A two step technique to detect flaws automatically is proposed in  where the authors used a single filter. This method allows first to identify potential defects in each image of the sequence, and second to match and track them from image to image. Many other weld defect detec- tion methods are so far presented and proposed in the literature. However, each technique presents its own advantages and drawbacks. A comprehensive review paper to compare these techniques is now missing in the litera- ture. In this article, we shall focus our attention on a well- known technique namely the anisotropicdiffusionmodel used to the weld detection defects .
This paper is organized as follows. Section 2 overviews the micro-crack properties in polycrystalline solar wafer. Section 3 overviews the conventional and proposed anisotropicdiffusionmodel. Section 4 shows the experimental results from polycrystalline solar wafer images. The performance comparison with the Tsai et al. method is also discussed. Section 5 gives the conclusion of our research.
Any acquired images either: photographic, astronomical, medical or others are subject to noise degradation which reduces the quality of the image. The noise is introduced due to thermal fluctuations in sensors, quantization effects, and properties of communication channels. It affects the perceptual quality of the image decreasing not only the appreciation of the image but also the performance of the task for which the image has been intended. The challenge in the image filtering is to design methods, which can selectively smooth a degraded image or image sequence without altering edges and losing significant features. In the case of still image, the filtering acts in a space of two dimensions (2D), whereas in a sequence images (or video image), the temporal component is added (2D+t) and should be taken into account. To effectively adapt the local structures of the image and to preserve discontinuities, it should be recommended to the use of a non linear filter. Recently, a new approach based on Partial Differential Equations (PDEs) , has emerged as a more powerful and a successfully approach for studying a variety of problems including image restoration, image segmentation, and image denoising. The PDE methods have remarkable advantages in both theory and computation. They allow handling and processing visually important geometric features such as gradients, tangents, curvatures and modeling visually meaningful dynamic process such as linear and nonlinear diffusion. In our approach, we use the concept of PDEs to formulate an anisotropicdiffusionmodel. The key idea is to perform an adaptive smoothing which allowing isotropic smoothing in low gradients (e.g. homogeneous area), while avoiding diffusion in high gradients (e.g.
than 1 diffusion-encoding direction is re- quired to characterize regions of aniso- tropic diffusion. If only a single diffusion direction was probed, interpretation of the DWIs would be complicated by vari- able signal intensity in white matter tracts, depending on their orientation rel- ative to the direction of the diffusion gra- dient, which could also be affected by changes in the orientation of the patient’s head. Although this anisotropy can be ex- ploited in DTI, to be discussed in detail below, it is not desirable for routine clin- ical DWI. To avoid this problem, one can compute parameters with the property of rotational invariance from the original DWI data because these measures math- ematically eliminate any directional de- pendence that might confuse clinical interpretation.
Abstract. We propose a finite volume method on general meshes for the numerical simulation of an incompressible and immiscible two-phase flow in porous media. We consider the case that can be written as a coupled system involving a degenerate parabolic convection-diffusion equation for the saturation together with a uniformly elliptic equation for the global pressure. The numerical scheme, which is implicit in time, allows computations in the case of a heterogeneous and anisotropic permeability tensor. The convective fluxes, which are non monotone with respect to the unknown saturation and discontinuous with respect to the space variables, are discretized by means of a special Godunov scheme. We prove the existence of a discrete solution which converges, along a subsequence, to a solution of the continuous problem. We present a number of numerical results in space dimension two, which confirm the efficiency of the numerical method.
shock-diffusion equation (Fu et al., 2007b), sub-regions histogram equalization (Ibrahim and Kong, 2009), Sobolev gradient flows (Calder et al., 2010), fuzzy logic (Gui and Liu, 2011), Laplacian operators (Ma et al., 2014), Wavelets (Zafeiridis et al., 2016) and many more. As seen, different concepts are used for image sharpening. Among such, tremendous research has been made based on the unsharp mask concept in the past period due to its rapidness and simplicity. Still, it unavoidably degrades the processed image by the overshoot effect (Polesel et al., 2000). Such effect occurs around the edge sides, making these edges perceived with visible white shades (Cao et al., 2011). Thus, it is required to enhance the processing ability of the standard unsharp mask to provide artefact-free outcomes with better sharpness. Despite the major thrive in image sharpening, there still an adequate chance for ameliorating this filter. Therefore, an anisotropicdiffusion-based unsharp mask filter, so-called ADUSM, is introduced in this study to provide enhanced sharpness for the processed images without delivering any unwanted effects.
