2d Phase Unwrapping Matlab


An MR technique for simultaneous quantitative imaging of water content, conductivity and susceptibility, with application to brain tumours using a 3T hybrid MR-PET scanner. NASA Astrophysics Data System (ADS) Chen, Jiafeng; Chen, Haiqin; Yang, Zhengang; Ren, Haixia. Writing simple 2D unwrapping algorithm to unwrap the wrapped phase maps obtained in the earlier step. PUMA Phase Unwrapping via MAx flows_专业资料 68人阅读|7次下载. 2D and 3D phase unwrapping. All images were analyzed off-line using algorithms developed using MATLAB. Although several therapeutic alternatives, including hormonal therapy and surgery, are available to treat endometriosis patients, recurrence rates are high. > >Cheers, >David > I think you can just take the difference of the two values and map it into the -pi/2 to pi/2 plane. m QualityGuidedUnwrap2D. Gdeisat, "Fast two-dimensional phase-unwrapping algorithm based on sorting by reliability following a noncontinuous path", Applied Optics, Vol. However, as previously mentioned, I encountered the same problem as Thuc Phan. PhaseUnwrapping 国外实验室的相位解缠代码,实现二维和三维缠绕相位的解缠-Foreign laboratory phase unwrapping code, the realization of two-dimensional. 2D SWI/phase unwrapped imaging also improved delineation of normal venous structures and nonpathologic calcifications and helped distinguish calcifications from. 1 Placementofbranch cuts: If the sum of the phase gradients along a 2 × 2path yields a non-zero value of 2π±m, a residue of charge or polarity ±m (red), otherwise a zero (green) is assigned to the middle of this pixel cluster. and with an increasing usage. Use features like bookmarks, note taking and highlighting while reading Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software. The issue is that the phase value found is between $-\pi$ and $\pi$ (or $0$ and $2\pi$) but it needs to be "unwrapped" to be continuous. Figure 2: Embryo 11 wrapped. Kemao, “Real-time pipelined heterogeneous system for windowed Fourier filtering and quality guided phase unwrapping algorithm using Graphic Processing Unit,” AIP Conference Proc. Lalor, and M. Equiva-lently, one may find the numbers of extra cycles added to. In 2D phase unwrapping, there are sources of errors four that complicate the phase unwrapping process. The method investigates and compares each pixel value of phase with its neighboring pixels and cautiously adds 2π to phase value if the phase difference is greater than a set threshold phase value. MATLAB’s Unwrap v/s Minimum LP Norm 11 Unwrap Using MATLAB’s unwrap() function Unwrap Using Minimum Lp Norm Algorithm [1] [1] Dennis C. Pritt: Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software. Two-dimensional phase unwrapping is a classical problem encountered in several fields such as electromagnetic theory, optics and DInSAR data processing. 7437-7444 (2002). Brain Area Segmentation B. PPT – Color Histogram Normalization using Matlab and Applications in CBIR PowerPoint presentation | free to download - id: 17a279-ZDc1Z. These sources of errors are as follows. A 2D phase unwrapping algorithm, called UNROLL, is presented here. 2009-09-26 00:00:00 The fringes projection technique allows evaluating 3D profiles from testing objects without contact. In MRI, there are several situations in which phase unwrapping can be circumvented. I'm really enjoy to use the matlab for data analysis. available software for cardiovascular image analysis Each block is implemented as a separate Matlab file and - Phase unwrapping algorithm 2D+T, 3D+T, 3+3D+T. Unfortunately they are also one of the easiest ways to break an installation, by adding an update site that clashes with another update site, or even the ImageJ core. Martin, Armin W. 3 Conservative. In this letter, we propose a novel framework for. Generally, the Doppler phase is obtained by modulo 2π and requires phase unwrapping to yield physically sound data. Kemao, “Real-time pipelined heterogeneous system for windowed Fourier filtering and quality guided phase unwrapping algorithm using Graphic Processing Unit,” AIP Conference Proc. Shift the phase of an array so that there are no jumps of more than the desired angle (default pi) 2D fast Fourier. The Updater has a convenient Manage update sites dialog that is populated by a central index. 5)*n/(2*N)), and you will find that the output is now real (no imaginary component). Phase_Unwrapping_2D. All algorithms were implemented in Matlab and executed on a 3. human gait recognition is MATLAB 7. it has value only from -pi to pi). Sci Rep 9, 88 (2019. Graph cut based 2D phase unwrapping GCphase code; Unwrapping MR phase images by a Markov random field model MRFphase code; Satellite radar interferometry: Two- dimensional phase unwrapping Code. 'phase' Returns the phase spectrum with unwrapping. P가 행렬이면 unwrap은 열을 기준으로 동작합니다. For this reason, there is a large amount of research [14, 15] and solution approaches to both 1D and 2D phase unwrapping problem. phase jumps and remove them by adding or subtracting multiples of 2p. Volkov and Yimei Zhu, Deterministic phase unwrapping in the presence of noise, Opt. Introduction The Shape Decomposition Approach Fringeline Tracking for Phase Unwrapping. Gyroscope gyrocompass in matlab; Fit 2d gaussian function to data in matlab; Sift( scale invariant feature transform) in matlab; Hodgkin huxley like model neuron in matlab; Phase unwrapping using recursive orthogonal referring (puror) in matlab. m GuidedFloodFill. The following Matlab project contains the source code and Matlab examples used for goldsteinunwrap2d r1. Results Mid-ventricular phase-contrast images corresponding to peak systole and early filling are shown in. Matlab for Unwrapping Spectral Phase. To recover the absolute phase, a common practice is to use temporal phase unwrapping (TPU) algorithms with the help of Gray-code patterns or multi-wavelength fringes. update: Updates the given workstation objects. Condat, “A primal-dual splitting method for convex optimization involving Lipschitzian, proximable and linear composite terms,” J. In our method, the TIE was solved using the fast cosine transform, and a phase correction operation was introduced after the TIE was solved. It also provides classes for T1, T2, and T2* parameter mapping, multi-dimensional phase unwrapping, measuring image thickness, and other miscellaneous functions. Click/roll the. > >Cheers, >David > I think you can just take the difference of the two values and map it into the -pi/2 to pi/2 plane. 