Abstract
This paper focuses on multi-scale approaches for variational methods and corresponding gradient flows. Recently, for convex regularization functionals such as total variation, new theory and algorithms for nonlinear eigenvalue problems via nonlinear spectral decompositions have been developed. Those methods open new directions for advanced image filtering. However, for an effective use in image segmentation and shape decomposition, a clear interpretation of the spectral response regarding size and intensity scales is needed but lacking in current approaches. In this context, L1 data fidelities are particularly helpful due to their interesting multi-scale properties such as contrast invariance. Hence, the novelty of this work is the combination of L1-based multi-scale methods with nonlinear spectral decompositions. We compare L1 with L2 scale-space methods in view of spectral image representation and decomposition. We show that the contrast invariant multi-scale behavior of L1 − TV promotes sparsity in the spectral response providing more informative decompositions. We provide a numerical method and analyze synthetic and biomedical images at which decomposition leads to improved segmentation.
| Original language | English |
|---|---|
| Title of host publication | Scale Space and Variational Methods in Computer Vision - 6th International Conference, SSVM 2017, Proceedings |
| Publisher | Springer |
| Pages | 80-93 |
| Number of pages | 14 |
| Volume | 10302 LNCS |
| ISBN (Print) | 9783319587707 |
| DOIs | |
| Publication status | Published - 18 May 2017 |
Publication series
| Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
|---|---|
| Volume | 10302 LNCS |
| ISSN (Print) | 03029743 |
| ISSN (Electronic) | 16113349 |
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Keywords
- Calibrable sets
- Denoising
- Eigenfunctions
- L-TV
- Multiscale segmentation
- Nonlinear spectral decomposition
- Scale-spaces
Cite this
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Combining contrast invariant L1 data fidelities with nonlinear spectral image decomposition. / Zeune, Leonie; van Gils, Stephanus A.; Terstappen, Leon; Brune, Christoph.
Scale Space and Variational Methods in Computer Vision - 6th International Conference, SSVM 2017, Proceedings. Vol. 10302 LNCS Springer, 2017. p. 80-93 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10302 LNCS).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review
TY - GEN
T1 - Combining contrast invariant L1 data fidelities with nonlinear spectral image decomposition
AU - Zeune, Leonie
AU - van Gils, Stephanus A.
AU - Terstappen, Leon
AU - Brune, Christoph
PY - 2017/5/18
Y1 - 2017/5/18
N2 - This paper focuses on multi-scale approaches for variational methods and corresponding gradient flows. Recently, for convex regularization functionals such as total variation, new theory and algorithms for nonlinear eigenvalue problems via nonlinear spectral decompositions have been developed. Those methods open new directions for advanced image filtering. However, for an effective use in image segmentation and shape decomposition, a clear interpretation of the spectral response regarding size and intensity scales is needed but lacking in current approaches. In this context, L1 data fidelities are particularly helpful due to their interesting multi-scale properties such as contrast invariance. Hence, the novelty of this work is the combination of L1-based multi-scale methods with nonlinear spectral decompositions. We compare L1 with L2 scale-space methods in view of spectral image representation and decomposition. We show that the contrast invariant multi-scale behavior of L1 − TV promotes sparsity in the spectral response providing more informative decompositions. We provide a numerical method and analyze synthetic and biomedical images at which decomposition leads to improved segmentation.
AB - This paper focuses on multi-scale approaches for variational methods and corresponding gradient flows. Recently, for convex regularization functionals such as total variation, new theory and algorithms for nonlinear eigenvalue problems via nonlinear spectral decompositions have been developed. Those methods open new directions for advanced image filtering. However, for an effective use in image segmentation and shape decomposition, a clear interpretation of the spectral response regarding size and intensity scales is needed but lacking in current approaches. In this context, L1 data fidelities are particularly helpful due to their interesting multi-scale properties such as contrast invariance. Hence, the novelty of this work is the combination of L1-based multi-scale methods with nonlinear spectral decompositions. We compare L1 with L2 scale-space methods in view of spectral image representation and decomposition. We show that the contrast invariant multi-scale behavior of L1 − TV promotes sparsity in the spectral response providing more informative decompositions. We provide a numerical method and analyze synthetic and biomedical images at which decomposition leads to improved segmentation.
KW - Calibrable sets
KW - Denoising
KW - Eigenfunctions
KW - L-TV
KW - Multiscale segmentation
KW - Nonlinear spectral decomposition
KW - Scale-spaces
UR - http://www.scopus.com/inward/record.url?scp=85019673913&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-58771-4_7
DO - 10.1007/978-3-319-58771-4_7
M3 - Conference contribution
AN - SCOPUS:85019673913
SN - 9783319587707
VL - 10302 LNCS
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 80
EP - 93
BT - Scale Space and Variational Methods in Computer Vision - 6th International Conference, SSVM 2017, Proceedings
PB - Springer
ER -