Geodesic methods for biomedical image segmentation

In this short note we give and discuss a general multilinear expression of the structure function of an arbitrary semicoherent system in terms of its minimal path and cut sets. We also examine the link between the number of minimal path and cut sets consisting of 1 or 2 components and the concept of structure signature of the system.

A heuristic minimal path sets method for analyzing seismic reliability of lifeline networks is proposed. For large-scale lifeline networks reliability computation can become prohibitive or inaccurate using the current enumeration methods. Although a few studies have considered both node and link failures, none of these methods has utilized the minimal paths method. This paper proposes a minimal path algorithm to evaluate reliability of relatively large lifeline networks with unreliable nodes and links. As the primary task, the method can deduce all minimal paths of a directed/undirected network. In the algorithm, minimal paths for both nodes and links are traced performing several procedures. The terminal-pair reliability of the network is then evaluated by performing an efficient Monte Carlo simulation as an alternative to exact reliability calculation methods. In terms of computational speed, the results obtained compare well with existing algorithms. The algorithm requires minimum memory storage and minimum user-defined data to represent the topology of a network. A series of case studies illustrate that the method can be used to evaluate reliability of the large-scale lifeline systems subject to node and link failures, efficiently.

Image segmentation is the first step in image analysis and pattern recognition, and it is one of the most difficult tasks in image processing, and determines the quality of the final result of analysis. Image segmentation requires the improvement because most image segmentation solution is problem based. Biomedical image segmentation is different than normal image segmentation. Because normal image is taken from camera which is free of noise. While biomedical image is taken from MRI, CT, Microscopic Instrument or X-ray which is it noisy and fuzzy. Medical image segmentation methods generally have restrictions because medical images have very similar gray level and texture among the interested. While extracting region of interest in biomedical image, region of interest can avoid the processing of irrelevant image point. Biomedical Image segmentation is necessary when we want the computer to make decision, surgical planning and robotically assisted surgical invention. Biomedical image segmentation is nothing but the classification of similar pixel and their following extraction into separate segment. There are different methods to do the Biomedical image segmentation but they are slow. he method which is described in this paper is fast and efficient. This paper gives comparative research of different method of each of category. The method described in the paper is for fast biomedical image segmentation

Minimal pathset and minimal cutsets using search technique

This article will include three important methods for extracting minimal path sets from a complex network, and a comparison will be made between these methods to choose the best one for accessing minimal path sets. Also, this article will discuss HEWEIDY'S METHOD, which is a new and effective method for calculating the importance of each component of a complex network and its levels. This method depends entirely on the relationship between minimal path sets and minimal cut sets, and the latter we will extract from minimal path sets.

This paper presents a geodesic voting method to segment tree structures, such as retinal or cardiac blood vessels. Many authors have used minimal cost paths, or similarly geodesics relative to a weight potential P, to find a vessel between two end points. Our goal focuses on the use of a set of such geodesic paths for finding a tubular tree structures, using minimal interaction. This work adapts the geodesic voting method that we have introduced for the segmentation of thin tree structures to the segmentation of tubular trees. The original approach of geodesic voting consists in computing geodesics from a set of end points scattered in the image to a given source point. The target structure corresponds to image points with a high geodesic density. Since the potential takes low values on the tree structure, geodesics will locate preferably on this structure and thus the geodesic density should be high. Geodesic voting method gives a good approximation of the localization of the tree branches, but it does not allow to extract the tubular aspect of the tree. Here, we use the geodesic voting method to build a shape prior to constrain the level set evolution in order to segment the boundary of the tubular structure. We show results of the segmentation with this approach on 2D angiogram images and 3D simulated data.