'phase' returns the phase spectrum with unwrapping. In 1D, the unwrap function will help. example phUnwrap = dsp. The phase can be observed to between - p and p and although the embryos are visible, the magnitude of the phase difference cannot be measured without an unwrapping. Simulated Data 2 and 3 were unwrapped with UMPIRE, PRELUDE (in 2D and 3D mode. Output ox Output vector Specifies the output. MATLABMATLAB TutorialTutorial MATLAB Basics & Signal Processing Toolbox 2. The intent of these functions is to provide a simple interface to the python control systems library (python-control) for people who are familiar with the MATLAB Control Systems Toolbox (tm). By numerically the fringe pattern and its quadrature, we obtained the modulated fringe pattern shown in figure (2. 2D Phase Unwrapping using SRNCP. , Pritt, Mark D. m GoldsteinUnwrap2D. Then it moves on, searching for another discontinuity. 2D & 3D phase unwrapping plugins for Matlab. Herraez, D. Make a Script that convert 2d picture into 3d Drawing ($30-250 USD) Phase unwrapping in digital. To recover the absolute phase, a common practice is to use temporal phase unwrapping (TPU) algorithms with the help of Gray-code patterns or multi-wavelength fringes. Bibliography. m FloodFill. In 1D, the unwrap function will help. Phase unwrapped data were then imported into MATLAB and high-pass filtered with a kernel that excluded the lowest 10% of frequencies. 3 Analog Holographic Interferometry Theory and Setups 52 2. The Type Model. The default is True for MATLAB compatibility. 460-479, 2013. Calibrated 2D phase unwrapping algorithm based on least-squares and iteration MATLAB Release Compatibility. br Seminar GERAD Montreal, February 4th, 2016 Joint work with Ian Herszterg and Marcus Poggi. 2D Phase Unwrapping using SRNCP. phase unwrapping, branch-cut, and MAP dynamic programming phase unwrapping. use_numpy_matrix ([flag, warn]) Turn on/off use of Numpy matrix class for state space operations. The netherlands August 2012 Contents abstract Preface 1 Introduction 3 1. 67 have phase differences that are larger than π compared to the rest of the data. Processing was performed using MATLAB (USA). % This m-file has been automatically generated using qMRgenBatch(qsm_sb) % Command Line Interface (CLI) is well-suited for automatization % purposes and Octave. This is important for both frequency- and time-domain simulations in INTERCONNECT. % Fast unwrapping 2D phase image using the algorithm given in: % % M. html#abs-2002-03500 Jian Wang Miaomiao Zhang. 运行戈尔茨坦枝剪相位展开方法GoldsteinUnwrap2D。 (3D实施质量的制导方法,可根据要求提供)-2D PHASE UNWRAPPING ALGORITHMS Run QualityGuidedUnwrap2D for the phase quality guided phase unwrapping method. Ghiglia and Mark D. Is there a GPU code for 2D phase unwrapping ?. This section lays out the Q# type model and describes the syntax for specifying and working with types. A sparse-representation-based direct minimum -norm algorithm is proposed for a two-dimensional MRI phase unwrapping. In this work, a new two dimensional phase unwrapping algorithm is proposed and results from the proposed algorithm are compared with standard phase unwrapping algorithms. This page is an index of available plugins for ImageJ. MATLAB compatibility module¶. R is similar to the award-winning 1 S system, which was developed at Bell Laboratories by John Chambers et al. 1(f)] has already been extensively studied and well addressed. a) True phase variation, b) wrapped phase into [-( (] range, c) wrapped phase with noise at one of the phase jumps, d) incorrectly unwrapped phase because of noise In figure a) arrows indicate the phase jumps at the boundary between brain and nonbrain area and the incorrect unwrapping of phase map of brain image from conventional 1D unwrapping. An Octave & MATLAB toolbox for. html#abs-2002-03500 Jian Wang Miaomiao Zhang. 15 healthy volunteers (51 ± 19 years) underwent MRI including (1) breath-holding 2D-1dir and (2) free breathing 2D-3dir PC. 2 Analog Holography, Holographic Interferometry, and Phase-Shifting Holographic Interferometry 47 2. TOCTOC Part 2: Signal Processing Toolbox • Representing Signals • Basic Waveform Generation • Convolution • Impulse Response • Frequency Response • Discrete Fourier Transform • Filters Part 1: Introduction • Toolboxes & Simulink • Commands & functions • Help system • Variables. phase jumps and remove them by adding or subtracting multiples of 2p. 2D phase unwrapping was performed by the use of a minimum-cost-match algorithm [7]. Phase wraps in each image are denoted by white arrows. This is important for both frequency- and time-domain simulations in INTERCONNECT. Under sampling 3. MATLAB Central - File detail - 2D phase unwrapping algorithms. By the Fourier shift theorem,. Absolute phase recovery with gray coding The conventional unwrapping method only recovers the rela-tive phase for each pixel. Efficient multiscale phase unwrapping methodology with modulo wavelet transform DAVID BLINDER,1,2,* HEIDI OTTEVAERE,3 ADRIAN MUNTEANU,1,2AND PETER SCHELKENS1,2 1Vrije Universiteit Brussel, Department of Electronics and Informatics (ETRO), Pleinlaan 2, B-1050. Other phase evaluating techniques are the Fourier Transform Method, skeletonizing or the heterodyne technique. ndarray m x n ndarray : m: number of channels, n: number of samples Returns ----- phase : numpy. image processing. Phase unwrapping of velocity data was achieved using a recursive orthogonal referring approach (PUROR) that removes streaks resulting from conventional 2D phase unwrapping (details in manuscript under review in MRM). 82 %Call the 2D phase unwrapper from C language. The phase unwrapping technique successfully deals with noise and with areas of minimal connectivity. Unwrapping can be done using the Minimum L P Norm Phase Unwrap algorithm. 4 Outline 2 Phase Unwrapping algorithms 2. 67 have phase differences that are larger than π compared to the rest of the data. m GuidedFloodFill. The study, “ β-Catenin Signaling Inhibitors ICG-001 and C-82 Improve Fibrosis in Preclinical Models of Endometriosis ”, was published in the journal Scientific Reports. This method usually leads to a large sparse. With clear instructions and savvy advice from technology expert Preston Gralla, you’ll learn how to go online, play games, listen to music, watch movies & TV, monitor your health, and answer calls with a wave of your hand. In order to ensure that the integration of phase gradi-ents remains path. This MATLAB code implements a methodology that can accelerate existing phase unwrapping algorithms using a multiscale approach. Ghiglia and Mark D. Revision 58300, 20-Dec-2018: The document was updated to comply with the changes of the 18. • Analyzed various algorithms for 2D phase unwrapping, specifically placing of branch cuts and floodfill • Understood various implementations of two-dimensional algorithms and developed a self- implementation of O. human gait recognition is MATLAB 7. m PhaseDerivativeVariance. JOONE Framework implements a new approach in the use of Artificial Neural Networks, in other terms Artificial Intelligence. Gestions des commandes et des fonctions help aide. Professional Interests: Optics, Astronomy, Lasers, Numerical Analysis quality-guided path following phase unwrapping. 