Quality-guided Phase Unwrapping Algorithm Research Articles

Phase unwrapping algorithm using breadth-first-search and multi-level segmentation of phase quality interval in digital holography

A quality-guided phase unwrapping algorithm is proposed based on the breadth-first-search and multi-level segmentation of the phase quality interval. In the proposed method, the pixels having phase quality values below a threshold associated with a given segment are unwrapped based on the breadth-first-search strategy implemented in a recursive manner. The pixel selection based on the multi-level phase quality interval segmentation allows to perform noise-robust phase unwrapping and the recursive breadth-first-search technique offers computational efficiency in the implementation of proposed algorithm. Three segmentation strategies are investigated in reference to the phase unwrapping accuracy. Simulation and experimental results indicate that the proposed algorithm offers desirable trade-off between the phase unwrapping accuracy and computation time.

Accuracy improvement of the inSAR quality-guided phase unwrapping based on a modified PDV map.

In this paper, an accuracy improvement of the quality-guided phase unwrapping algorithm is proposed. Our proposal is based on a modified phase derivative variance which provides more details on local variations especially for important patterns such as fringes and edges, hence distorted regions may be re-unwrapped according to this new reliable PDV. The proposed improvement is not only effective on accuracy but also on time, the obtained results have shown that the running time with our proposal is less than that of a skillful optimization-based algorithm. To prove effectiveness, the experimental test is carried out on simulated and real data, and the comparison is made under several relevant criteria.

Quality guided alternative holographic data representation for high performance lossy compression

We analyze several representations for holographic data and determine the effectiveness of a common lossy compression algorithm for each representation. We demonstrate that a phase–amplitude representation, when used to represent holograms of diffuse objects, can be combined with a phase unwrapping algorithm to achieve much higher compression ratios (CRs) than direct compression of the complex valued holographic data. We compare the compression performance of the JPEG algorithm for several conventional and alternative holographic data representations. Additionally, we test two different phase unwrapping algorithms to improve phase compression performance. In particular, we propose and evaluate an alternative phase representation based on a quality guided phase unwrapping algorithm. This alternative representation offers higher performance to the other tested approaches, achieving CRs over 6 with a limited quality loss after reconstruction. We add the experimental reconstruction of the processed holograms to further validate our proposal.

Two 3D spatial phase unwrapping algorithms for dynamic 3D shape measurement

Phase unwrapping is a key step of three-dimensional (3D) shape measurement in fringe projection profilometry (FPP). In this paper, 3D quality-guided (3DQG) phase unwrapping algorithm and 3D fast phase unwrapping (3DFPU) algorithm are designed, programmed and applied in the 3D shape measurement of dynamic scenes. Simulated and actual experiments are conducted to compare the performance between the 3D algorithms for 3D wrapped phase in whole and their corresponding two-dimensional (2D) algorithms for 2D wrapped phase frame by frame. The results show that 3D spatial phase unwrapping (SPU) algorithms have higher unwrapping success rate in severely noisy regions and can overcome some discontinuous problems which is truly benefit for the accurate reconstruction of dynamic 3D.

Phase unwrapping based on adaptive image in-painting of fringe patterns in measuring gear tooth flanks by laser interferometry.

Phase unwrapping in regions of abnormal fringes remains an unresolved issue. In this paper, we present an approach that combines an image-inpainting strategy based on an adaptive window which is obtained according to the density and orientation of fringe patterns and a quality-guided algorithm for phase unwrapping. First, a threshold is set to a quality map to detect the target region. Second, the target region is filled with new phase values by the adaptive image-inpainting method. Then, a quality-guided phase unwrapping algorithm is applied to this newly generated wrapped phase map. Finally, postprocessing of the unwrapped result is performed. The method is validated through several simulation and experiments. The results demonstrate that the proposed algorithm is effective in the presence of abnormal fringes.

Optical method to quantify the evolution of whole-field stress in fractured coal subjected to uniaxial compressive loads

Understanding and quantitatively characterizing the hidden distribution and evolution of the whole-field stress in fractured coal is crucial for accurately predicting crack propagation and connection that affect the transport capability of coalbed methane in reservoirs during fracture stimulation. However, it is challenging to directly reveal and quantify the hidden stress field using traditional methods because of the difficulties associated with extracting and identifying the stress distribution around randomly distributed, discontinuous, irregular-geometry cracks as well as with fabricating a model with embedded cracks. This study presents an optical method to reveal and quantify the continuous evolutions of the whole-field principal stress difference and shear stress in fractured coal by combining three-dimensional (3D) printing technology and digital photoelasticity. 3D printing technology is used to replicate the transparent model of fractured coal. The ten-step phase-shifting method and quality-guided phase unwrapping algorithm in photoelasticity are used to estimate the whole field photoelastic parameters (isoclinic and isochromatic) in the fractured coal model. The comparison between experimental and numerical results is provided to further prove the efficacy of this method in handling the natural fractured coal structure. The effects of crack irregularity and discontinuity on the stress evolution in fractured coal are evaluated as well.