Abd-Elmoniem et al.  proposed an anisotropic dif- fusion approach to perform speckle reduction and coher- ence enhancement. They applied an anisotropic diﬀusiv- ity tensor into the diﬀusion equation to make the diﬀu- sion process more directionally selective. Although they gen- erally had good results, the approach used raised the fol- lowing questions. (1) It used isotropic Gaussian smooth- ing to regularize the ill-posed anisotropic diﬀusion equa- tion. Although this kind of regularization has been proved to be able to provide existence, regularization, and unique- ness of a solution , it is against the anisotropic fil- tering principle. (2) The diﬀusivity tensor provided by a Gaussian smoothed image may not be eﬀective for spa- tially correlated and heavy-tail distributed speckle noise. (3) Each speckle usually occupies several pixels in size. Without special treatment, there are chances to enhance the speckles, which is not desirable. Yu and Acton  proved that Lee [1, 2] and Frost’s  filter schemes were closely related to diﬀusion processes, and adopted Lee’s adaptive filtering idea into their anisotropic diﬀusion algo- rithm. However, the local statistics are actually isotropic, thus this method could not achieve the desired anisotropic processing.
Results of  suggest that fractal analysis of radiographic trabecular bone radiographic images is a good indicator of the alteration of the bone microarchitecture. In association with bone mineral density, fractal analysis improves the fracture risk evaluation. However, since this analysis is based on an isotropic model, it does not reveal bone texture anisotropy which is of special interest for the diagnosis of osteoporosis [7, 10].
To reduce image noise, various filtering techniques have been devised . In linear spatial filtering such as Gaussian filtering, the content of a pixel is given the value of the weighted average of its immediate neighbors. This filtering reduces the amplitude of noise fluctuations, but also degrades sharp details such as lines or edges, and the resulting images appear blurred and diffused . This undesirable effect can be reduced or avoided by designing nonlinear filters, the most common technique being median filtering. With median filtering, the value of an output pixel is determined by the median of the neighboring pixels . This filtering retains edges, but re- sults in a loss of resolution by suppressing fine details. Perona and Malik  developed a multiscale smoothing and edge detection scheme based on anisotropicdiffusion (AD), which is a new concept for image processing. Their AD method overcomes the major drawbacks of conventional spatial filtering, and significantly improves image quality while preserving spatial resolution -. The purpose of this study was to present an applica- tion of the AD method to cerebral CT perfusion studies using MDCT for improving the accuracy of perfusion parameters and to investigate its usefulness and feasibility in reducing radiation exposure.
measurements such as SNR, RMSE, SD. The proposed filter achieves better results in terms ofSNR, RMSE and SD measures.For the retinal image corrupted by 25% of speckle noise, the Standard Deviation (SD) andSignal-to-Noise Ratio (SNR) measures have not been reached expected value but the proposed filter has produced moderate values for each measures and the Root Mean Square Error (RMSE) has been improved. From the experimental results and performance analysis, it is observed that the proposed anisotropic filter preserves and enhances the vessel information that may be and also it is best suitable to remove the speckle noise present in the retinal images.
This work presents a segmentation and classification method for breast lesions in BUS images. This technique preprocesses the image with an anisotropicdiffusion filtering, in order to preserve and enhance useful information in the lesion boundaries, unlike from other filtering techniques that blur the image. The marker function plays an important role to remove the spurious minima which results in over segmentation. The MCC is used to measure along with the other performance evaluation parameters because it is efficient evaluation parameter of machine learning methods when data is unbalanced. The Marker-controlled watershed transformation is defined as a robust and flexible method for segmenting objects with closed contours, such as breast lesions. One advantage of our method is its simplicity to be implemented, because it does not require large computational cost to solve complex mathematical models, such as snake-deformation. SVM classifier efficiently classifies the Benign from Malignant and also works faster than ANN. The techniques are used in the CAD system to give support to the detection and diagnose of breast lesion in BUS image.
