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Fringe projection profilometry (FPP) has become one of the most popular 3D information acquisition techniques being developed over the past three decades. In FPP, phase unwrapping is a critical step in acquiring the correspondence information for 3D reconstruction. Unlike traditional FPP which uses methods such as temporal phase unwrapping, fast FPP measurement systems require phase unwrapping of single phase map probably with discontinuous objects. Phase unwrapping in fast FPP such brings three difficulties, the separation of discontinuous wrapped phases, the unwrapping of each wrapped phase and the linking of the discontinuous phase segments. During FPP measurement of multiple objects, their corresponding phase maps may locate in different part of the measurement image or side by side. Object separation based on the modulation values along could not well identify the discontinuous boundaries. In this paper, the object separation based on modulation is adapted first to remove the background and separate isolated wrapped phases. For each isolated wrapped phase, local orientation coherence based discontinuous phase separation is further used to identify the existence of discontinuous boundaries. After the segmentation, spatial unwrapping method is applied to each wrapped phase segments. In the last, the phase segments are linked using a base phase map. Experimental results show that our algorithm works well for multiple and overlapping object measurements.

Image analysis with ultra-high-speed camera and two dimensional dynamic numerical analysis are applied to study the rapid unstable growth of wing crack under the uniaxial compression. Growing wing crack terminates and restarts its unstable rapid growth in some cases. Such a termination and restart behavior of the growing crack is studied through the experiment and numerical analysis in this work. First, rectangle transparent specimen, including the initial crack inclined to the compressive axis, is subjected to the uniaxial compression till the wing cracks start unstable rapid growth from both ends of the initial crack. Images of growing cracks and those of stress distribution, visualized as the photo-elastic fringe pattern, are captured by the high speed camera with the frame rate of 500k frames per second. The behavior of growing crack and the change in the stress field due to the crack growth are discussed through the captured images. Next, two dimensional dynamic numerical analysis is carried out. PDS-FEM (Particle Discretization Scheme), which allows the discontinuity of the displacement in the continuous analytical domain, is combined with the central difference time integration scheme to simulate the rapid unstable growth of the wing crack dynamically. The accuracy of the proposed simulation is discussed through the comparison with the images, captured by the experiment.

A hologram recording technique, generally called as “wavefront printer”, has been proposed by several research groups for static three-dimensional (3D) image printing. Because the pixel number of current spatial light modulators (SLMs) is not enough to reconstruct the entire wavefront in recording process, typically, hologram data is divided into a set of subhologram data and each wavefront is recorded sequentially as a small sub-hologram cell in tiling manner by using X-Y motorized stage. However since previous works of wavefront printer do not optimize the cell size, the reconstructed images were degraded by obtrusive split line due to visible cell size caused by too large cell size for human eyesight, or by diffraction effect due to discontinuity of phase distribution caused by too small cell size. In this paper, we introduce overlapping recording approach of sub-holograms to achieve both conditions: enough smallness of apparent cell size to make cells invisible and enough largeness of recording cell size to suppress diffraction effect by keeping the phase continuity of reconstructed wavefront. By considering observing condition and optimization of the amount of overlapping and cell size, in the experiment, the proposed approach showed higher quality 3D image reconstruction while the conventional approach suffered visible split lines and cells.

We illustrate the design of acoustic metasurfaces based on geometric tapers and embedded in thin-plate structures. The metasurface is an engineered discontinuity that enables anomalous refraction of guided wave modes according to the Generalized Snell’s Law. Locally-resonant geometric torus-like tapers are designed in order to achieve metasurfaces having discrete phase-shift profiles that enable a high level of control of refraction of the wavefronts. Results of numerical simulations show that anomalous refraction can be achieved on transmitted anti-symmetric modes (A0) either when using a symmetric (S0) or anti-symmetric (A0) incident wave, where the former case clearly involves mode conversion mechanisms.

Image inpainting is to restore a damaged image with missing information – a fundamental problem and a hot research area in image processing. Many approaches, both geometry oriented and texture oriented, have been proposed on inpainting such as total variation (TV), Criminisi algorithm, etc. However, these approaches suffer from either limitations such as only suitable for small areas (cracks), staircase effect (discontinuity), or inefficient (time-consuming) to search the best matched patch (for filling-in). In this paper we propose a novel approach based on partial differential equation (PDE) and isophotes direction, named as Isophotes-TV-H-1. A corrupted image is first decomposed into two parts: the cartoon (smooth parts and edges of the image) and the texture. The cartoon part is inpainted through Isophotes- TV-H-1 while the texture part is done by an enhanced Criminisi algorithm which reduces the searching time for match and gives more reasonable match patches. The results of experiments on several images have demonstrated that, compared to existing methods, the proposed solution can recover the texture (of the damaged region) better, suppress error propagation and solve the problem of intensity discontinuity.