87 WrappedPhase=I2_phase; 88 mex Miguel_2D_unwrapper. Most raw data is recorded in multi-dimensional form. The Matlab implementation of the one-dimensional phase unwrapping algorithm that is presented in exercise 3 is faster than the other algorithms that were explained in this tutorial and in exercises 1 & 2. br Seminar GERAD Montreal, February 4th, 2016 Joint work with Ian Herszterg and Marcus Poggi. 4(b) show the effect of the unwrap function on the phase response of the example elliptic lowpass filter of § 7. Phase_Unwrapping_2D. Learn more about matlab, image analysis, signal processing MATLAB, Signal Processing Toolbox, Image Processing Toolbox. I'm a graduate student at the GIST in Korea. Performing correct unwrapping of 2D phase images in MATLAB 6 days left VERIFIED I need to correct a bug I have in a MATLAB routine that performs phase unwrapping of 2D images in MATLAB. This phase unwrapping algorithm is based on the theory and c++ code from: "Two-Dimensional Phase Unwrapping, Theory, Algorithms, and Software" written by Dennis C. 12 LabOne release. wavelet: Calculates the wavelet transform of a time series and significance levels. matlab之unwrap函数 风翼冰舟 2015-12-22 21:53:49 23174 收藏 4 最后发布:2015-12-22 21:53:49 首发:2015-12-22 21:53:49. In this letter, we propose a novel framework for. Consultez le profil complet sur LinkedIn et découvrez les relations de Aymen, ainsi que des emplois dans des entreprises similaires. 1 Introduction 2. The phase image is unwrapped using unwrap_phase in scikit_image python module (22, 23). This method usually leads to a large sparse. Herráez, D. The details of this algorithm are available in the paper: R. Figure 3: Simulated ow data. The phase info here is unwrapped for visualization and comparison. Phase wrapping In some cases, running a phase-only gain_cal might produce a plot with a phase jump of ~2π. 2D Phase Unwrapping using SRNCP. ecen 471: power management. Figure 33The phase map in x-direction after phase unwrapping for a concave mirror. For the 2D multi-echo data, the echoes with SNR >3:1 were used in the data processing. (c) 2D path-following unwrapping using the 2D-SRNCP algorithm. use_matlab_defaults Use MATLAB compatible configuration settings. 先载入一幅灰度图像,如下:(非灰度图)2. 41, Issue 35, pp. Ashraf A Saad 1 Electrical Engineering Department, University of Washington 2 Philips Healthcare, Ultrasound Division. wavelet: Calculates the wavelet transform of a time series and significance levels. Gdeisat, "Fast two-dimensional phase-unwrapping algorithm based on sorting by reliability following a noncontinuous path", Applied Optics, Vol. Furthermore, 3D images usually contain many more voxels than typical 2D images, and so speed is an issue, especially in applications such as automatic-shimming where rapid, automatic and robust methods for phase unwrapping are essential. Output ox Output vector Specifies the output. The Unwrapping is a reconstruction of the phase so that the distance between two neighboor pixels is always less than pi/4. Revision 58300, 20-Dec-2018: The document was updated to comply with the changes of the 18. Walaupun sebenarnya script ini untuk pemrograman Matlab, namun M-file juga dapat diganti menggunakan editor yang lain seperi notepad, wordpad atau microsoft. 460-479, 2013. The at operator lets you access the solution at any time in postprocessing. Phase characteristic of analog 4-though order LPF To compare the computational benefits of the proposed algorithm with that of MATLAB function UNWRAP we repeated phase characteristic calculations of the upper 25-Th order low-pass FIR filter several times varying the number of points in the complex array. Third, phase unwrapping is performed using spatial and temporal techniques and the tradeoff between processing speed and high accuracy is discussed in details. In this abstract, we present a new unwrapping algorithm, which uses a recursive orthogonal referring approach (PUROR) to remove streaks that result following conventional 2D phase unwrapping. The study, “ β-Catenin Signaling Inhibitors ICG-001 and C-82 Improve Fibrosis in Preclinical Models of Endometriosis ”, was published in the journal Scientific Reports. The method investigates and compares each pixel value of phase with its neighboring pixels and cautiously adds 2π to phase value if the phase difference is greater than a set threshold phase value. Munther Gdeisat and Dr. m ,4382,2008-12-22 PhaseResidues. Evidence exists to show that phase unwrapping performed before channel combination results in fewer artifacts (singularities, open ended fringe lines) than when phase unwrapping occurs after channel combination. In contrast to fixed path-following methods, branch-cut methods are more robust. Phase_Unwrapping_2D 二维相位展开算法 引导相位展开方法相质量运行QualityGuidedUnwrap2D的。 运行戈尔茨坦枝剪相位展开方法GoldsteinUnwrap2D。. This is an introduction to R (“GNU S”), a language and environment for statistical computing and graphics. To compile the 2D/3D unwrapper, use mex phaseUnwrap. In FPP, efficiently recov. When the continuous phase image contains sudden, abrupt phase changes 4. 5)*n/(2*N)), and you will find that the output is now real (no imaginary component). Gao, and Q. If P is a multidimensional array, unwrap operates on the first dimension whose size is larger than 1. JOONE Framework implements a new approach in the use of Artificial Neural Networks, in other terms Artificial Intelligence. 使用Matlab对灰度图像编程实现2D的傅里叶变换 1. phase unwrapping 程序源代码和下载链接。 应用背景转载由他人编写的C语言相位解缠程序,可以转换到matlab应用环境中,在. Is there a GPU code for 2D phase unwrapping ?. PhaseUnwrapper( Name,Value ) returns a phase unwrapper System object with each specified property set to the specified value. 