Experimental evaluation of the strain intensity factor at the inclusion tip using digital photoelasticity

Digital photoelasticity is used for the experimental evaluation of the strain intensity factor for a rigid line inclusion embedded in an elastic matrix. The multi-parameter stress field equations are derived using the Airy’s stress function approach. The ten-step phase shifting technique (PST) is used to obtain the whole field isochromatic and isoclinic data, and the adaptive quality-guided phase unwrapping (AQGPU) algorithm is used for unwrapping the phase map. An over-deterministic linear least squares approach is used to solve the multi-parameter stress field equations in an optimization framework to obtain the inclusion tip parameters and the actual inclusion tip location. The relations for strain intensity factor and stress intensity factor (SIF) with the parameters is presented. Photoelastic experiments are performed on two inclusion configurations where inclusion is kept along and inclined to the direction of loading. The obtained strain intensity factor is compared with the analytical solution, and a good match is observed.

Hierarchical quality-guided phase unwrapping algorithm.

A hierarchical quality-guided phase unwrapping algorithm in a shared memory environment is proposed. First, the wrapped phase is divided into regular blocks, and local wrap counts of every block are obtained by a quality-guided strategy. Then, the gradient of the block wrap counts of adjacent blocks and the quality of every block are defined by the boundary local wrap counts of every block. Each block's data can be regarded as an abstract phase point, and the quality-guided strategy can be used again to solve the block wrap counts of each block. Finally, the absolute wrap counts of each phase point are obtained by adding local wrap counts and corresponding block wrap counts, and then the final unwrapped phase is obtained. The performance of the proposed algorithm is verified through an unwrapping experiment performed on simulated data and the real interferometric synthetic aperture sonar wrapped phase in a shared memory environment. The results show that the proposed method greatly improves phase unwrapping efficiency while maintaining the correctness of unwrapped results.

PhaseNet: A Deep Convolutional Neural Network for Two-Dimensional Phase Unwrapping

Phase unwrapping is a crucial signal processing problem in several applications that aims to restore original phase from the wrapped phase. In this letter, we propose a novel framework for unwrapping the phase using deep fully convolutional neural network termed as PhaseNet. We reformulate the problem definition of directly obtaining continuous original phase as obtaining the wrap-count (integer jump of 2 $\pi$ ) at each pixel by semantic segmentation and this is accomplished through a suitable deep learning framework. The proposed architecture consists of an encoder network, a corresponding decoder network followed by a pixel-wise classification layer. The relationship between the absolute phase and the wrap-count is leveraged in generating abundant simulated data of several random shapes. This deliberates the network on learning continuity in wrapped phase maps rather than specific patterns in the training data. We compare the proposed framework with the widely adapted quality-guided phase unwrapping algorithm and also with the well-known MATLAB's unwrap function for varying noise levels. The proposed framework is found to be robust to noise and computationally fast. The results obtained highlight that deep convolutional neural network can indeed be effectively applied for phase unwrapping, and the proposed framework will hopefully pave the way for the development of a new set of deep learning based phase unwrapping methods.

Fast quality-guided phase unwrapping algorithm through a pruning strategy: applications in dynamic interferometry.

The quality-guided phase unwrapping algorithm is one of the most employed spatial algorithms due to its computational efficiency and robustness. It uses a quality map to guide the unwrapping process such that pixels are processed according to their quality values from highest to lowest. Several improvements have been proposed during the last few years with the purpose of using it in time-demanding applications. However, many of the proposals depend on the distribution of the values on the given quality map. In this paper, a novel pruning strategy based on a red-black tree data structure is proposed, whose complexity time is independent of the distribution of the given quality map. We take advantage of the partial ordering of the branches in a red-black tree together with a pruning strategy to speed up the unwrapping process. Experimental results, using real and simulated data, show that the complexity time of our proposal improves the existing quality-guide-based algorithms. Also, a series of interferometric patterns of a time-varying phase distribution experiment have been processed showing that our proposal can be used for real-time applications. The source code of the implemented algorithms is publicly available.