IRST (Infrared Search and Track) has been applied to many military or civil fields such as precise guidance, aerospace, early warning. As a key technique, small target detection based on infrared image plays an important role. However, infrared targets have their own characteristics, such as target size variation, which make the detection work quite difficult. In practical application, the target size may vary due to many reasons, such as optic angle of sensors, imaging distance, environment and so on. For conventional detection methods, it is difficult to detect such size-varying targets, especially when the backgrounds have strong clutters. This paper presents a novel method to detect size-varying infrared targets in a cluttered background. It is easy to find that the target region is salient in infrared images. It means that target region have a signature of discontinuity with its neighboring regions and concentrates in a relatively small region, which can be considered as a homogeneous compact region, and the background is consistent with its neighboring regions. Motivated by the saliency feature and gradient feature, we introduce minimum target intensity (MTI) to measure the dissimilarity between different scales, and use mean gradient to restrict the target scale in a reasonable range. They are integrated to be multiscale MTI filter. The proposed detection method is designed based on multiscale MTI filter. Firstly, salient region is got by morphological low-pass filtering, where the potential target exists in. Secondly, the candidate target regions are extracted by multiscale minimum target intensity filter, which can effectively give the optimal target size. At last, signal-to-clutter ratio (SCR) is used to segment targets, which is computed based on optimal scale of candidate targets. The experimental results indicate that the proposed method can achieve both higher detection precision and robustness in complex background.

The FDL method makes use of Fibonacci, Dual and Lucas numbers and has shown considerable success in predicting earthquake events locally as well as globally. Predicting the location of the epicenter of an earthquake is one difficult challenge the other being the timing and magnitude. One technique for predicting the onset of earthquakes is the use of cycles, and the discovery of periodicity. Part of this category is the reported FDL method. The basis of the reported FDL method is the creation of FDL future dates based on the onset date of significant earthquakes. The assumption being that each occurred earthquake discontinuity can be thought of as a generating source of FDL time series The connection between past earthquakes and future earthquakes based on FDL numbers has also been reported with sample earthquakes since 1900. Using clustering methods it has been shown that significant earthquakes (

Non-destructive testing methods based on ultrasonic waves are one of the most popular methods for damage detection in structures. Of these ultrasonic waves Lamb waves are of particular interest for the inspection of large structures for various reasons. Therefore scattering of Lamb waves from flaws has generated a considerable amount of research over last couple of decades. Most of the work has been done using computational tools like Finite Element Methods and experimental technique. In this paper an analytical approach is presented to develop a fundamental understanding of the scattering of Lamb waves from geometric discontinuities in 2 dimensions. We have considered simplest of all geometric discontinuity – a step, as this fundamental understanding can easily be extended to corrosion or crack.

During model-based image dehazing, the role of the accuracy of transmission estimation is crucial, which has a decisive effect on the final result. Considering that an ideal transmission map must be smooth, edge-preserving and free of redundant false details, a fusion-based dark channel prior (DCP) dehazing algorithm is presented in this paper. On the basis of DCP, a pixel-wise and a patch-wise transmission maps are obtained. Then an L0 smoothing filter and a large scale Gaussian filter are applied to them respectively. Finally, a much more accurate refined transmission map is attained through fusion and a haze-free image is restored using the atmosphere degradation model. Furthermore, a novel scheme for setting the lower bound of transmission adaptively is also put forward. Experiments demonstrate a better and faster dehazing capability over original DCP algorithm and state-of-the-art dehazing methods, especially in suppressing halo artifacts, restoring details and coping with the haze existing in small-scale areas of depth discontinuity occluded by foreground..

A method of stereo matching which is based on color image segmentation and cross adaptive window has been used to solve the problems of matching imprecision in depth discontinuity regions and low texture regions. This article first produces the matching cost based on color segmentation region by segmenting color image and the one based on cross adaptive window which makes use of color similarity, and then integrates the two to form the combined matching cost. At last it uses the fast searching method of optical parallax to narrow the matching range and then raise the efficiency rate. The result of this experiment can improve the matching accuracy in depth discontinuity regions and low texture regions and raise the matching speed.

Image interpolation methods at arbitrary view positions have become quite important due to the development of threedimensional multi-view image display devices. Accurate depth information is required for natural image generation. Over the past several decades, a variety of stereo-image-based depth estimation methods have been developed to obtain high-quality depth data. However, obtaining accurate depth information still remains problematic due to difficult correspondence matching in image occlusion regions. In particular, for the discontinuous depth edge region, unclear color values exist, which lead to ineffective of corresponding matching. Thus, we propose a discontinuity preserving depth estimation method to solve the problem. The distance transform (DT) calculates the distance to the closest edge for each pixel of the input image. By controlling the color weighting term using DT values of stereo images, we carry out better correspondence matching in discontinuous regions. Experimental results indicate that the proposed method outperforms other methods. Visual comparison of the experimental results demonstrates that the proposed stereo-imagebased depth estimation method improves the quality of the depth map in discontinuous edge regions.