Abstract: Virtual Restoration of archaeological heritage stems from the need to create a clearer and better image of the beautiful historic monuments now in ruins. It gives the viewer a sense and feel of how the heritage originally looked. For this, there are many restoration projects of the major historic sites, paintings etc, going on across the world. Computers have been introduced to archaeology and cultural heritage as tools for promoting scientific work and as electronic aids for providing users with substantial information on archaeological heritage. Small holes and breakages in the monuments/paintings can severely degrade its appeal to viewers. Image restoration is the operation of taking a corrupted/noisy image and estimating the clean original image. In this work, we have proposed a method to automatically detect the defect in the corrupted image using Perona Malik AnisotropicDiffusion and Binary Thresholding, followed by Image Inpainting with Navier-Stokes Method, which have been found to be effective in the art of restoring lost/selected parts of an image based on the background information in a visually plausible way.
The diffusion time has to be less than the echo time and is partly determined by the value of b desired. Large values of b can be achieved with modest gradient strengths, if the pulse duration is relatively long. This, however, limits the diffusion time. Longer diffusion times allow more barriers to be encountered and would sample a larger range of restricted diffusion distances. This is illustrated in Fig. 4.6 where images varying only in the value of the Td values (44 and 103 msec) are compared. There is an increase in contrast between the ascending and descending tracts and the surrounding brain as Td is increased. This effect could be used in principle to assess the distribution of fibre sizes in particular tracts as one could plot a cumulative curve of signal intensity versus Td. In practice the fibre diameter distribution in the corticospinal tract, for example, is very heavily weighted towards one end with more than 95% of fibres having a diameter of 5jn or less and only 35 000 of the million or so fibres having a fibre diameter of 15- 20/x (5).
Abstract—An algorithm is developed to interpolate node unknowns from cell-centered ones for the construction of dif- fusion schemes on skewed meshes. And a cell-centered scheme for solving anisotropic problems is then constructed. Its main characteristic lie in that an explicit expression is obtained for the interpolation. And the discontinuity can be dealt with strictly. The effectiveness of the scheme is demonstrated by the numerical experiments.
extended to use a diffusion matrix instead of a scalar, allowing a better reduction of the noise at contour locations. This new extension based on the eigen vectors of the structure tensor, combines a smoothing of isotropic, planar and linear local structures. In this each smoothing is weighted according to the corresponding LMMSE filter. It does not require user to choose a contrast parameter for the edges of the structures but relies instead on the local statistics of the image i.e. local mean and local variance of image and also on standard deviation estimation of the noise for the underlying noise model. As a result of using a Linear Minimum Mean Square Error filter and estimation of noise level at each iteration, this filter is very robust to the total diffusion time and converges fast.
The early detection of micro-cracks in solar cells is im- portant in the production of PV modules. In this study, an image processing scheme composed of segmentation procedures based on anisotropicdiffusion and shape classi- fication is presented. The results show that the segmenta- tion procedures can detect and identify micro-crack pixels efficiently in the presence of various forms of noise. The anisotropicdiffusion filtering with gray level-based diffusion coefficient proposed in this study produced excellent en- hancement and improved segmentation. The advantage of this filtering technique is its ability to enhance the pixels with low gray scale and high gradient such as the micro- crack defects in solar cell. Trained with SVM using 240 samples, this artificial classifier produced a correct classifi- cation rate of consistently higher than 88% with average sensitivity and specificity of 97.7% and 80.2%, respectively. These results are very promising as it demonstrates a first attempt of integrated image processing and ma- chine learning platform toward its eventual application of micro-crack inspection of solar cells.