2 Reconstruction of phase fron phase gradients 2. We note that Q# is a strongly-typed language, such that careful use of these types can help the compiler to provide strong guarantees about Q# programs at compile time. Walaupun sebenarnya script ini untuk pemrograman Matlab, namun M-file juga dapat diganti menggunakan editor yang lain seperi notepad, wordpad atau microsoft. Whenever the jump between consecutive angles is greater than or equal to π radians, unwrap shifts the angles by adding multiples of ±2π until the jump is less than π. 03500 CoRR https://arxiv. if your phase data is noise-free or low-noise, Calibration=false, otherwise, Calibration=true. Cusack’s 3D phase-unwrapping algorithm in MATLAB. First, it computes a reliability map from second differences between a pixel and its eight neighbours. Gdeisat, "Fast two-dimensional phase-unwrapping algorithm based on sorting by reliability following a noncontinuous path", Applied Optics, Vol. goldstein phase unwrapping code Search and download goldstein phase unwrapping code open source project / source codes from CodeForge. The phase info here is unwrapped for visualization and comparison. Gdeisat, “Fast two-dimensional phase-unwrapping algorithm based on sorting by reliability following a noncontinuous path”, Applied Optics, Vol. 2D and 3D Phase Unwrapping using SRNCP 2D & 3D phase unwrapping plugins for Matlab. 4(b) show the effect of the unwrap function on the phase response of the example elliptic lowpass filter of § 7. Phase unwrapping via Grid Cuts. The net change from center to corner is the same in both cases, + 6 pi, which is correct. [email protected] M-file berfungsi sebagai editor script Matlab. By inserting reversible modulo operators in the wavelet transform, the number of. However, as previously mentioned, I encountered the same problem as Thuc Phan. org/abs/2002. This video presents the operation of the phase-unwrapping algorithm by rounding-least-squares. Bioucas-Dias and G. 40 Figure 35The surface reconstruction for concave mirror via 4-th two-dimensional order. 2007-01-01. MATLAB Central - File detail - 2D phase unwrapping algorithms. Pritt This program uses weighted least-squares phase unwrapping technique (i. To compile the 2D/3D unwrapper, use mex phaseUnwrap. Phase unwrapping. In contrast to fixed path-following methods, branch-cut methods are more robust. any special packages/toolboxes and needs any Matlab compatible C compiler. Seaborn Paired Colors. Pages in category "Plugins" The following 200 pages are in this category, out of 261 total. The 3D version of the algorithm is therefore more immune to noise compared to the 2D variant. For a given location over time, a path over time through a directed graph of possible velocities at each time is determined by minimization of derivatives over time. Comparison of phase unwrapping methods applied to a segment of Signature1000 AD2CP HR vertical velocity observations in Colvos Passage. Phase unwrapping in 2D. The more samples used the longer the lag experienced(All filters have lag). σ circ (φ) plot deviates from the reference line at higher σ circ values. 运行戈尔茨坦枝剪相位展开方法GoldsteinUnwrap2D。 (3D实施质量的制导方法,可根据要求提供)-2D PHASE UNWRAPPING ALGORITHMS Run QualityGuidedUnwrap2D for the phase quality guided phase unwrapping method. If P is a multidimensional array, unwrap operates on the first dimension whose size is larger than 1. Phase unwrapping. This will help us identifying the best architecture for our Neural Network. For example, monitors in FDTD and MODE typically return data in 4D matrices where the first three dimensions of the matrix correspond to the spatial dimensions X, Y, Z, and the 4th dimension corresponds to the frequency or time dimension, depending on the type of monitor. 4 Outline 2 Phase Unwrapping algorithms 2. 1(f)] has already been extensively studied and well addressed. The second dimension is the number of channels. The wraps in the image are reduced as explained in [11] by using the mode frequency 31. 07 and P(3,1) = 6. 698-709, 2007. Holography is the only truly three-dimensional imaging method available, and MATLAB has become the programming language of choice for engineering and physics students. to customize it. unwrap phase Syntax int fftw_fft_unwrap_phase (int nSize, double * vPhase, int nAngleUnit = FFT_ANGLE_DEGREE ) Parameters nSize [input] size of vPhase vPhase [modify] the original data of phase for input, and the result of of the transformation for output. This was partly done by cleaning up the decision logic. With clear instructions and savvy advice from technology expert Preston Gralla, you’ll learn how to go online, play games, listen to music, watch movies & TV, monitor your health, and answer calls with a wave of your hand. Fast 2D phase unwrapping implementation in MATLAB. This is a critical step in the InSAR processing chain, yet still one of its most challenging problems; this fact makes of phase unwrapping a crucial problem to InSAR based DEM production. Branch cut methods. The animation uses MATLAB. This is an update of Bruce Spottiswoode's 2D phase unwrapping algorithms. Bibliography [1] [2] John W. SAR Polar Format Implementation with MATLAB Grant D. By the Fourier shift theorem,. Advertisement. by Vigneault D. A cost minimization-based phase-unwrapping algorithm was applied to each 2D sagittal section in the 3D volume. This is an introduction to R (“GNU S”), a language and environment for statistical computing and graphics. In order to ensure that the integration of phase gradi-ents remains path. 2D PHASE UNWRAPPING 、 切换的幅值和相位的内容,并执行 2D IFFTs 以查看结果。 本练习将希望一些洞察如何在 Matlab 中执行二维. The wraps in the image are reduced as explained in [11] by using the mode frequency 31. Many articles are to be found in the technical literature claiming the robustness and noise immunity of the proposed algorithm. There are many digital signal-processing techniques that use the four quadrant arctangent function to calculate the phase of signal. In this letter, we propose a novel framework for. unwrap_phase: Unwrap (correct) phase angles to produce smoother phase plots. m GoldsteinUnwrap2D. 5)*n/(2*N)), and you will find that the output is now real (no imaginary component). 87 WrappedPhase=I2_phase; 88 mex Miguel_2D_unwrapper. b = cfirpm(n,f,a) is a synonym for b = cfirpm(n,f,{@multiband,a}). Anyone knows how can I get the phase plot correctly? I simply did semilogx(f,unwrap(rad2deg(phase(T)))) to get that phase plot, and expect a -180 degree drop at the resonance. developed using MATLAB. Aside from the phase unwrapping and linear interpolation, this method provided a true investigation of the raw displacements from the DENSE imaging. unwrap phase Syntax int fftw_fft_unwrap_phase (int nSize, double * vPhase, int nAngleUnit = FFT_ANGLE_DEGREE ) Parameters nSize [input] size of vPhase vPhase [modify] the original data of phase for input, and the result of of the transformation for output. 