Linear least squares approach for evaluating crack tip fracture parameters using isochromatic and isoclinic data from digital photoelasticity

In this work, digital photoelasticity technique is used to estimate the crack tip fracture parameters for different crack configurations. Conventionally, only isochromatic data surrounding the crack tip is used for SIF estimation, but with the advent of digital photoelasticity, pixel-wise availability of both isoclinic and isochromatic data could be exploited for SIF estimation in a novel way. A linear least square approach is proposed to estimate the mixed-mode crack tip fracture parameters by solving the multi-parameter stress field equation. The stress intensity factor (SIF) is extracted from those estimated fracture parameters. The isochromatic and isoclinic data around the crack tip is estimated using the ten‐step phase shifting technique. To get the unwrapped data, the adaptive quality guided phase unwrapping algorithm (AQGPU) has been used. The mixed mode fracture parameters, especially SIF are estimated for specimen configurations like single edge notch (SEN), center crack and straight crack ahead of inclusion using the proposed algorithm. The experimental SIF values estimated using the proposed method are compared with analytical/finite element analysis (FEA) results, and are found to be in good agreement.

Phase unwrapping algorithm based on multi-frequency fringe projection and fringe background for fringe projection profilometry

A phase unwrapping algorithm specially designed for the phase-shifting fringe projection profilometry (FPP) is proposed. It combines a revised dual-frequency fringe projectionalgorithm and a proposed fringe background based quality guided phase unwrapping algorithm (FB-QGPUA). Phase demodulated from the high-frequency fringe patterns is partially unwrapped by that demodulated from the low-frequency ones. Then FB-QGPUA is adopted to further unwrap the partially unwrapped phase. Influences of the phase error on the measurement are researched. Strategy to select the fringe pitch is given. Experiments demonstrate that the proposed method is very robust and efficient.

Threshold automatic selection hybrid phase unwrapping algorithm for digital holographic microscopy

Conventional quality-guided (QG) phase unwrapping algorithm is hard to be applied to digital holographic microscopy because of the long execution time. In this paper, we present a threshold automatic selection hybrid phase unwrapping algorithm that combines the existing QG algorithm and the flood-filled (FF) algorithm to solve this problem. The original wrapped phase map is divided into high- and low-quality sub-maps by selecting a threshold automatically, and then the FF and QG unwrapping algorithms are used in each level to unwrap the phase, respectively. The feasibility of the proposed method is proved by experimental results, and the execution speed is shown to be much faster than that of the original QG unwrapping algorithm.

A Quality-Guided and Local Minimum Discontinuity Based Phase Unwrapping Algorithm for InSAR/InSAS Interferograms

Phase unwrapping is one of the key problems in reconstructing the digital elevation model of a scene from its interferometric synthetic aperture radar (InSAR) or interferometric synthetic aperture sonar (InSAS) data. In this letter, we propose a quality-guided and local minimum discontinuity based phase unwrapping algorithm, which enhances the precision of the unwrapped result by local minimum discontinuity optimization in low quality areas, and still keeps a high efficiency. The new algorithm can be divided into two steps. Firstly, the quality-guided phase unwrapping algorithm is performed on the original wrapped phase image, which helps to remove all the discontinuities caused by the wrapping operation quickly, but tends to spread the unwrapped errors in low quality areas. Secondly, the initial unwrapped result is divided into high and low quality areas according to its quality map, and the minimum discontinuity optimization process is performed in the low quality areas of the initial unwrapped result, which helps to remove the remaining improving loops defined as a loop with more positive jumps than negative ones. This prevents the unwrapped errors spreading from low quality areas to high quality areas and accelerates the optimization process by restricting the optimization place in low quality areas. Tests performed on InSAR and real InSAS data confirm the accuracy and efficiency of the proposed algorithm.

Image-inpainting and quality-guided phase unwrapping algorithm

For the wrapped phase map with regional abnormal fringes, a new phase unwrapping algorithm that combines the image-inpainting theory and the quality-guided phase unwrapping algorithm is proposed. First, by applying a threshold to the modulation map, the valid region (i.e., the interference region) is divided into the doubtful region (called the target region during the inpainting period) and the reasonable one (the source region). The wrapped phase of the doubtful region is thought to be unreliable, and the data are abandoned temporarily. Using the region-filling image-inpainting method, the blank target region is filled with new data, while nothing is changed in the source region. A new wrapped phase map is generated, and then it is unwrapped with the quality-guided phase unwrapping algorithm. Finally, a postprocessing operation is proposed for the final result. Experimental results have shown that the performance of the proposed algorithm is effective.

