An adaptive image denoising method based on local parameters optimization

In image denoising algorithms, the noise is handled by either modifying term-by-term, i.e., individual pixels or block-by-block, i.e., group of pixels, using suitable shrinkage factor and threshold function. The shrinkage factor is generally a function of threshold and some other characteristics of the neighbouring pixels of the pixel to be thresholded (denoised). The threshold is determined in terms of the noise variance present in the image and its size. The VisuShrink, SureShrink, and NeighShrink methods are important denoising methods that provide good results. The first two, i.e., VisuShrink and SureShrink methods follow term-by-term approach, i.e., modify the individual pixel and the third one, i.e., NeighShrink and its variants: ModiNeighShrink, IIDMWD, and IAWDMBMC, follow block-by-block approach, i.e., modify the pixels in groups, in order to remove the noise. The VisuShrink, SureShrink, and NeighShrink methods however do not give very good visual quality because they remove too many coefficients due to their high threshold values. In this paper, we propose an image denoising method that uses the local parameters of the neighbouring coefficients of the pixel to be denoised in the noisy image. In our method, we propose two new shrinkage factors and the threshold at each decomposition level, which lead to better visual quality. We also establish the relationship between both the shrinkage factors. We compare the performance of our method with that of the VisuShrink and NeighShrink including various variants. Simulation results show that our proposed method has high peak signal-to-noise ratio and good visual quality of the image as compared to the traditional methods: Weiner filter, VisuShrink, SureShrink, NeighBlock, NeighShrink, ModiNeighShrink, LAWML, IIDMWT, and IAWDMBNC methods.     

Modulo 2pi fringe orientation angle estimation by phase unwrapping with a regularized phase tracking algorithm

The fringe orientation angle provides useful information for many fringe-pattern-processing techniques. From a single normalized fringe pattern (background suppressed and modulation normalized), the fringe orientation angle can be obtained by computing the irradiance gradient and performing a further arctangent computation. Because of the 180 degrees ambiguity of the fringe direction, the orientation angle computed from the gradient of a single fringe pattern can be determined only modulo pi. Recently, several studies have shown that a reliable determination of the fringe orientation angle modulo 2pi is a key point for a robust demodulation of the phase from a single fringe pattern. We present an algorithm for the computation of the modulo 2pi fringe orientation angle by unwrapping the orientation angle obtained from the gradient computation with a regularized phase tracking method. Simulated as well as experimental results are presented.     

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.     

Image segmentation model based on adaptive adjustment of global and local information

In this article, an adaptive mixture model for image segmentation that synthesizes both global information and local information using a new adaptive balance function has been proposed. Given the variety of possible image characteristics that may have to be processed, the proposed model can adaptively adjust the weighting to drive curve evolution trends and states. In this way, the intensity information of weak boundaries and complex backgrounds can be extracted more precisely, thus enabling the model to produce better results for low‐contrast images and complex structures. In addition, a Gaussian filtering process has been added to the model to smooth and standardize the level set function, and a parameter has been introduced to speed up the curve evolution. A penalty term is also used to eliminate the need for complex re‐initialization procedures. Experimental results for various kinds of images efficiently demonstrate the good performance of the proposed model in terms of both speed and accuracy. © 2016 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 26, 179–187, 2016     

Quality-guided phase unwrapping technique: comparison of quality maps and guiding strategies

Quality-guided phase unwrapping is a widely used technique with different quality definitions and guiding strategies reported. It is thus necessary to do a detailed comparison of these approaches to choose the optimal quality map and guiding strategy. For quality maps, in the presence of noise, transform-based methods are found to be the best choice. However in the presence of discontinuities, phase unwrapping is itself unresolved and hence quality-guided phase unwrapping is not sufficient. For guiding strategies, classical, two-section, and stack-chain guiding strategies are chosen for comparison. If accuracy is the foremost criterion then the classical guiding strategy with a data structure of indexed interwoven linked list is best. If speed is of essence then the stack-chain guiding strategy is the one to use.     

Flexible error-reduction method for shape measurement by temporal phase unwrapping: phase averaging method

Temporal phase unwrapping is an important method for shape measurement in structured light projection. Its measurement errors mainly come from both the camera noise and nonlinearity. Analysis found that least-squares fitting cannot completely eliminate nonlinear errors, though it can significantly reduce the random errors. To further reduce the measurement errors of current temporal phase unwrapping algorithms, in this paper, we proposed a phase averaging method (PAM) in which an additional fringe sequence at the highest fringe density is employed in the process of data processing and the phase offset of each set of the four frames is carefully chosen according to the period of the phase nonlinear errors, based on fast classical temporal phase unwrapping algorithms. This method can decrease both the random errors and the systematic errors with statistical averaging. In addition, the length of the additional fringe sequence can be changed flexibly according to the precision of the measurement. Theoretical analysis and simulation experiment results showed the validity of the proposed method.     