4(b) show the effect of the unwrap function on the phase response of the example elliptic lowpass filter of § 7. Kemao, “Real-time pipelined heterogeneous system for windowed Fourier filtering and quality guided phase unwrapping algorithm using Graphic Processing Unit,” AIP Conference Proc. The unwrapping process could be performed by the “unwrap. Other phase evaluating techniques are the Fourier Transform Method, skeletonizing or the heterodyne technique. M-file berfungsi sebagai editor script Matlab. Introduction to one -dimensional phase unwrapping. Phase Shifting Interferometry. The wrapped data clearly demonstrates the problem. Whenever the jump between consecutive angles is greater than or equal to π radians, unwrap shifts the angles by adding multiples of ±2π until the jump is less than π. Phase unwrapping is provided for phase contrast magnetic resonance (MR) imaging. For this reason, there is a large amount of research [14, 15] and solution approaches to both 1D and 2D phase unwrapping problem. Comparison of phase unwrapping methods applied to a segment of Signature1000 AD2CP HR vertical velocity observations in Colvos Passage. Il en existe d'autres que l'on pourra trouver dans les différentes boîtes à outils (toolbox) qui viennent compléter le logiciel de base. Noninterferometric phase retrieval techniques, such as TIE-based systems, have obvious advantages over interferometric techniques. 1 Placementofbranch cuts: If the sum of the phase gradients along a 2 × 2path yields a non-zero value of 2π±m, a residue of charge or polarity ±m (red), otherwise a zero (green) is assigned to the middle of this pixel cluster. To recover the absolute phase, a common practice is to use temporal phase unwrapping (TPU) algorithms with the help of Gray-code patterns or multi-wavelength fringes. Is this normal? After creating an executable file of the Labview with the Mathscript do you think it will run faster? Another question is: I want to use fftn() and ifftn. Hemodynamic Measurement Using Four-Dimensional Phase-Contrast MRI: Quantification of Hemodynamic Parameters and Clinical Applications Hojin Ha, PhD, 1 Guk Bae Kim, PhD, 2 Jihoon Kweon, PhD, 3 Sang Joon Lee, PhD, 1, 4 Young-Hak Kim, MD, PhD, 3 Deok Hee Lee, MD, PhD, 5 Dong Hyun Yang, MD, PhD, 5 and Namkug Kim, PhD 5, 6. The Phase Extractor block extracts the unwrapped phase of a complex input. Typically, when using Matlab and the CPU of a. Remote Sensing & GIS Video Tutorials Recommended for you 12:09. Using these parameters, the final encoded phase can be reconstructed in many different ways, e. Simulated Data 2 and 3 were unwrapped with UMPIRE, PRELUDE (in 2D and 3D mode. Phase unwrapping in 2D. 6 Phase Unwrapping Even after having determined the interference phase by a method such as HI phase shifting a problem remains: The cosine function is periodic, i. These three images, two fringe images and one stair image, are then packed into each respective channel of a 2D image which can be further compressed with existing 2D image com-pression techniques (e. Lalor, and M. For the alternative phase unwrapping followed by HP filtering approaches, several different phase unwrapping methods were examined. m in the zip. The following Matlab project contains the source code and Matlab examples used for goldsteinunwrap2d r1. tagging/displacement-encoding pulses [6]. deg:Degrees{1} Uses degrees as the unit for angles. Zernike phase contrast, and Nomarski differential interference contrast) usually provide only the visualization of the phase of biological structures in a qualitative way, although it is possible to extract quantitative phase information with the differential interference contrast method 1. the interference phase distribution is indefinite to an additive. Lalor, and M. Brain Area Segmentation B. ==Start of tab5 content===== Accessing data. m GuidedFloodFill. There is also an image of the wrapped phase image this program has been tested with and its. m QualityGuidedUnwrap2D. Unwrapping can be done using the Minimum L P Norm Phase Unwrap algorithm. First, it computes a reliability map from second differences between a pixel and its eight neighbours. Matlab angle unwrap. Bioucas-Dias and G. 1 Nyquist criterion 2. Tutorial Matlab - Free download as Powerpoint Presentation (. Outline of the Work. The more samples used the longer the lag experienced(All filters have lag). The 3D 4FT FPU method produces phase unwrapping errors at considerably higher noise levels. Matlab and Octave have a function called unwrap() which implements a numerical algorithm for phase unwrapping. The Unwrap block unwraps each channel of its input matrix or input vector by adding 2πk to each successive channel element, and updating k at each phase jump. (Conference on Information Sciences and Systems (CISS), March. 2D & 3D phase unwrapping plugins for Matlab. All algorithms were implemented in Matlab and executed on a 3. m ,4382,2008-12-22 PhaseResidues. 2D&3D phase unwrapping plugin for Matlab. 利用函数fft2,对其进行快速傅立叶变换,并利用函数fftshift将变换后的图像原点移动到频率矩形的中心。. Phase unwrapping in 2D. 'angle' returns the phase spectrum without unwrapping. Q = unwrap(P) unwraps the radian phase angles in a vector P. In this paper, we propose a generic framework using a novel wavelet transform that can be combined with many types of phase unwrapping algorithms. Valadão, "Phase unwrapping via graph cuts", IEEE Transactions on Image processing, vol. def get_phase(time_series): """ Computes phase from time series using a hilbert transform and computing the angles between the real and imaginary part for each sample Parameters ----- time_series : numpy. Therefore, 2D phase unwrapping (PU) is required to obtain /. Francis Lilley. The joint kernel is the multiplication of 4 univariate rectangular kernels. ; Shapiro, Linda G. 2009-09-26 00:00:00 The fringes projection technique allows evaluating 3D profiles from testing objects without contact. Vessel Recognition in Color Doppler Ultrasound Imaging. 