The DOI matches its Crossref record; 37 of the 37 references it cites were found in a registry or an index.
Phase Unwrapping via Graph Cuts
Abstract
Phase unwrapping is the inference of absolute phase from modulo-2pi phase. This paper introduces a new energy minimization framework for phase unwrapping. The considered objective functions are first-order Markov random fields. We provide an exact energy minimization algorithm, whenever the corresponding clique potentials are convex, namely for the phase unwrapping classical Lp norm, with p > or = 1. Its complexity is KT (n, 3n), where K is the length of the absolute phase domain measured in 2pi units and T (n, m) is the complexity of a max-flow computation in a graph with n nodes and m edges. For nonconvex clique potentials, often used owing to their discontinuity preserving ability, we face an NP-hard problem for which we devise an approximate solution. Both algorithms solve integer optimization problems by computing a sequence of binary optimizations, each one solved by graph cut techniques. Accordingly, we name the two algorithms PUMA, for phase unwrappping max-flow/min-cut. A set of experimental results illustrates the effectiveness of the proposed approach and its competitiveness in comparison with state-of-the-art phase unwrapping algorithms.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Fast approximate energy minimization via graph cuts
Boykov, Y., Veksler, O., & Zabih, R. (2001) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.969114 · Cited by 6,988
An experimental comparison of min-cut/max- flow algorithms for energy minimization in vision
Boykov, Y., & Kolmogorov, V. (2004) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2004.60 · Cited by 4,577
Image Formation by Induced Local Interactions: Examples Employing Nuclear Magnetic Resonance
LAUTERBUR, P. C. (1973) · Nature · doi:10.1038/242190a0 · Cited by 3,611
What energy functions can be minimized via graph cuts?
Kolmogorov, V., & Zabih, R. (2004) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2004.1262177 · Cited by 3,127
Synthetic aperture radar interferometry
Rosen, P. A., Hensley, S., Joughin, I. R., Li, F. K., Madsen, S. N., Rodriguez, E., & Goldstein, R. M. (2000) · Proceedings of the IEEE · doi:10.1109/5.838084 · Cited by 2,670
Satellite radar interferometry: Two‐dimensional phase unwrapping
Goldstein, R. M., Zebker, H. A., & Werner, C. L. (1988) · Radio Science · doi:10.1029/rs023i004p00713 · Cited by 2,413
Blake, A., & Zisserman, A. (1987) · The MIT Press eBooks · doi:10.7551/mitpress/7132.001.0001 · Cited by 2,105
Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software
Ghiglia, D. C., & Pritt, M. D. (1998) · Medical Entomology and Zoology · Cited by 2,031
A new approach to the maximum-flow problem
Goldberg, A. V., & Tarjan, R. E. (1988) · Journal of the ACM · doi:10.1145/48014.61051 · Cited by 1,882
Correction for geometric distortion in echo planar images from B 0 field variations
Jezzard, P., & Balaban, R. S. (1995) · Magnetic Resonance in Medicine · doi:10.1002/mrm.1910340111 · Cited by 1,421
Cited by
Overview of quantitative susceptibility mapping
Deistung, A., Schweser, F., & Reichenbach, J. R. (2017) · NMR in Biomedicine · doi:10.1002/nbm.3569 · Cited by 338
Brain mechanical properties predict longitudinal cognitive change in aging and Alzheimer’s disease
Pavuluri, K., Huston, J., Ehman, R. L., Manduca, A., Vemuri, P., Jack, C. R., Senjem, M. L., & Murphy, M. C. (2025) · Neurobiology of Aging · doi:10.1016/j.neurobiolaging.2025.01.001 · Cited by 18
Yin, Z., Lu, X., Cohen Cohen, S., Sui, Y., Manduca, A., Van Gompel, J. J., Ehman, R. L., & Huston, J. (2021) · European Radiology · doi:10.1007/s00330-021-07918-6 · Cited by 17
Metadata
- Authors
- Bioucas-Dias, J. M., & Valadao, G.
- Venue
- IEEE Transactions on Image Processing
- Published
- 2007-03
- Volume
- 16
- Issue
- 3
- Pages
- 698-709
- ISSN
- 1057-7149 (ISSN-L)
- OpenAlex
- W2158755508
- Cited by
- 572
- References
- 37
- FWCI
- 21.38
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Phase Unwrapping via Graph Cuts. https://app.cochat.ai/papers/10.1109/tip.2006.888351
- The paper
- Bioucas-Dias, J. M., & Valadao, G. (2007). Phase Unwrapping via Graph Cuts. IEEE Transactions on Image Processing. https://doi.org/10.1109/tip.2006.888351
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