2D phase screen methods have been frequently applied to estimate atmospheric turbulence in free space optic communication and imaging systems. In situations where turbulence is “strong” enough to cause severe discontinuity of the wavefront (small Fried coherence length), the transmitted optic signal behaves more like “rays” rather than “waves”. However, to achieve accurate simulation results through ray modeling requires both a high density of rays and a large number of eddies. Moreover, their complicated interactions require significant computational resources. Thus, we introduce a 3D ray model based on simple characteristics of turbulent eddies regardless of their particular geometry. The observed breakup of a beam wave into patches at a receiver and the theoretical description indicates that rays passing through the same sequence of turbulent eddies show “group” behavior whose wavefront can still be regarded as continuous. Thus, in our approach, we have divided the curved trajectory of rays into finite line segments and intuitively related their redirections to the refractive property of large turbulent eddies. As a result, our proposed treatment gives a quick and effective high-density ray simulation of a turbulent channel which only requires knowledge of the magnitude of the refractive index deviations. And our method points out a potential correction in reducing equivalent C n 2 by applying adaptive optics. This treatment also shows the possibility of extending 2D phase screen simulations into more general 3D treatments.

Atmospheric turbulence has a significant impact on the quality of a laser beam propagating through the atmosphere over long distances. Turbulence causes intensity scintillation and beam wander from propagation through turbulent eddies of varying sizes and refractive index. This can severely impair the operation of target designation and Free-Space Optical (FSO) communications systems. In addition, experimenting on an FSO communication system is rather tedious and difficult. The interferences of plentiful elements affect the result and cause the experimental outcomes to have bigger error variance margins than they are supposed to have. Especially when we go into the stronger turbulence regimes the simulation and analysis of the turbulence induced beams require delicate attention. We propose a new geometrical model to assess the phase shift of a laser beam propagating through turbulence. The atmosphere along the laser beam propagation path will be modeled as a spatial distribution of spherical bubbles with refractive index discontinuity calculated from a Gaussian distribution with the mean value being the index of air. For each statistical representation of the atmosphere, the path of rays will be analyzed using geometrical optics. These Monte Carlo techniques will assess the phase shift as a summation of the phases that arrive at the same point at the receiver. Accordingly, there would be dark and bright spots at the receiver that give an idea regarding the intensity pattern without having to solve the wave equation. The Monte Carlo analysis will be compared with the predictions of wave theory.

Currently simulating on laser propagation in atmosphere usually need to deal with beam in strong turbulence, which may lose a part of information via Fourier Transform to simulate the transmission, makes the phase of beam as a 2-D array wrap by 2π . An effective unwrapping algorithm is needed for continuing result and faster calculation. The unwrapping algorithms in atmospheric propagation are similar to the unwrapping algorithm in radar or 3-D surface rebuilding, but not the same. In this article, three classic unwrapping algorithms: the block least squares (BLS), mask-cut (MCUT), and the Flynn’s minimal discontinuity algorithm (FMD) are tried in wave-front reconstruction simulation. Each of those algorithms are tested 100 times in 6 same conditions, including low(64x64), medium(128x128), and high(256x256) resolution phase array, with and without noises. Compared the results, the conclusions are delivered as follows. The BLS-based algorithm is the fastest, and the result is acceptable in low resolution environment without noise. The MCUT are higher in accuracy, though they are slower with the array resolution increased, and it is sensitive to noise, resulted in large area errors. Flynn’s algorithm has the better accuracy, and it occupies large memory in calculation. After all, the article delivered a new algorithm that based on Active on Vertex (AOV) Network, to build a logical graph to cut the search space then find minimal discontinuity solution. The AOV is faster than MCUT in dealing with high resolution phase arrays, and better accuracy as FMD that has been tested.

Windowed Fourier ridges algorithm can provide a quality map to assist the quality-guided phase unwrapping. Its performance for discontinuous phase maps is investigated in this paper, where the influence of window size in the algorithm is examined. Three discontinuous phase boundaries, straight, curved, and fused, are tested for both noiseless and noisy situations. Encouraging results are observed. Small window size can be used for higher boundary detection accuracy and can be enlarged if noise is heavy and/or the discontinuities are not obvious in a small area.

The paper presents a method to locate discontinuities in form of transversal cracks in beams, based on vibration measurements. Patterns characterizing frequency changes of the first ten weak-axis bending vibration modes are determined for all possible locations on the structure, using a relation contrived by the authors. It base on the correlation between the strain energy stored in a segment of the beam, which is proportional with the square of the mode shape curvature of the considered vibration mode at that location, and the frequency change for this mode by the occurrence of a discontinuity on that segment. The patters consist from a series of ten values representing the normalized relative frequency shifts for the first ten vibration modes. For a structure similarly supported, by continuous or periodical measurements, potential frequency changes can be detected. By processing these data the so-called damage location index for that crack is found out, also as a series of ten values representing the relative frequency shifts of the ten vibration modes. To precise locate the crack a pattern matching method involving the database with all possible patterns and the damage location index is used. Knowing the location, it is easy to determine by analytic calculus the crack depth. The method is easy to be used, provide accurate results, demands modest computational effort and has the advantage that the measurements may be carried out in situ with rather simple equipment. The method was validated by experiments.

In this paper, a variational method for motion segmentation has been proposed, which is realized by first estimate discontinuity-preserving optical flow field and then segmenting. Specifically, the complementarity between estimation and segmentation was emphasized, so two main improvements were presented: firstly, a segmentation-oriented diffusion tensor has been suggested in the optical flow model, which combines the image and flow information and determine the boundaries more effectively; Secondly, according to the characteristic of vector field, a motion segmentation model with considerations of both motion boundaries and region information were established. The results were illustrated with examples of sequence images which show the usefulness of the proposed approach for various problems.© (2012) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.