使用Matlab对灰度图像编程实现2D的傅里叶变换 1. For this application, unwrapping was performed in three-dimensions (with time during the cardiac cycle being the 3rd. Like the MATLAB function with the same name, returns True if the supplied numpy array or matrix X looks like a vector, meaning it has a one non-singleton axis (i. – Prototype design in Matlab, Python & iPython Notebooks –– Global phase unwrapping with 2D. unwrapping, which must be fixed by some other post-processing option. Tags Add Tags. Condat, “A primal-dual splitting method for convex optimization involving Lipschitzian, proximable and linear composite terms,” J. a well-behaved area containing no unwrapping artifacts. Therefore in order to get the real phase an unwrapping technique must be employed. The 3D 4FT FPU method produces phase unwrapping errors at considerably higher noise levels. phase jumps and remove them by adding or subtracting multiples of 2p. 2 Analog Holography, Holographic Interferometry, and Phase-Shifting Holographic Interferometry 47 2. Introduction The Shape Decomposition Approach Fringeline Tracking for Phase Unwrapping. N phase_unwrapping C HistogramPhaseUnwrapping: Class implementing two-dimensional phase unwrapping based on This algorithm belongs to the quality-guided phase unwrapping methods. t array-like. The at operator lets you access the solution at any time in postprocessing. Figures 1(a) and 1(b) present a computer-generated phase map with a size of 256 × 256 on a flat background in 2D and 3D visualizations, respectively. ecen 471: power management. Highlights of the changes and additions to the UHFLI product are:. ECE 738 Project Brain segmentation and Phase unwrapping in MRI data JongHoon Lee Outline Nature of fast MRI: EPI Nature of fast MRI: EPI Specific Problems Specific Problems Specific Problems Specific Problems Specific Problems Goal Approach Approach Details Approach Details Results. Using these parameters, the final encoded phase can be reconstructed in many different ways, e. Use the default jump threshold π by specifying the second argument as []. Many of them come with the Fiji distribution of ImageJ. MATLAB Central contributions by Amal George M. 'phase' returns the phase spectrum with unwrapping. For the 2D multi-echo data, the echoes with SNR >3:1 were used in the data processing. In contrast to fixed path-following methods, branch-cut methods are more robust. Ghiglia and Mark D. 2 Reconstruction of phase fron phase gradients 2. The Unwrapping is a reconstruction of the phase so that the distance between two neighboor pixels is always less than pi/4. PhaseUnwrapping 国外实验室的相位解缠代码,实现二维和三维缠绕相位的解缠-Foreign laboratory phase unwrapping code, the realization of two-dimensional. on Acoustics, Speech, and Signal Processing (ICASSP), Las Vegas, Nevada, April 2008) Marco F. 00 V with 0. Herráez, D. 83 %To compile the C code: in MATLAB command window, type 84 %Miguel_2D_unwrapper. M-file berfungsi sebagai editor script Matlab. The intent of these functions is to provide a simple interface to the python control systems library (python-control) for people who are familiar with the MATLAB Control Systems Toolbox. PhaseUnwrapper returns a phase unwrapper System object that adds or subtracts appropriate multiples of 2 π to each input element to remove phase discontinuities (unwrap). Lalor, and M. Vessel Recognition in Color Doppler Ultrasound Imaging. MATLAB Central contributions by Carey Smith. matfile_varwrite — Write a variable in a Matlab binary MAT-file. Unwrapping can be done using the Minimum L P Norm Phase Unwrap algorithm. Unwrap the phase angles by first comparing the elements columnwise. (The reverse of the original. All images were analyzed off-line using algorithms developed using MATLAB. Two Dimensional Phase Unwrapping-Theory Algorithms and Software 翻译(第五章) 热门文章 小波变换对图像的分解与重构(含matlab代码) 19797. (j) The 2D intensity map and (k) 3D isometric plot of the unwrapped phase map produced by unwrapping the image in (i) using Flynn algorithm. Currently, I have the FFT of these two sine curves, the phase shift is just the delay in time, which coresponds to the change of the phase angle. The wrapped data clearly demonstrates the problem. need to use more complex 2D phase unwrappers in order to deal with these images. ISPRS Special 1: TanDEM-X intereferogram generation and phase unwrapping using snap and snaphu - Duration: 12:09. MATLAB emulation functions. Phase unwrapping. It is used to calculate the phase estimate ψ est (r). There are many digital signal-processing techniques that use the four quadrant arctangent function to calculate the phase of signal. The phase map is a 2D array of double [64 bit real (~15 bit precision)], with values ranging from 0 to pi. Fast unwrapping 2D phase image using the algorithm given in: M. If P is a matrix, unwrap operates columnwise. % Fast unwrapping 2D phase image using the algorithm given in: % % M. – Prototype design in Matlab, Python & iPython Notebooks –– Global phase unwrapping with 2D. Phase_Unwrapping_2D 二维相位展开算法 引导相位展开方法相质量运行QualityGuidedUnwrap2D的。 运行戈尔茨坦枝剪相位展开方法GoldsteinUnwrap2D。. 1 (R14SP3), Neural Network Toolbox Version 4. 2 General method and assumption 10 2. c) with a spatial carrier of frequency m = 1. The geometric phase 1,2 plays a fundamental role in a broad range of physical phenomena 3,4,5. ut_calendar_fix. Appendix A: Phase Unwrapping 113 Fig. a) True phase variation, b) wrapped phase into [-( (] range, c) wrapped phase with noise at one of the phase jumps, d) incorrectly unwrapped phase because of noise In figure a) arrows indicate the phase jumps at the boundary between brain and nonbrain area and the incorrect unwrapping of phase map of brain image from conventional 1D unwrapping. 82 %Call the 2D phase unwrapper from C language. Initial control (n = 10) testing compared 2D BH QSM (ECG-triggered 2D gradient echo acquired at end-expiration) and 3D NAV QSM (ECG-triggered navigator gated gradient echo acquired in free breathing using a phase-ordered automatic window selection algorithm to partition data based on diaphragm position). P가 행렬이면 unwrap은 열을 기준으로 동작합니다. matlab-unwrapping algorithms/ matlab-unwrapping algorithms/2D phase unwrapping algorithms-毕业设计/ matlab-unwrapping algorithms/2D phase unwrapping algorithms-毕业设计/MATLAB Central - File detail - 2D phase unwrapping algorithms. Matlab for Unwrapping Spectral Phase. Absolute phase recovery with gray coding The conventional unwrapping method only recovers the rela-tive phase for each pixel. Figure 3: Simulated ow data. Gdeisat, "Fast two-dimensional phase-unwrapping. m GoldsteinUnwrap2D. , it can have multiple axes, but all must have length 1, except for one of them). Flagging the data around the phase jump will remove the jump but also will remove the flagged pointing data. html#abs-2002-03500 Jian Wang Miaomiao Zhang. 使用Matlab对灰度图像编程实现2D的傅里叶变换 1. A cost minimization-based phase-unwrapping algorithm was applied to each 2D sagittal section in the 3D volume. Generally, the Doppler phase is obtained by modulo 2π and requires phase unwrapping to yield physically sound data. , phase unwrapping (PU), becomes indispensable. 