Fast and robust three-dimensional best path phase unwrapping algorithm

What we believe to be a novel three-dimensional (3D) phase unwrapping algorithm is proposed to unwrap 3D wrapped-phase volumes. It depends on a quality map to unwrap the most reliable voxels first and the least reliable voxels last. The technique follows a discrete unwrapping path to perform the unwrapping process. The performance of this technique was tested on both simulated and real wrapped-phase maps. And it is found to be robust and fast compared with other 3D phase unwrapping algorithms.     

Network approaches to two-dimensional phase unwrapping: intractability and two new algorithms

Two-dimensional (2-D) phase unwrapping, that is, deducing unambiguous phase values from a 2-D array of values known only modulo 2pi, is a key step in interpreting data acquired with synthetic aperture radar interferometry. Noting the recent network formulation of the phase unwrapping problem, we apply here some well-established ideas of network theory to formalize the problem, analyze its complexity, and derive algorithms for its solution. It has been suggested that the objective of phase unwrapping should be to minimize the total number of places where unwrapped and wrapped phase gradients differ. Here we use network constructions to show that this so-called minimum L0-norm problem is NP-hard, or one that complexity theory suggests is impossible for efficient algorithms to solve exactly. Therefore we must instead find approximate solutions; we present two new algorithms for doing so. The first uses the network ideas of shortest paths and spanning trees to improve on the Goldstein et al. residue-cut algorithm [Radio Sci. 23, 713 (1988)]. Our improved algorithm is very fast, provides complete coverage, and allows user-defined weights. With our second algorithm, we extend the ideas of linear network flow problems to the nonlinear L0 case. This algorithm yields excellent approximations to the minimum L0 norm. Using interferometric data, we demonstrate that our algorithms are highly competitive with other existing algorithms in speed and accuracy, outperforming them in the cases presented here.     

Temporal phase unwrapping and its application in shearography systems

Temporal phase unwrapping is applied to a two-camera polarization phase-stepped system. A simple algorithm for the phase-change calculation is given, together with simulations, to indicate its validity and strength. This method can be applied directly for detection of phase changes as a function of time. It is proposed to use this method in a shearography setup. The phase distribution in the shearogram can then be obtained, without the standard 2pi ambiguities, by application of the required total shear in a number of smaller steps, provided that each step is small enough to be free from these 2pi phase steps.     

Temporal phase unwrapping: application to surface profiling of discontinuous objects

The recently proposed technique of temporal phase unwrapping has been used to analyze the phase maps from a projected-fringe phase-shifting surface profilometer. A sequence of maps is acquired while the fringe pitch is changed; the phase at each pixel is then unwrapped over time independently of the other pixels in the image to provide an absolute measure of surface height. The main advantage is that objects containing height discontinuities are profiled as easily as smooth ones. This contrasts with the conventional spatial phase-unwrapping approach for which the phase jump across a height discontinuity is indeterminate to an integral multiple of 2pi. The error in height is shown to decrease inversely with the number of phase maps used.     

Simultaneous wavenumber measurement and coherence detection using temporal phase unwrapping

Wavelength scanning interferometry and swept-source optical coherence tomography require accurate measurement of time-varying laser wavenumber changes. We describe here a method based on recording interferograms of multiple wedges to provide simultaneously high wavenumber resolution and immunity to the ambiguities caused by large wavenumber jumps. All the data required to compute a wavenumber shift are provided in a single image, thereby allowing dynamic wavenumber monitoring. In addition, loss of coherence of the laser light is detected automatically. The paper gives details of the analysis algorithms that are based on phase detection by a two-dimensional Fourier transform method followed by temporal phase unwrapping and correction for optical dispersion in the wedges. A simple but robust method to determine the wedge thicknesses, which allows the use of low-cost optical components, is also described. The method is illustrated with experimental data from a Ti:sapphire tunable laser, including independent wavenumber measurements with a commercial wavemeter. A root mean square (rms) difference in measured wavenumber shift between the two of ~4 m?1 has been achieved, equivalent to an rms wavelength shift error of ~0.4 pm.     

Reliable phase unwrapping algorithm based on rotational and direct compensators

Phase unwrapping still plays an important role in many data-processing chains based on phase information. Here, we introduce a new phase unwrapping approach for noisy wrapped phase maps of continuous objects to improve the accuracy and computational time requirements of phase unwrapping using a rotational compensator (RC) method. The proposed algorithm is based on compensating the singularity of discontinuity sources. It uses direct compensation for adjoining singular point (SP) pairs and uses RC for other SP pairs. The performance of the proposed method is tested through both simulated and real wrapped phase data. The proposed algorithm is faster than the original algorithm with the RC and has proved efficiency compared to other phase unwrapping methods.     