Because of aircraft vibration, pixel discontinuity (blank pixels) occurs frequently in ortho-images when using a top-down approach and a nearest neighboring resampling method for pushbroom images. In this paper we propose a scheme to handle the pixel discontinuity. The pixel discontinuity is induced by the attitude variation in pitch and heading of an airplane. The deviation of pixel locations needs to be analyzed first to check if the proposed scheme is applicable. We use a linear CCD imager installed on a stabilizer to filter out the high frequency noise in an airplane for image acquisition. This scheme is suitable since the angular rates of the pitch and heading are both within ±0.7°/sec statistically and the deviation of the pixel locations is less than 1.0 pixel. The proposed scheme includes the following steps: (1) Derive the pixel locations of ortho-images using a top-down approach. Then allocate the pixel values to its 4 neighboring grids by an inverse bilinear interpolation based on their weighted factors in ortho-images. (2) After completing the ortho-rectification of full images, perform the dynamic range adjustment on the ortho-images according to the maximum pixel value of raw images and ortho-images. After applying the proposed scheme, we find that the pixel discontinuity is removed and the image quality is improved substantially. The difference of pixel value between raw images and ortho-images is also presented at regions with low, middle and high radiance to evaluate the proposed scheme quantitatively.

The angle arc method is proposed firstly to analyse the transmission line angle problem of physics. Linear segment approach is used to deal with boundary integral equation. With this method, nodes on the angle location take on discontinuity boundary condition is solved ,which result in solution is difficult. A general computer program based on angle arc method of the linear boundary element method(LBEM) is programed,and several represented computational examples are given to validate the method. The calculation results are well in agreement with that of the previous published data. It has been shown that this method is provided with a great deal of merits such as simple operation,convenient calculation and can valid to overcome the difficulty in angle problem, so it will have fine general availability.

This paper describes general framework of extraction of image straight-line segments based on the integration of intensity discontinuity and edge continuity in digital image. First, multiple "edge contours" are traced out from digital image by implementing classic LOG algorithm and contour tracing principle. In this step, Zero-Cross points are detected without implementing traditional 'edge labeling' procedure and thus, the continuity between adjacent edge points are maintained for the convenience of edge linking and can take advantage of contour tracing principle; After that, Houghbased heuristic linking algorithm is developed to extract initial straight-line segments from "edge contour" respectively. In this step, important prior knowledge, e.g., "seed" point and direction of straight-line segments, is deduced from Hough transformation and based on the knowledge, possible straight-line segments contained in each "edge contour" are extracted through heuristic linking via adjacent continuity again; Finally, initial straight-line segments are testified and improved with Least Squares Template Matching (LSTM) technique by estimating the similarity of intensity distribution between initial straight-line segment and its ideal intensity template. The experiment of extracting straight-line segments from aerial or ground image respectively, for building 3D reconstruction demonstrates that the proposed approach is robust and effective. Contributions are concluded as well.

We present a terahertz two dimensional phase imaging method with multiwavelength. This novel approach can image object with larger optical length compared to using the largest wavelength in the terahertz spectrum and does not involve the usual phase unwrapping in the detection of phase discontinuity. Furthermore, this technique can significantly decreases the background noise and allows one to resolve very fine structures for non-destructive detection. The validity of this new method can be demonstrated by processing the terahertz raster-scan two-dimensional(2D) image data of a polyethylene wedge and a piece of foam with a rectangle groove. The measurements show that the multiwavelength phase imaging is a straightforward and efficient phase data processing method in terahertz imaging application.

Full acoustic wavefield data were acquired from an aluminum plate with various structural discontinuities and artificial defects using an air-coupled transducer mounted on a scanning stage. Piezoelectric transducers permanently mounted on the specimen were used as wave sources. These source transducers were elements of a permanently attached sparse array. A time series of wavefield images clearly shows details of guided waves as they propagate outward from the source, reflect from specimen boundaries, and scatter from discontinuities within the structure. Distinct S 0 and A 0 Lamb wave modes are directly visible on constant time snapshots of the captured wavefield. However, the waves propagating outward from the source, and waves reflected from boundaries, obscure the weaker waves that are scattered from defects. To facilitate analysis of weaker scattered waves, source waves are removed from the full wavefield data using both time and frequency domain methods. The effectiveness of each method is evaluated in the wavenumber-wavenumber domain and results are fused to obtain images of scattered wavefields. The method is demonstrated on a through hole, to which a notch is added to simulate a crack. The angular dependence of the scattered wavefield is experimentally determined for source waves incident on the notch from two directions, one toward the side of the notch and the other toward the end of the notch.