2D phase-unwrapping algorithms (PUAs) are commonly used to obtain a continuous phase map from the sawtooth-shaped phase map. any special packages/toolboxes and needs any Matlab compatible C compiler. Comparison of phase unwrapping methods applied to a segment of Signature1000 AD2CP HR vertical velocity observations in Colvos Passage. M-file berfungsi sebagai editor script Matlab. For position the kernel is 3-pixels-wide, the phase intensity kernel is π/10-. 1 members found this post helpful. 2D Graphic Matlab 用一组线性相位的滤波器组来对图像进行处理,以检验该线性系统的各项参数是否符合要求。 using a linear- phase filter to the image processing, to test the linear systems of the various parameters whether it meets the requirements. Conducting experiments to reconstruct the 3D shape of a real object using the above methods 4. Phase contrast MRI (pcMRI) has been used to investigate flow pulsatility in cerebral arteries, larger cerebral veins, and the cerebrospinal fluid (CSF). 연속되는 각도 값 간의 비약이 π 라디안보다 크거나 같으면 unwrap은 비약이 π 미만이 될 때까지 ±2π의 배수를 더해 각도를 변위합니다. 先载入一幅灰度图像,如下:(非灰度图)2. Ghiglia and M. , Bluemke D. Introduction The Shape Decomposition Approach Fringeline Tracking for Phase Unwrapping. This algorithm was written in MatLab and results show that this technique is suitable to measure profiles using fringes projection if images obtained. Phase_Unwrapping_2D 二维相位展开算法 引导相位展开方法相质量运行QualityGuidedUnwrap2D的。 运行戈尔茨坦枝剪相位展开方法GoldsteinUnwrap2D。. m in the zip. 연속되는 각도 값 간의 비약이 π 라디안보다 크거나 같으면 unwrap은 비약이 π 미만이 될 때까지 ±2π의 배수를 더해 각도를 변위합니다. Découvrez le profil de Aymen SHABOU, PhD sur LinkedIn, la plus grande communauté professionnelle au monde. The 3D version of the algorithm is therefore more immune to noise compared to the 2D variant. Juarez-Salazar et al. This was partly done by cleaning up the decision logic. 12/11/2017; 18 minutes to read +4; In this article. 87 WrappedPhase=I2_phase; 88 mex Miguel_2D_unwrapper. Lalor, and M. However, this requires a large number of additional images, which are only used for phase disambiguation purpose but not contribute to the final 3D results. Returns the phase spectrum without unwrapping. You should be aware that there are many algorithms that are a. The source code and files included in this project are listed in the project files section, please make sure whether the listed source code meet your needs there. In FPP, efficiently recov. MATLAB Central contributions by Carey Smith. Robust and fast 2D weighted phase unwrapping based on Ghiglia and. 79KB) 附件内容(只显示9中的7个) BranchCuts. MATLAB emulation functions. weighted Laplace unwrapping) with a solution using iterative algorithm, namely. Identification of translational displacements between N-dimensional data sets using the high order SVD and phase correlation W. Use the default jump threshold π by specifying the second argument as []. The MATLAB desktop contains a help browser covering both reference and tutorial material. Create a signal that consists of two sinusoids of frequencies 15 Hz and 40 Hz. Ghiglia and M. If P is a multidimensional array, unwrap operates on the first dimension whose size is larger than 1. For position the kernel is 3-pixels-wide, the phase intensity kernel is π/10-. Gao, and Q. Endocardial and. image processing. This is an update of Bruce Spottiswoode's 2D phase unwrapping algorithms. The first dimension is the length of the channel. need to use more complex 2D phase unwrappers in order to deal with these images. Processing was performed using MATLAB (USA). Ashraf A Saad 1 Electrical Engineering Department, University of Washington 2 Philips Healthcare, Ultrasound Division. As far as we know, sequential methods such as the branch-cut methods are the best known phase unwrapping methods [2] , [3]. Перевести эту страницу. Also, it matches +/- residues by having the search box size by the outer loop and the residue index being the inner loop. Unwrap starts counting up phase beginning at the edges and starts out with those small values. Q = unwrap(P) corrects the radian phase angles in a vector P by adding multiples of ±2π when absolute jumps between consecutive elements of P are greater than or equal to the default jump tolerance of π radians. M-file atau MATLAB Editor/Debugger (Editor Pencarian Kesalahan) Window ini merupakan tool yang disediakan oleh Matlab (minimal seri 5 keatas). Lalor, and M. A phase unwrapping method for image demodulation comprises receiving a plurality of images of a fringe pattern captured by rotating the fringe pattern by a predetermined rotation angle. Fringe projection profilometry (FPP) has become a more prevalently adopted technique in intelligent manufacturing, defect detection, and some other important applications. If P is a matrix, unwrap operates columnwise. (b) 3D surface plot of phase. cpp 89 %The wrapped phase should have the single (float in C) 90 %data type. of the wrapped phase image this program has been. Generated on Wed May 6 2020 03:17:19 for OpenCV by 1. Noninterferometric phase retrieval techniques, such as TIE-based systems, have obvious advantages over interferometric techniques. Valadão, "Phase unwrapping via graph cuts", IEEE Transactions on Image processing, vol. 5 is the default): add or substract 1 to ensure phase continuity. This was partly done by cleaning up the decision logic. Discover Live Editor. Paper: TBC Downloadable MATLAB code: TBC. Introduction The Shape Decomposition Approach Fringeline Tracking for Phase Unwrapping. 00 V with 0. A new fringeline-tracking approach for color Doppler ultrasound imaging phase unwrapping A new fringeline-tracking approach for color Doppler ultrasound imaging phase unwrapping Saad, Ashraf A. Matlab angle unwrap. m ,4382,2008-12-22 PhaseResidues. Returns the phase spectrum without unwrapping. htm,17364,2003-02-14 PhaseDerivativeVariance. 