Combining contrast invariant L1 data fidelities with nonlinear spectral image decomposition

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

1 Citation (Scopus)

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 languageEnglish
Title of host publicationScale Space and Variational Methods in Computer Vision - 6th International Conference, SSVM 2017, Proceedings
PublisherSpringer
Pages80-93
Number of pages14
Volume10302 LNCS
ISBN (Print)9783319587707
DOIs
Publication statusPublished - 18 May 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10302 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Fingerprint

Image Decomposition
Spectral Decomposition
Fidelity
Spectral Response
Decomposition
Decompose
Invariant
Image Filtering
Nonlinear Eigenvalue Problem
Image Representation
Multiscale Methods
Gradient Flow
Scale Space
Total Variation
Sparsity
Variational Methods
Image Segmentation
Invariance
Regularization
Segmentation

Keywords

  • Calibrable sets
  • Denoising
  • Eigenfunctions
  • L-TV
  • Multiscale segmentation
  • Nonlinear spectral decomposition
  • Scale-spaces

Cite this

Zeune, L., van Gils, S. A., Terstappen, L., & Brune, C. (2017). Combining contrast invariant L1 data fidelities with nonlinear spectral image decomposition. In Scale Space and Variational Methods in Computer Vision - 6th International Conference, SSVM 2017, Proceedings (Vol. 10302 LNCS, pp. 80-93). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10302 LNCS). Springer. https://doi.org/10.1007/978-3-319-58771-4_7
Zeune, Leonie ; van Gils, Stephanus A. ; Terstappen, Leon ; Brune, Christoph. / Combining contrast invariant L1 data fidelities with nonlinear spectral image decomposition. Scale Space and Variational Methods in Computer Vision - 6th International Conference, SSVM 2017, Proceedings. Vol. 10302 LNCS Springer, 2017. pp. 80-93 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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Zeune, L, van Gils, SA, Terstappen, L & Brune, C 2017, Combining contrast invariant L1 data fidelities with nonlinear spectral image decomposition. in Scale Space and Variational Methods in Computer Vision - 6th International Conference, SSVM 2017, Proceedings. vol. 10302 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10302 LNCS, Springer, pp. 80-93. https://doi.org/10.1007/978-3-319-58771-4_7

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 proceedingConference contributionAcademicpeer-review

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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.

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Zeune L, van Gils SA, Terstappen L, Brune C. Combining contrast invariant L1 data fidelities with nonlinear spectral image decomposition. In 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)). https://doi.org/10.1007/978-3-319-58771-4_7