Two-dimensional phase unwrapping method is important in a great number of applications. Flynn's minimum discontinuity phase unwrapping algorithm can be used to solve many different kinds of phase unwrapping problems successfully, but its main drawback is that, since it takes the whole wrapped phase image as the scanning areas, it requires a large amount of computations and has low efficiency in searching for the phase's discontinuity within the improving loop search area. To overcome this drawback, a novel minimum discontinuity phase unwrapping algorithm using pretreatment and edge detection is proposed. In the new algorithm, a pretreatment operation is carried out on the wrapped phase image to identify the isolated noisy pixels and exclude them from the search areas. Then, the phase's discontinuity areas within wrapped phase image are detected based on edge detection techniques and taken as the improving loop search areas. By these means, the efficiency of the new minimum discontinuity phase unwrapping algorithm is significantly improved because the required scanning range is cut down to a large extent. This new algorithm is described in detail and tested by using a noisy IFSAR experimental wrapped phase image. Unwrapped results make it clear that the new algorithm works very well and is more effectively than the Flynn's minimum discontinuity algorithm.

Phase unwrapping is the task of recovering the true phase values, given the wrapped phase values in an image. Flynn's minimum discontinuity phase unwrapping algorithm can deal with many different kinds of phase unwrapping problems successfully. However, since it takes the whole wrapped phase image as the improving loop search areas, Flynn's algorithm has low efficiency in searching for the phase's discontinuity. To overcome this drawback, a new minimum discontinuity phase unwrapping algorithm based on tabu search is proposed in this paper. In the proposed algorithm, the nodes of the wrapped image are divided into different N levels according to the corresponding quality of the wrapped image and the nodes with high levels are added into tabu list. In the iteration process of improving loops search, the tabu list is updated according to the aspiration criterion to allow the search areas extend to nodes with high levels. By this means, it searches the highest probability nodes belonging to paths of improving loops first and the lowest probability nodes last. As a result, it significantly improves the efficiency of the algorithm. The proposed algorithm is described in detail and verified by use of an experimental wrapped phase image with noise and undersampling. Unwrapped results show that the proposed algorithm works well and is more effectively than the Flynn's minimum discontinuity algorithm.

Isoclinic parameter is one of the important parameters in (digital) photoelasticity. This paper presents a comparative study of two phase unwrapping methods for the parameter. The two phase unwrapping methods are a line-wise method and a semi-region-wise method. The paper focuses on the way that how the methods handle the wrapped isoclinic map(s), which is used to start unwrapping, having the edge-cut line and non-edge-cut line in the final or unwrapped isoclinic map. The edge-cut line and non-edge-cut line are the line of isoclinic jumps that link the points of discontinuity (isotropic points) with some points locating at the boundaries and inside the isoclinic map, respectively. For the evaluation, three models, the circular disk and ring under diametral compression and circular disk under three radial loads, were used. The comparative results show that the semi region-wise method is superior to the line wise method. Keywords: Digital photoelasticity, isoclinic parameter, line-wise phase unwrapping, semi region-wise phase unwrapping

We present a new color image segmentation method that combined texture measures and the JSEG (J measure based JSEGmentation) algorithm. In particular, two major contributions are set forth in this paper. (1) The two measures defined in JSEG and the Laws texture energy is discussed respectively and then we find that the over-segmentation problem of JSEG could be attributed partly to the absence of color discontinuity in the J measure. (2) A new measure is proposed by integrating the Laws texture energy measures into the J measure, on which our segmentation method is based. The new segmentation method taking account of both textural homogeneity and color discontinuity in local regions can be used to detect proper edges at the boundaries of shadows and highlights. Performance improvement due to the proposed modification was demonstrated on a variety of real color images.

Common image edge detectors identify a mixture of image discontinuities caused by a local change of illumination, texture or geometry. This document describes a method to separate depth-edges as a special instance of geometry edges from all other edges in a single image, without a complicated sensor. A single color camera and a red, green and blue light is used for scene illumination. Color shadows produced by the active illumination provide discriminative features to detect depth-edges. Experimental results are used to demonstrate the discriminative power of the proposed method and the performance of the depth-edge detection has been studied analytically for different illumination conditions.

Three-dimensional edge measurement is critical in many applications such as blade manufacturing due to the stringent requirements on aerodynamic performance of blades. Optical metrology techniques provide very good tools in terms of speed and accuracy, but face some challenges as well, such as discontinuity, irregularity, and size variation in the edge shape. This paper presents several methods that include stereovision techniques to capture a sharp edge and phase-shifting to capture an edge profile of a blunt edge. For sharp edge measurement with stereovision, multiple cameras are used to view the edge from different directions. Then the captured images are processed to obtain the point cloud of the edge. For blunt edge measurement, a phase-shifting method is applied. After the edge profile is obtained, all edge information can be extracted. In this paper, different illumination methods are discussed and different edges are measured. Experimental data shows that these methods are practical in obtaining accurate edge or edge profile.

Traditional sinusoidal phase-shifting algorithms involve the calculation of an arctangent function to obtain the phase, which results in slow measurement speed. This paper presents a novel high-speed two-step triangular phase-shifting approach for 3-D object measurement. In the proposed method, a triangular gray-level-coded pattern is used for the projection. Only two triangular patterns, which are phase-shifted by 180 degrees or half of the pitch, are needed to reconstruct the 3-D object. A triangular-shape intensity-ratio distribution is obtained by calculation of the two captured triangular patterns. Removing the triangular shape of the intensity ratio over each pattern pitch generates a wrapped intensity-ratio distribution. The unwrapped intensity-ratio distribution is obtained by removing the discontinuity of the wrapped image with a modified unwrapping method commonly used in the sinusoidal phase-shifting method. An intensity ratio-to-height conversion algorithm, which is based on the traditional phase-to-height conversion algorithm in the sinusoidal phase-shifting method, is used to reconstruct the 3-D surface coordinates of the object. Compared with the sinusoidal and trapezoidal phase shifting methods, the processing speed is faster with similar resolution. This method therefore has the potential for real-time 3-D object measurement. This has applications in inspection tasks, mobile-robot navigation and 3-D surface modeling.