2 Analog Holography, Holographic Interferometry, and Phase-Shifting Holographic Interferometry 47 2. However, as previously mentioned, I encountered the same problem as Thuc Phan. The main research work in the project involves: (1) Introduction of the virtual instrument technique to capture and process optical phase images; (2) Processing of phase images acquired with different wavelengths using MATLAB to reveal show the 2D and 3D surface structures. Herraez, D. The input can be a vector or matrix. Holography is the only truly three-dimensional imaging method available, and MATLAB has become the programming language of choice for engineering and physics students. This is an update of Bruce Spottiswoode's 2D phase unwrapping algorithms. Unwrap the phase angles by first comparing the elements columnwise. M4JPEG is an Image Steganography Tool where the user can. Lalor, and M. In our method, the TIE was solved using the fast cosine transform, and a phase correction operation was introduced after the TIE was solved. SWI uses a fully flow compensated, long echo, gradient recalled echo (GRE) pulse sequence to acquire images. Spectral Modulation Interferometry: A high-sensitivity, high-speed approach to quantitative phase imaging Ruibo Shang Thesis submitted to the faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of Master of Science In Electrical and Computer Engineering Yizheng Zhu, Chair. >> >> Jerry > >Check out Sandia Labs. Our Matlab code is available upon request. An Introduction to R. Zhang, etc, Robust 2D phase unwrapping algorithm based on the transport of intensity equation, Measurement Science and Technology, 30 (2018) 015201 2. The systems are solved by the backslash operator, and the solutions plotted for 1d and 2d. Cusack’s 3D phase-unwrapping algorithm in MATLAB. Use the default jump threshold π by specifying the second argument as []. m PhaseDerivativeVariance. 1 Here, i and j are the pixel indeces and K is the affinity/kernel function. br Seminar GERAD Montreal, February 4th, 2016 Joint work with Ian Herszterg and Marcus Poggi. (8)], which decrease on each iteration. 4 Outline 2 Phase Unwrapping algorithms 2. Many of them come with the Fiji distribution of ImageJ. When the continuous phase image contains sudden, abrupt phase changes 4. We reformulate the problem definition of directly obtaining continuous original phase as obtaining the wrap-count. A common problem that arises in 2D phase unwrapping is the so-called path dependent problem, wherein the integration result depends on the path. Walaupun sebenarnya script ini untuk pemrograman Matlab, namun M-file juga dapat diganti menggunakan editor yang lain seperi notepad, wordpad atau microsoft. To recover the absolute phase, a common practice is to use temporal phase unwrapping (TPU) algorithms with the help of Gray-code patterns or multi-wavelength fringes. conventional 2D phase unwrapping. TIE-based systems are simple to construct, immune to vibrations, no phase unwrapping is needed, and can be employed with partially coherent sources [8–17]. Problem statement 2D phase unwrapping 3D phase unwrapping Publicity—free source code. Phase unwrapped data were then imported into MATLAB and high-pass filtered with a kernel that excluded the lowest 10% of frequencies. matlab-unwrapping algorithms/ matlab-unwrapping algorithms/2D phase unwrapping algorithms-毕业设计/ matlab-unwrapping algorithms/2D phase unwrapping algorithms-毕业设计/MATLAB Central - File detail - 2D phase unwrapping algorithms. we develop a simple and robust phase-unwrapping algorithm based on the transport of intensity equation (TIE). An MR technique for simultaneous quantitative imaging of water content, conductivity and susceptibility, with application to brain tumours using a 3T hybrid MR-PET scanner. Revisiting Homomorphic Wavelet Estimation and Phase Unwrapping Roberto H. The issue is that the phase value found is between $-\pi$ and $\pi$ (or $0$ and $2\pi$) but it needs to be "unwrapped" to be continuous. N phase_unwrapping C HistogramPhaseUnwrapping: Class implementing two-dimensional phase unwrapping based on This algorithm belongs to the quality-guided phase unwrapping methods. First, the algorithm converts the weighted--norm-minimization-based phase unwrapping problem into a linear system problem whose system (coefficient) matrix is a large, symmetric one. Writing simple 2D unwrapping algorithm to unwrap the wrapped phase maps obtained in the earlier step. A method of nuclear magnetic resonance imaging of an object is disclosed, the method including: receiving MR data including magnitude and phase information generated using an MR scan having a series of different echo times; generating one or more measured MR images based on the MR data; and processing the measured MR images to generate. In this research, absolute phase is required for accurate calibration. unwrapped = phaseUnwrap(wrapped); to get the unwrapped image. Moreover, 3D implementation would improve the results by adding additional information from adjacent slices. All of the commonly used phase unwrapping algorithms relate the phase values by first differentiating the phase field and subsequently. 82 %Call the 2D phase unwrapper from C language. Appendix A: Phase Unwrapping 113 Fig. The Adobe Flash plugin is needed to view this content. Furthermore, 3D images usually contain many more voxels than typical 2D images, and so speed is an issue, especially in applications such as automatic-shimming where rapid, automatic and robust methods for phase unwrapping are essential. Phase unwrapping. br Seminar GERAD Montreal, February 4th, 2016 Joint work with Ian Herszterg and Marcus Poggi. The velocity values are unaliased. 03500 db/journals/corr/corr2002. The net result is that unwrap ends up with close to 0 at the corners and -6 pi at the center. Syntax p = unwrap(p) Description p = unwrap(p) corrects the phase angles in vector p by adding multiples of 2*pi where needed, to smooth the transitions across branch cuts. 2D phase unwrapping. Problem statement 2D phase unwrapping 3D phase unwrapping Publicity—free source code. An ITK-Based Framework for 2D-3D. These sources of errors are as follows. Q = unwrap(P) corrects the radian phase angles in a vector P by adding multiples of ±2π when absolute jumps between consecutive elements of P are greater than or equal to the default jump tolerance of π radians. When the continuous phase image contains sudden, abrupt phase changes 4. Method for unwrapping phase in magnetic resonance image deive and magnetic resonance image device using the method CN105043298A (en) * 2015-08-21: 2015-11-11: 东北大学: Quick three-dimensional shape measurement method without phase unwrapping based on Fourier transform US9911062B1 (en) * 2015-10-20: 2018-03-06. Phase unwrapping is provided for phase contrast magnetic resonance (MR) imaging. The phase image is unwrapped using unwrap_phase in scikit_image python module (22, 23). Phase unwrapping in 2D you may be able to simply use "unwrap" on the two different. Like the MATLAB function with the same name, returns True if the supplied numpy array or matrix X looks like a vector, meaning it has a one non-singleton axis (i.