Level set methods are useful tools for medical image segmentation. In this paper, a novel image segmentation technique was developed that combines region statistical information with the level set method. The classical level set methods depend mainly on local edge-based image features to guide the convergence of the contour. This makes the method sensitive to noise and the initial estimate. The method has two features. The first is that it uses obtain region-based information by a mixture model. The second feature is that we combine region statistical information with curvature-based regularization penalizing the length of curve. The method is useful for a large variety of segmentation problems. We present some preliminary experimental results using synthetic images and, magnetic resonance (MR), ultrasound (US), computed tomography (CT) images to demonstrate our methods. The experimental results show that by incorporating region statistical information into the level set framework, an accurate and robust segmentation can be achieved.

Computing system reliability is a classical engineering reliability problem and was modeled using different computational approaches for many years. For systems which include a large number of components, one modeling approach is to consider the system components as vertices of a network graph, with the integrated components connected by edges. Wireless sensor networks follow very close this network graph model, with the access medium used for communication between the sensor nodes modeled as edges and the sensor nodes modeled as vertices. Probability and reliability theory consider the minimal path set as the lowest number of components whose functioning assures the operation of the system. This work models the reliability of wireless sensor networks using minimal path sets defined as the minimal set of functioning sensor networks that ensures a certain threshold of events detected by the sensor network.

To solve the problems on quick achieving reliability and the minimal path sets (MPS) of a system with GO Methodology, a Binary Decision Diagram (BDD) based new GO methodology algorithm is introduced. This technique can avoid the shared signals and combination explosion problems simultaneously. Detailed steps with a case study are presented to explain the analysis procedure of this technique, firstly, establish the GO model and transform it into a directed acyclic diagram (DAG), logic tree and BDD successively; then minimize the BDD according to the Without Rule; at last, this system reliability and MPS can be achieved. The results of the studied case verify the validity and effectiveness of this algorithm.

Introduction/purpose: The research aimed to analyze the key aspects of human-computer interaction, studying the evolution of this field from its beginnings to contemporary trends. Focusing on different aspects of this interaction, it studied how methods, technologies and principles have evolved over time and shaped our experiences in the digital environment. Methods: The research methodology was based on the analysis of relevant literature and research papers devoted to human-computer interaction. Systematic review and evaluation of sources identified the key information on the evolution of user interaction with computers. Through evaluation of available studies, changes in interface design methods, interaction technologies and understanding of user needs over time were identified. Results: Based on data synthesis, the key aspects of human-computer interaction were identified. An analysis of the literature revealed changes in interface design methods, interaction technologies, and understanding of user needs over time. Specific results included information on the evolution of interaction aspects, including improvements in efficiency, intuitiveness and personalization of experiences. Conclusion: The key conclusion of the research is that innovations and evolution of technology have significantly influenced the way users interact with computer systems. Improvements in interface design, recognition technologies, and personalization of experiences are key factors in creating better user experiences and optimizing human-computer interaction. The research points to the continuous development and changes in the field of human-computer interaction, emphasizing the need for further research and innovation in this area.

The resilience of a software architecture plays a vital role in the security of a software system, and poor resilience in a software architecture translates to the insecurity of the software system. However, achieving effective quantification of resilience in software engineering is a challenging problem during the system architecture construction stage. Although some methods have been proposed to evaluate the resilience of software systems with the development of resilience security theory, existing methods have shortcomings, such as the lack of connotation of evaluation metrics and overly large time complexity, which lead to limited applications for resilience evaluation in software architecture.To bridge this gap, we propose a software architecture resilience evaluation method based on the minimal path. Starting from the activity diagram, we construct a minimal path set to divide the system missions and build a state-conversion model that quantifies resilience metrics and calculates resilience evaluation results. Additionally, we compare our method with three other evaluation methods for architecture resilience, analyze the factors that affect software architecture resilience, and validate the effectiveness of our method.

In order to take advantage of the computer in the numerical calculation, in view of the fault tree qualitative analysis, a new method of fault tree analysis, numerical methods, was proposed on the basis of absorbing merits of the prime number method and determinant method. The fault tree's minimum cut sets and path sets can be calculated effectively with this method. Consequently, a specific example about calculation of the minimum cut sets was demonstrated with Scilab in this paper.