We investigated analytically and numerically the occurrence of modulation instability in fibers with periodic changes both in dispersion and gain. Previously, it has been known that the modulation instability is suppressed in dispersion managed solitons where dispersion is managed in such a way that the local dispersion alternates between the normal and the anomalous regimes. In this work, we enhanced the advantage of the dispersion management scheme by additionally introducing proper gain/loss profiles in fibers. The gain/loss profile is given by Γ(z)=0.5/D(z)*(dD/dz), where D(z) represents the dispersion profile. The fundamental gain spectrum of the modulation instability in the dispersion and gain managed fibers have been derived analytically and confirmed by numerical calculation. Our investigation reveals that in the dispersion and gain fibers the modulation instabilities are always much more suppressed compared to the case that only dispersion managed. In practical dispersion management schemes, dispersion profiles show discontinuity, and thus, the corresponding gain/loss profiles tend to finite. In these cases, the gain/loss profiles were approximated by lumped gains/losses of finite values. Our numerical calculations confirm that this approximation also works well.

Local Spherical Interface Approximation (LSIA) for modelling the propagation of electromagnetic wave fields through analog interfaces is introduced. The method belongs to a class of Local Elementary Interface Approximation (LEIA) in which the propagation is modelled by decomposing the field into local elementary fields. In the method introduced here both the phase-distribution of the field and the boundary of discontinuity are assumed to be locally spherical, which enables the use of Coddington's equations in the determination of the reflected and transmitted fields. The amplitude reflection and transmission is treated with the help of the intensity law of geometrical optics and the energy conservation law. Convergence comparison between LSIA and Local Plane Interface Approximation (LPIA) is performed for a sinusoidal diffraction grating. The accuracy of the method is illustrated with a numerical example.

To allow multiple viewers to see the correct perspective and to provide a single viewer with motion parallax cues during head movement, more than two views are needed. Since it is prohibitive to acquire, process, and transmit a continuum of views, it would be preferable to acquire only minimal set of views and to generate intermediate images by using the estimated disparities. For high quality of the generated image, the first, we propose how to generate the intermediate images using multi-resolution and irregular-quadtree decomposition. Irregular-quadtree decomposition is aligned at the object boundary which is the disparity discontinuity. By finding the peak over the absolute values of the high pass filtered output that is applied to the row and column average, the horizontal and vertical dividing locations of the block are computed. The second, regions of occlusion are decided by similarity comparisons among the matched block alternatives, then filled with the pixels of left or right image by the principles we proposed. Finally, the images at arbitrary viewpoints of generated and yielding a 31.1 dB PSNR at middle location between both viewpoints.

We study into the ways of eliminating the interferogram fringe discontinuities and obtaining the connected interference fringes, which is needed for wave reconstruction. For this purpose, the decision function was calculated for pairs of fringe discontinuity points with regard to a variety of fringe geometric characteristics. The studies are conducted using computer-simulated interferograms. The developed algorithms are shown to be suitable for eliminating fringe discontinuities and obtaining connected interferogram fringes.

It has been found that, at certain solar and sensor viewing geometries and for certain atmospheric conditions, some discontinuity lines appear in the retrieved atmospheric and ocean color products from measurements of Sea-viewing Wide Field-of-view Sensor (SeaWiFS). Such discontinuity lines, which do not often happen in the SeaWiFS products, appear along lines with constant scattering angles between the solar and sensor viewing directions. The discontinuity lines are clearly not real. They are artifacts from the SeaWiFS atmospheric corrections. The atmospheric correction, which is the key data processing in the ocean color remote sensing, removes more than 90% of the sensor-measured signals that are contributed from atmosphere and ocean surface effects in the visible wavelengths. In this paper, a brief description of the SeaWiFS atmospheric correction algorithm, in particular, the technique that is used in retrieving the aerosol models and aerosol radiance contributions in the visible wavelengths, is provided. Results from some specific simulations that explain the causes of the discontinuity lines in the derived products are presented. We show that these discontinuities are results of the imperfect atmospheric correction due to some effects of the aerosol models that are used for the SeaWiFS data processing. A simple modification to the current atmospheric correction algorithm to correct such effects is proposed and tested with SeaWiFS data.

A lens system can be represented as a point in the N-dimensional parameter space. There is a set of quantities called merit functions associated with points in this parameter space that define the performance of the lens system. Ideally this set can be reduced to a single quantity called the merit function. Lens design iterations consist of transferring from one point in parameter space to another where the merit function indicates an improvement. By repeating this process the designer may eventually reach a satisfactory solution. Even when the functions involved are theoretically continuous, the transferring in parameter space may never be strictly continuous because it is a numerical process. Yet, it should be possible to take arbitrary short steps on going from one point to another. Long steps, or leaps, can abruptly lead to undesirable regions from where it may be difficult to return to the previous, more desirable region. There are three common methods to set up the merit function: Levenberg’s damped least squares (DLS), G. Spencer’s constrained damped least squares (CDLS) and E. Glatzel’s automatic adaptive correction (AAC). This paper reviews the pros and cons of these methods. A discontinuity found in Spencer’s method will be discussed in detail.