Discrete Green's methods and their application to two-dimensional phase unwrapping

A fully self-contained discrete framework with discrete equivalents of Stokes's, Gauss's, and Green's theorems is presented. The formulation is analogous to that of continuous operators, but totally discrete in nature, and the exact relationships derived are shown to hold provided that a set of predefined rules is followed in building discrete contours and domains. The method allows for an analytical rigor that is not guaranteed if one translates the classical continuous formulations onto a discretized approximated framework. We clarify several issues related to the use of discrete operators, which may play a crucial role in specific applications such as the two-dimensional phase-unwrapping problem, chosen as our main application example, and we show that reconstruction on irregular domains and/or in the presence of undersampling and noise is better formulated in the discrete framework than in the continuous domain.     

Robust, simple, and fast algorithm for phase unwrapping

Phase unwrapping has been and still is a cumbersome concern that involves the resolution of several different problems. When dealing with two-dimensional phase unwrapping in fringe analysis, the final objective is, in many cases, the realization of that analysis in real time. Many algorithms have been developed to carry out the unwrapping process, with some giving satisfactory results even when high levels of noise are present in the image. However, these algorithms are often time consuming and far removed from the goal of real-time fringe analysis. A new approach to the construction of a simple and fast algorithm for two-dimensional unwrapping that has considerable potential for parallel implementation is presented.     

Object-image-based method to construct an unweighted quality map for phase extraction and phase unwrapping

A method to construct an unweighted quality map for phase extraction and phase unwrapping is proposed, based on an object image pattern. The object image pattern must be recorded under the same conditions as that of the corresponding interference patterns, except that the lights coming from the reference arm of the interferometer are hidden. An unweighted quality map that can represent the valid and invalid regions in the interference patterns is completed successfully, based on two factors: the fact that the object region in the object image pattern is homologous with the valid region (i.e., the interference region) in the interference patterns, and on distinguishing between the object and background regions in the object image pattern using neighbor window threshold filtering and fitting the boundary of the object image. The application of the proposed method to the real measurement shows its feasibility and correctness. This paper might provide an alternative method for constructing an unweighted quality map for phase extraction and phase unwrapping.     

Phase reconstruction and unwrapping from holographic interferograms of partially absorbent phase objects

A method for automated phase reconstruction from holographic interferograms of nonideal phase objects based on a two-dimensional Fourier transform is described. In particular, the problem of phase unwrapping is solved because earlier techniques are inappropriate for the phase unwrapping from interferograms of partially absorbent objects. A noise-level-dependent criterion for the binary mask that defines the unwrapping path for the flood algorithm is derived. The method shows high noise immunity, and the result is reliable provided that the true phase is free of discontinuities. The phase distribution in the outmasked regions is estimated by a linear least-squares fit to the surrounding unwrapped pixels.     

Phase and amplitude reconstruction from a single carrier-frequency interferogram without phase unwrapping

A rapid algorithm for phase and amplitude reconstruction from a single spatial-carrier interferogram is proposed by bringing a phase-shifting mechanism into reconstruction of a carrier-frequency interferogram. The algorithm reconstructs phase through directly obtaining and integrating its real-value derivatives, avoiding a phase unwrapping process. The proposed method is rapid and easy to implement and is made insensitive to the profile of the interferogram boundaries by choosing a suitable integrating path. Moreover, the algorithm can also be used to reconstruct the amplitude of the object wave expediently without retrieving the phase profile in advance. The feasibility of this algorithm is demonstrated by both numerical simulation and experiment.     

Residue vector, an approach to branch-cut placement in phase unwrapping: theoretical study

What we believe to be a novel technique of branch-cut placement in the phase unwrapping is proposed. This approach is based on what we named residue vector, which is generated by a residue in a wrapped phase map and has an orientation that points out toward the balancing residue of opposite polarity. The residue vector can be used to guide the manner in which branch cuts are placed in phase unwrapping. Also, residue vector can be used for the determination of the weighting values used in different existing phase unwrapping methods such as minimum cost flow and least squares. The theoretical foundations of the residue-vector method are presented, and a branch-cut method using its information is developed and implemented. A general comparison is made between the residue-vector map and other existing quality maps.     

Phase recovering without phase unwrapping in phase-shifting interferometry by cubic and average interpolation

A simple phase estimation employing cubic and average interpolations to solve the oversampling problem in smooth modulated phase images is described. In the context of a general phase-shifting process, without phase-unwrapping, the modulated phase images are employed to recover wavefront shapes with high fringe density. The problem of the phase reconstruction by line integration of its gradient requires a form appropriate to the calculation of partial derivatives, especially when the phase to recover has higher-order aberration values. This is achieved by oversampling the modulated phase images, and many interpolations can be implemented. Here an oversampling procedure based on the analysis of a quadratic cost functional for phase recovery, in a particular case, is proposed.