ward, 1984; Bott, 1989; Walcek and Aleksic, 1998). These advection algorithms were implemented based on a fixed uniform mesh system. The successive global refinement can be used to capture the details of small-scale flow features, but is prohibitively expensive and not feasible for practi- cal applications. Alternatively, the nesting technique, plac- ing finer meshes within coarser meshes, is often used for achieving local higher resolution in many air quality mod- els (Garcia-Menendez and Odman, 2011; Frohn et al., 2002; Wang, 2001). In static mesh nesting, the solutions obtained from the global coarse mesh model provide the boundary conditions for the nested mesh regional model; in turn, the solutions in the global model are updated with the high res- olution solutions. However this may lead to spurious oscil- lations at the interface between the coarse mesh and nested fine mesh, especially when concentration gradients are large cross the interface. Although the numeral techniques such as blending, nudging and selective damping approaches can be used to remove these oscillations, the small-scale features on the fine meshes may be damped (Garcia-Menendez and Odman, 2011; Zhang et al., 1986; Debreu and Blayo, 2008; Alapaty et al., 1998). Moreover, due to highly unsteady at- mospheric flows, it is almost impossible to construct a static optimal nested mesh suitable for an accuracy simulation over a long time period. The use of dynamically adaptive mesh techniques can therefore be considered in such as way that the mesh resolution can be adjusted locally in response to the evolution of the flow and passive tracer (Piggott et al., 2009; Behrens, 2007).
A substantial works have been conducted to study the pre-processing of hand skeletal bone from background and soft-tissue region. Majority of the works involve the appli- cation of threshold setting which is considered ineffective in the hand bone segmenta- tion due to the fact that the soft-tissue region contains pixel intensity that similar to spongy bone of the hand skeletal bone. Besides, most of the work, after obtaining the region-of-interest (ROI), implements the active contour model which has inherent weaknesses like high sensitivity towards intensity gradient, high dependency on initia- tion location and low ability in growing into concavity. Some works implement the sta- tistical analysis to determine the membership of each pixel, whether belong to the bone or the soft-tissue region. Some works combine various techniques segmentation in other field into the hand skeletal bone segmentation. The development of the study has been summarized the following paragraphs:
orientations of normal and tangential vector fields for two co-registered images, the diffusion flux is rotated and scaled adaptively to image features. The images can have different greyscale values and different spatial resolutions. The proposed approach is particularly good at isolating oriented features in images which are important for medical and materials science applications. By enhancing the edges it enables both easy identification and volume fraction measurements aiding segmentation algorithms used for quantification. The approach is tested on a standard denoising and deblurring image recovery problem, and then applied to 2D and 3D reconstruction problems; thereby highlighting the capabilities of the algorithm. Using synthetic data from SPECT co-registered with MRI, and real NCT data co-registered with x-ray CT, we show how the method can be used across a range of imaging modalities. Keywords: iterative tomographic reconstruction, hybrid modalities, emission and neutron tomography, regularization methods, anisotropicdiffusion (Some figures may appear in colour only in the online journal) 1. Introduction
The anisotropic creep model has been implemented in a finite element code, and several validation tests have been performed. In particular, the response of the model in undrained triaxial tests has been compared with the corre- sponding results obtained with the elasto-plastic S-CLAY1 model, showing a similar behaviour both for the predicted stress path for slow loading rates and for similar rotation of the normal consolidation surface. In order to assess the capability of the model to capture the real behaviour of soft soils, test data of a marine deposit have been used as a benchmark. Undrained triaxial extension test results have been simulated with both the isotropic and the anisotropic creep model, under the same conditions of the laboratory tests. The results show how the isotropic model overesti- mates the undrained strength of the material whereas, in contrast, the anisotropic creep model gives predictions close to the experimental data. It was also shown that it is necessary to account for changes of anisotropy due to viscous strains to achieve a proper prediction of the un- drained shear strength in triaxial extension. Another test was simulated to investigate the behaviour of the model in undrained compression, showing a satisfactory agreement between predictions and measurements.