A new phase unwrapping algorithm is proposed based on temporal phase unwrappping. Given a series of wrapped phase maps generated from different fringe periods, a jump mask (or matrix) was introduced which reveal the 2π phase jump between successive levels. Using this jump mask, a series of wrapped phase can be unwrapped by summing up integers in specific column of the mask. The summation of the integers is the total multiple of 2π phase jump between wrapped and unwrapped phase. Deduction of the mask, practical experiment and discussion are carried out in detail. This method can measure discontinuity in object and accelerates the phase unwrapping procedure.

The implementation of an image-based virtual navigation system is presented. An adaptive nonuniform sampling method of 4D light field is implemented based on slit images. Using the quadtree structure, this approach reduces the storage cost and accelerates the sampling process. The cause of holes is discussed and a hole-filling algorithm is designed. To avoid frame discontinuity, issues and approaches of memory management, track prediction and collision detection are discussed. Finally, an example navigation system of Science and Technology University of Macao shows the efficiency of the algorithms discussed.

A new phase unwrapping algorithm is proposed in this paper. This algorithm, based on the global continuity of the physical information being measured, is shown to be reliable by experimental results. Unlike the brunch-cut method, this new algorithm needs not placing brunch cuts but ratifying the errors in the initial unwrapped phase map obtained by the conventional method using the least difference of phase-cross-section. It is suitable for unwrapping phase map in the presence of errors such as noise, phase discontinuity more than (pi) and insufficient sampling. In addition, the new method is simple and requires little computing time.

A well-founded and computationally fast method is presented for filtering and interpolating noisy and discontinuous wrapped phase fields that preserves both the 2π discontinuities that come from the wrapping effect and the true discontinuities that may be present. It also permits the incorporation of an associated quality map, if it is available, in a natural way. Examples of its application to the computation recovery of discontinuous phase fields from speckle interferometry fracture measuring are presented.

The paper contains results of experimental investigations of the pressure field distribution in the vicinity of underwater sources of non-continuous radiating surface. Two sources were examined, each in form of 16-element array. The arrays are composed of circular piezoceramic pistons of the same dimensions and radiating properties. The elements of the first source are pistons of 25-mm-diam and resonant frequency equal to 600 kHz. The second of examined sources is using piezoelements of 10-mm-diam and resonant frequency of 1.5 MHz. Shown and characterized is the impact of the discontinuity of radiating surface on the nonlinear distortion process in the vicinity of the multi-element source.

We have proposed a boundary extraction algorithm for cross-sectional critical dimension (CD) measurements of the scanning electron microscope (SEM) images in machine/computer vision. Noisy SEM images have the image discontinuity of roof edge with peak. A task is to extract a low contrast boundary or edge with about one pixel width in a noisy cross sectional SEM image. Also CD measurements require that the algorithm locate a boundary or an edge at the correct position. Our policy is to detect the edges with high degree of confidence at first, and then to extract the edges with the high probabilities of edge that are calculated by using gray levels of neighboring pixels. Our proposed algorithm integrates the Gaussian pyramid to suppress noise, morphological operations to detect the edges with high degree of confidence, the relaxation method to recover the gaps in the detected edges, and the hierarchical approach. Application of the proposed algorithm to cross sectional SEM images of DRAMs shows its validity.

A novel approach to reconstruct shape from shading information is presented, which considers both the global and local shading. Firstly, a 2D gray-level image is divided into several simple patches with snake model. Secondly, the shape of the patches is reconstructed respectively. Thirdly, the different patches are jointed into a whole one. And at last, the mosaic surface is smoothed. According to this method, not only the distortion caused by image discontinuity but also the effects of local noises is eliminated. Results of experiments are given to illustrate the usefulness of the approach.

This article propose a new Fourier transform profilometry based on modulation measurement. We briefly call it FTP based on MM. Its main advantage is that it can measure the surface of a complex object in the same direction of projecting light, so it has no the difficulties due to shadow and spatial discontinuity that exist in conventional FTP and also PMP methods. In the paper, we give the principle of the method, the set-up of measurement system, and some primary experimental results. The results proved that this method is a promising method for acquiring 3D data of complex object.

One of the principal tasks of numerically simulating integrated optical devices is the accurate calculation of modal fields and propagation constants. Our recently proposed 'wave-matching-method' for dielectric waveguides with rectangular and piecewise constant refractive index profiles is based on expansions of the electromagnetic field into functions with harmonic and exponential dependence on the transverse coordinates. Local expansions for regions with constant permittivity are joined by minimizing a least squares expression for the remaining misfit at the discontinuity lines. For this paper the wave-matching analysis has been applied to a number of more complex structures: a conventional, deeply etched two-waveguide coupler, an ARROW- waveguide, a three dimensional four-waveguide coupler and three-waveguide coupler with multimode central rib (radiatively coupled waveguides). We have found good overall agreement where a direct comparison with published results is possible.

