Algebraic phase unwrapping along the real axis: extensions and stabilizations

Kitahara, Daichi; Yamada, Isao

doi:10.1007/s11045-013-0234-7

Cited by 17 publications

(13 citation statements)

References 40 publications

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“…Assuming f (|z|e iθ ) = 0, the integral in Eq. (B9) is well-defined and Arg(f (|z|e iθ )) is continuous and analytic provided that f is continuous and analytic [60].…”

Section: Discussionmentioning

confidence: 99%

“…3. Algebraic phase unwrapping of a linear polynomial interpolation of ϕ using the numerically stabilized Strum sequence method of Kitahara and Yamada [60]. 49) is violated.…”

Section: Unwrapped Phase Statisticsmentioning

confidence: 99%

“…(47) for Θ1, determination of winding numbers by assuming Eq. (49) for Θ2, and algebraic phase unwrapping of a linear polynomial interpolation according to Ref [60]. for Θ3.…”

mentioning

confidence: 99%

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Phase unwrapping and one-dimensional sign problems

2018

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Sign problems in path integrals arise when different field configurations contribute with different signs or phases. Phase unwrapping describes a family of signal processing techniques in which phase differences between elements of a time series are integrated to construct noncompact unwrapped phase differences. By combining phase unwrapping with a cumulant expansion, path integrals with sign problems arising from phase fluctuations can be systematically approximated as linear combinations of path integrals without sign problems. This work explores phase unwrapping in zero-plus-one-dimensional complex scalar field theory. Results with improved signal-to-noise ratios for the spectrum of scalar field theory can be obtained from unwrapped phases, but the size of cumulant expansion truncation errors is found to be undesirably sensitive to the parameters of the phase unwrapping algorithm employed. It is argued that this numerical sensitivity arises from discretization artifacts that become large when phases fluctuate close to singularities of a complex logarithm in the definition of the unwrapped phase.1 Other interesting LQCD observables face distinct StN problems. For instance, isoscalar meson correlation functions are uncharged under U (1) symmetries and possess exponential StN problems but not U (1) phase fluctuations. Excited-state energies are extracted from differences of correlation functions with the same quantum numbers and face StN problems arising from the exponentially precise cancellations needed to project out ground-state contributions and leave exponentially faster decaying excited-state contributions. In large nuclei, StN problems associated with MeV excitation energies are negligible compared to the phase fluctuation StN problem associated with the multi-GeV rest mass of the nucleus. LQCD calculations of isoscalar mesons and exotic hadrons conversely face StN problems primarily from sources besides U (1) phase fluctuations, and phase unwrapping is not immediately applicable to these systems. 2 Cumulant expansions of noncompact "extensive phases" have also been applied to sign problems in QCD and other theories at nonzero chemical potential [51][52][53][54][55][56].

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“…Assuming f (|z|e iθ ) = 0, the integral in Eq. (B9) is well-defined and Arg(f (|z|e iθ )) is continuous and analytic provided that f is continuous and analytic [60].…”

Section: Discussionmentioning

confidence: 99%

“…3. Algebraic phase unwrapping of a linear polynomial interpolation of ϕ using the numerically stabilized Strum sequence method of Kitahara and Yamada [60]. 49) is violated.…”

Section: Unwrapped Phase Statisticsmentioning

confidence: 99%

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Phase unwrapping and one-dimensional sign problems

2018

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“…This causes artifacts in the convolution with the Laplacian. We correct for this using phase unwrapping [10].…”

Section: Phase-based Acceleration Magnificationmentioning

confidence: 99%

Video Acceleration Magnification

Zhang

Pintea

Gemert

2017

2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)

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The ability to amplify or reduce subtle image changes over time is useful in contexts such as video editing, medical video analysis, product quality control and sports. In these contexts there is often large motion present which severely distorts current video amplification methods that magnify change linearly. In this work we propose a method to cope with large motions while still magnifying small changes. We make the following two observations: i) large motions are linear on the temporal scale of the small changes; ii) small changes deviate from this linearity. We ignore linear motion and propose to magnify acceleration. Our method is pure Eulerian and does not require any optical flow, temporal alignment or region annotations. We link temporal secondorder derivative filtering to spatial acceleration magnification. We apply our method to moving objects where we show motion magnification and color magnification. We provide quantitative as well as qualitative evidence for our method while comparing to the state-of-the-art.

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“…Phase unwrapping is applied as with the acceleration methodology in order to create the full composite signal [8] [15].…”

Section: Phase-based Magnificationmentioning

confidence: 99%

Higher Order of Motion Magnification for Vessel Localisation in Surgical Video

Janatka

Sridhar

Kelly

et al. 2018

Medical Image Computing and Computer Assisted Intervention – MICCAI 2018

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Locating vessels during surgery is critical for avoiding inadvertent damage, yet vasculature can be difficult to identify. Video motion magnification can potentially highlight vessels by exaggerating subtle motion embedded within the video to become perceivable to the surgeon. In this paper, we explore a physiological model of artery distension to extend motion magnification to incorporate higher orders of motion, leveraging the difference in acceleration over time (jerk) in pulsatile motion to highlight the vascular pulse wave. Our method is compared to first and second order motion based Eulerian video magnification algorithms. Using data from a surgical video retrieved during a robotic prostatectomy, we show that our method can accentuate cardio-physiological features and produce a more succinct and clearer video for motion magnification, with more similarities in areas without motion to the source video at large magnifications. We validate the approach with a Structure Similarity (SSIM) and Peak Signal to Noise Ratio (PSNR) assessment of three videos at an increasing working distance, using three different levels of optical magnification. Spatio-temporal cross sections are presented to show the effectiveness of our proposal and video samples are provided to demonstrates qualitatively our results.

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Algebraic phase unwrapping along the real axis: extensions and stabilizations

Cited by 17 publications

References 40 publications

Phase unwrapping and one-dimensional sign problems

Phase unwrapping and one-dimensional sign problems

Video Acceleration Magnification

Higher Order of Motion Magnification for Vessel Localisation in Surgical Video

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