In order to properly understand the subsurface structures, the issue of inversion of geophysical data has received much attention from researchers. Since accurate reconstruction of the shape and boundaries of the mass using gravimetric data is very important in some issues, it is important to use an effective and efficient method that has a high ability to draw and reconstruct the boundaries of a mass. In recent years, the Level Set method introduced by Asher and Stein has been widely used to solve this problem. From the expansion of the Level Set function in some bases of the problem, the effective number of parameters is greatly reduced and an optimization problem is created which its behavior is better than the least squares problem. As a result, the Level Set parameterization method will be presented for the reconstruction of inversion models. A common advantage of the parametric Level Set method is the careful examination of the boundary for optimum sensitivities, which significantly reduces the dimensional problem, and many of the difficulties of traditional Level Set methods, such as regularization, reconstruction, and basis function. Level Set parameterization is performed by radial basis functions (RBF),which causes an optimal problem with an average number of parameters and high flexibility,and the computational and optimization process for Newton's method is more accurate and smooth. The model is described by the zero contour of a Level-Set function, which in turn is represented by a relatively small number of radial basis functions. This formulation includes some additional parameters such as the width of the radial basis functions and the smoothness of the Heaviside function. The latter is of particular importance as it controls the sensitivity to changes in the model. In this algorithm adaptively chooses the required smoothness parameter and tests the method on a suite of idealized Earth models. In this evolutionary approach, the reduction gradient method usually requires many iterations for convergence, and the functions are weakened for low-sensitivity problems. Although the use of Quasi-Newton methods to improve the Level Set function increases the degree of convergence, they are computationally challenging, and for large problems and relatively finer grids, a system of equations must be solved in each iteration. Moreover, based on the fact that the number of underlying parameters in a parametric approach is usually much less than the number of pixels resulting from the discretization of the Level Set function, we make a use of a Newton-type method to solve the underlying optimization problem. In this research, the algorithm is used to investigate its strengths and weaknesses for applying geophysical gravity data, coding and programming, and it is tested using several two-dimensional synthetic models. Finally, the method is tested on gravity data from the Mobrun ore body, north east of Noranda, Quebec, Canada. The results of this study show that the application of the optimization algorithm of the Level Set function will lead to a relatively more accurate and realistic detection of mass boundaries. It shows that the tested mass has spread from a depth of 10 meters to a depth of 160 meters.

Background and Aim: Image brightness heterogeneity is one of the major challenges in computer image processing that can lead to inaccurate results in image segmentation. Despite the existence of numerous segmentation methods, few studies have been conducted on the effect of brightness heterogeneity and the selection of the best color channels in segmentation. In this paper, different color spaces have been used for automatic detection of skin lesions. Methods: In this study, the LSE (Level Set Evolution) segmentation method along with intensity smoothing has been used for computer recognition of skin lesions. First, the brightness heterogeneity is reduced and a more uniform image is created. Then, the proposed segmentation divides the image domain into distinct regions. This method results in more accurate recognition of skin lesions. Results: The proposed method has been tested on 200 dermoscopic images from the known PH2 dataSet using different color channels. The results show that this method performs better than other methods. Accuracy of 97%, sensitivity of 98%, specificity of 99% and Dice coefficient of 92% have been obtained. Conclusion: This method has the ability to accurately isolate and diagnose lesions and can help doctors in the treatment process of skin lesions.

In this paper the propagation of detonation waves in high explosives as well as gaseous mixtures are studied by combining the DSD theory and the Level Set method. In first step, the D-k and D-D-k relations for high explosive materials and gaseous mixtures are obtained. Then, using Level Set method, the detonation front is tracked in different geometries. A good agreement between DSD results and direct numerical simulations is observed for high explosive materials, where the curvature has an important role in detonation dynamic. Nevertheless, for gaseous mixtures the agreement is not as good as high explosives. In order to study the critical diameter problem in gaseous mixtures, the problem of detonation wave diffracting from a channel into an unconfined space is investigated. In this problem, the detonation failure criterion, based on the critical curvature concept, is utilized. A considerable difference between critical diameters which had been predicted by DSD theory and the experimental results is observed. The results indicate that the critical diameter in gaseous compositions (where the unsteadiness and chemical kinetic are more crucial than the curvature) is often underestimated by the DSD theory.

Introduction: Breast cancer can be considered as the most common cancer among women in the world. Hence, finding appropriate diagnosis methods is a critical and sensitive challenge in the health of the human community. Various methods have been proposed for breast screening in women, and one of the safest methods is magnetic resonance imaging. Tumors do not have morphological features of their own. Therefore, differentiating between benign and malignant lesions is normally very time-consuming and difficult. In this study, a computer-aided autodiagnosis system is developed for diagnosis and classification of axial magnetic resonance images of the breast in two classes of benign and malignant. Methods: Initially, suspected parts of the lesion were separated as a rectangular box around the lesion by an experienced radiologist. Then, we used, for the first time, a Level Set– based algorithm to precisely separate the lesion considering the unevenness of the images and to remove false positive regions using morphological operations and removing veins. In the next stage, four groups of features expressing particular states of the lesion structure are extracted from the separated parts of the lesions. These four groups are textural, kinetic, frequency, and morphological features. Here a new group of features called the Gabor-Haralik features, which present a particular efficiency, was extracted for each lesion. Finally, MLP classification was used to classify the lesions. Results: The proposed method was tested on 46 lesions. By utilizing Gabor-Haralik features, we achieved mean sensitivity, specificity, accuracy, and F-measure of 95. 41, 90. 70, 92. 76, and 92. 19%, respectively. Conclusion: The performance measures indicate the efficiency of the proposed diagnosis system for classification of benign and malignant breast lesions in magnetic resonance imaging.

Instantaneous grain geometry is one of the most affecting parameters on the performance of the solid rocket motors (SRMs). This paper presents the simulation of geometrically complicated solid propellant grain burn back using the Level Set method. The initial form of the grain is assumed in this method. Propagation of the grain boundaries in a velocity field is described using the Hamilton-Jacobi type equation. The solution of this equation in successive time steps gives the new burning boundaries of the grain. For this purpose, the initial geometry of grain is modeled in any CAD software. Then, the initial burning surfaces of grain are implicitly defined by the sign distance function and are used as the initial conditions of the Level Set equation. The geometrical characteristics of grain, such as burning surface area, port area, burning perimeter, and port volume are determined by Heaviside and Delta Dirac functions. The result of simulation is validated by an analytically predictable case, which shows excellent agreement. Burn back analysis is done for some practical grains including two cases that the test data were available. Using an unsteady zero dimension interior ballistic analysis, the resulting motor pressure curves are compared with the experimental data showing good agreement. The capability of the approach to handle the analyzing of problems, including non uniform burning velocity and arbitrary burnout configurations of grain are shown in examples.

This paper proposes an effective algorithm based on the Level Set method (LSM) to solve shape and topology optimization problems. Since the conventional LSM has several limitations, a binary Level Set method (BLSM) is used instead. In the BLSM, the Level Set function can only take 1 and -1 values at convergence. Thus, it is related to phase-field methods. We don’t need to solve the Hamilton-Jacobi equation, so it is free of the CFL condition and the reinitialization scheme. This favorable properties lead to a great time advantage in this method. In this paper, the BLSM is implemented with the additive operator splitting (AOS) scheme and several numerical issues of the implementation are discussed.The proposed scheme is much more efficient than the conventional Level Set method. Several 2D examples are presented which demonstrate the effectiveness and robustness of the proposed method.