The microfabrication of silicon V-grooves allows to obtain very good positioning accuracies, it is therefore often used for precise alignment of optical fibers. In many cases, it is necessary to etch at the same time V-grooves with variable widths, or V-grooves crossing eachother. In such commonly encountered case, well-known overetching effects appear, leading to structures that are quite uncontrolled in size and depth. Corner compensation methods can reduce such effects to some extent, in some cases. In this report, we present another method which can be used to minimize convex angels overetching. This method can be used alone or in addition to classical corner compensation methods. In some cases, it could even be used when such methods are not possible. We first present the convex angle overetching, and derive the relation between underetching and etching depth. The method relies on discontinuities of the mask, which allow to keep a precise etching geometry until the discontinuity is underetched: the beginning of the corner underetching is thus delayed while the wanted structure is etched with a high accuracy. The control of the underetching rate is obtained through a precise alignment between the mask edges and the crystal orientation. The experiments show that our method allows to reduce significantly the overetching of convex angles. This method is useful to improve or simplify the fabrication of several kinds of microstructures for MEMS or MOEMS applications. We show how it makes feasible a microstructure which mixes closely spaced V-grooves and metal interconnection lines, and how it can improve the fabrication of crossing microchannels.

Availability of gasdynamical discontinuity waves (shock and entropic waves) and isentopic waves (depression-type waves or compressive shock waves) is the characteristic singularity of supersonic flows. An interaction of these waves leads to formation of the composite shock-wave configurations. Computation of these shock-wave configurations is reduced to multiple solution of two subproblems -- an interaction of discontinuity waves between themselves and an of discontinuity waves with isentropic waves. Unlike subproblems of first type the suproblems which related to interaction of discontinuities waves with isentropic waves is not enough researched. The reason of this situation is that an interaction between discontinuity waves and is occurred at the some finite field. Thereby approximation calculus for computation of these subproblems is used. In presented investigation analytical solution of these subproblems are offered.

In blind image restoration the parameters of the imaging system are unknown, and must be estimated along with the restored image. Assuming that the images are piecewise smooth, the most part of the information needed for the estimation of the degradation parameters is expected to be located across the discontinuity and hence a better estimation of the paper we adopt a fully Bayesian approach which enables the joint MAP estimation of the image field and the ML estimations of the degradation parameters and the MRF hyperparameters. Owing to the presence of an explicit, binary line process, we exploit suitable approximations to greatly reduce the computational cost of the method. In particular, we employ a mixed-annealing algorithm for the estimation of the intensity and the line fields, periodically interrupted for updating the degradation parameters and the hyperparameters, based on the current estimate of the image field. The degradation parameters are updated by solving a least square problem of very small size. To update the hyperparameters we exploit MCMC techniques and saddle point approximations to reduce the computation of expectations to low cost time averages over binary variables only.

The focus of this paper is on CT helical weighting algorithms using one source rotation, or 2 pi, worth of projection data. Currently known 2 pi helical weighting algorithms include a fan-angle dependency, and do not lend themselves to fast reconstruction, for two reasons. First, it can be shown that the weight distributions present a line of discontinuity across the sinogram (projection space), which defines two separate sinogram regions. Second, the expressions for the weighting functions differ for those two regions. Accordingly, reconstruction of P different image planes (all using a given projection) requires P weightings and filterings of that projection. In this paper, it is shown that, by first generalizing the concept of the interpolation/extrapolation function used in the weighting, to the concept of distance function, and second by selecting particular classes of such distance functions, the discontinuity across the sinogram can be eliminated. By imposing specific sufficient conditions on such distance functions, single analytical expressions across the entire 2 pi sinogram are obtained. Decomposition of these particular "single" distance functions leads to two-filtering reconstruction algorithms, for which a given projection needs to be filtered only two times for an arbitrary number P of reconstruction planes. Finally, another generalization of the concept of helical weighting leads to one-filtering weight functions that depend only on the sum of the projection--and fan angles. Accordingly, after rebinning the fan-beam projections to parallel projections, the corresponding 2 pi helical weighting algorithms do not include a dependency over the ray parameter. Equivalently, for these algorithms, weighting commutes with filtering, and reconstruction of an arbitrary number P of image planes requires only one filtering per projection. These algorithms are shown to be consistent with the hypothesis of a linear z variation of the projections.

Control grid interpolation (CGI) was suggested to overcome the drawbacks of the block matching algorithm such as blocking artifacts. In CGI, smooth motion field is obtained because motion vectors are spatially transformed from the control points. However, when there are more than two objects which move in different directions, distortion may be involved near the motion boundaries due to the continuity of the motion field. To cope with this problem, we use motion discontinuity pattern and the motion vectors are transformed according to the motion discontinuity. For the determination of motion discontinuity pattern, the similar vectors are grouped together and the grouping pattern is checked. Since this determination is carried out by simple calculation of the motion vectors which are available at the decoder, no side information is necessary and the additional complexity is negligible. The modified CGI with motion discontinuity outperforms the conventional CGI in objective and subjective qualities.© (1998) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.