Complex-amplitude-based phase unwrapping method for digital holographic microscopy

Abstract A complex-amplitude-based phase unwrapping approach for digital holographic microscopy is proposed in this paper. A quality map is derived directly from the reconstructed complex amplitude distribution of object wave to evaluate noise influence and phase reliability in the wrapped phase image. Quality-guided phase unwrapping algorithm is then implemented with the quality map to retrieve continuous phase profile. Unwrapping errors caused by unreliable phase data are successfully suppressed. The effectiveness of this method is demonstrated with simulation and experimental results.

Quality-guided phase unwrapping algorithm based on reliability evaluation

For optical interferometry, a new quality-guided phase unwrapping algorithm based on the reliability evaluation of each pixel of the wrapped phase is proposed. First, the parameters used as quality measures in the past quality-guided algorithms are classified into the reliability measure and the quality measure, and the intensity of the object image belongs to the reliability measure. Then, by computing and applying a threshold to the intensity of the object image, the valid region (i.e., the interference region) is distinguished into the reliable region and the doubtful region. The wrapped phase in the reliable region is subsequently unwrapped by the way of multipaths integration, and different paths are guided by separate quality measures. Finally, starting from the reliable region, the doubtful region is unwrapped by the way that each path takes in the reliable region. Experimental results have shown that the proposed algorithm not only performs well, but also computes efficiently.

Corrections to “An Improved Quality-Guided Phase-Unwrapping Algorithm Based on Priority Queue” [Mar 11 364-368

In the above letter (ibid., vol. 8, no. 2, pp. 364-368, Mar. 2011), in the Abstract, a sentence is incorrect. The correct sentence is presented here.

An Improved Quality-Guided Phase-Unwrapping Algorithm Based on Priority Queue

Phase unwrapping is one of the key problems in reconstructing the elevation map of a scene from interferometric synthetic aperture radar or interferometric synthetic aperture sonar (InSAS) data. In this letter, an improved quality-guided phase-unwrapping algorithm is proposed, which depends on the quality value and its surrounding quality information to guide the path of unwrapping more accurately. In order to design highly efficient quality-guided algorithm, a guided map deduced from the quality map is introduced and taken as the new quality map which the quality-guided algorithm should completely depend on. A quantized quality-guided method is designed, which adopts the quantized new quality map and the priority queue designed to optimize the process of unwrapping. The quantized quality map establishes the relation between the quality values and the indexes of array, which can save the time of inserting one pixel into the priority queue according to its integral quality value. Priority queue keeps all the pixels by their quantized quality in a nondecreasing order by maintaining the doubly linked lists in an increasing order. An optimized strategy is used to accelerate the process of finding the pixel with the highest quality value in the priority queue. Tests performed on real InSAS data and simulated interferograms confirm the accuracy and efficiency of the proposed algorithm, and the improved algorithm is suitable for our real-time processing InSAS system.

Windowed Fourier filtered and quality guided phase unwrapping algorithm: on locally high-order polynomial phase

A windowed Fourier filtered and quality guided (WFF-QG) phase unwrapping algorithm was proposed recently [Appl. Opt. 47, 5420-5428 (2008)], based on the windowed Fourier transform [Appl. Opt. 47, 5408-5419 (2008)] where the phase is assumed to be locally quadric. We consider a locally higher order polynomial phase. After the phase is filtered and unwrapped by the WFF-QG, it is postprocessed by a congruence operation (CO), so that the unwrapped phase is congruent to the original wrapped phase. The unwrapped phase can now be assumed to be a locally high-order polynomial, and, consequently, least squares fitting (LSF) is proposed to suppress the noise. This postprocessing algorithm is abbreviated as CO-LSF. The CO-LSF is theoretically a reasonable choice to improve the WFF-QG results, especially when the noise is severe. This is because for severe noise, a large window is necessary for reliable phase extraction in the WFF-QG. However, this large window makes the quadric phase assumption less reasonable and leads to a large phase error. The CO-LSF thus helps to reduce the phase error by more reasonably assuming that the phase is a high-order polynomial. The polynomial order of 4 is suggested for the CO-LSF, as higher order polynomials do not give significant improvement to the WFF-QG. One disadvantage of the CO-LSF is that it is more sensitive to phase discontinuities than the WFF-QG.