In this paper, we propose a novel curvature-penalized minimal path model via an orientation-lifted Finsler metric and the Euler elastica curve. The original minimal path model computes the globally minimal geodesic by solving an Eikonal partial differential equation (PDE). Essentially, this first-order model is unable to penalize curvature which is related to the path rigidity property in the classical active contour models. To solve this problem, we present an Eikonal PDE-based Finsler elastica minimal path approach to address the curvature-penalized geodesic energy minimization problem. We were successful at adding the curvature penalization to the classical geodesic energy. The basic idea of this work is to interpret the Euler elastica bending energy via a novel Finsler elastica metric that embeds a curvature penalty. This metric is non-Riemannian, anisotropic and asymmetric, and is defined over an orientation-lifted space by adding to the image domain the orientation as an extra space dimension. Based on this orientation lifting, the proposed minimal path model can benefit from both the curvature and orientation of the paths. Thanks to the fast marching method, the global minimum of the curvature-penalized geodesic energy can be computed efficiently. We introduce two anisotropic image data-driven speed functions that are computed by steerable filters. Based on these orientation-dependent speed functions, we can apply the proposed Finsler elastica minimal path model to the applications of closed contour detection, perceptual grouping and tubular structure extraction. Numerical experiments on both synthetic and real images show that these applications of the proposed model indeed obtain promising results.

We present an algorithm for computing the closest point, transform to an explicitly described manifold on a rectilinear grid in low dimensional spaces. The closest point transform finds the closest point on a manifold and the Euclidean distance to a manifold for the points in a grid. We consider manifolds composed of simple geometric shapes, such as, a set of points, piecewise linear curves or triangle meshes. The algorithm solves the eikonal equation |∇u| = 1 with the method of characteristics. For many problems, the computational complexity of the algorithm is linear in both the number of grid points and the complexity of the manifold. Many query problems can be aided by using orthogonal range queries (ORQ). There are several standard data structures for performing ORQ's in 3-D, including kd-trees, octrees, and cell arrays. We develop additional data structures based on cell arrays. We study the characteristics of each data structure and compare their performance. We present a new algorithm for solving the single-source, non-negative weight, shortest-paths problem. Dijkstra's algorithm solves this problem with computational complexity O ((E + V)log V) where E is the number of edges and V is the number of vertices. The new algorithm, called Marching with a Correctness Criterion (MCC), has computational complexity O (E + RV), where R is the ratio of the largest to smallest edge weight. Sethian's Fast Marching Method (FMM) may be used to solve static Hamilton-Jacobi equations. It has computational complexity O (N log N), where N is the number of grid points. The FMM has been regarded as an optimal algorithm because it is closely related to Dijkstra's algorithm. The new shortest-paths algorithm discussed above can be used to develop an ordered, upwind, finite difference algorithm for solving static Hamilton-Jacobi equations. This algorithm requires difference schemes that difference not only in coordinate directions, but in diagonal directions as well. It has computational complexity O(RN), where R is the ratio of the largest to smallest propagation speed and N is the number of grid points.

Neural networks offer various possibilities for function approximation. When provided a set of data points, the network learns to approximate the underlying function that generates those points. Although the network can be very efficient, the amount computation needed during the learning process can be very high. In order to improve this process, we explore the parallelization for the random scanning of starting points selected for the gradient descent algorithm using Cell-BE multiprocessor environment. We show the application of this method for approximating 3D nonlinear function, as well as for predicting 2D time series. We show that the parallel tracing of gradient descent trajectories of the 3D function approximation allows identifying a suitable starting condition for implementing an efficient gradient descent, while being able deliver the required accuracy of approximation in a shorter time. In 2D time series prediction the attained advantage is the possibility to achieve simultaneous prediction for various numbers of steps ahead. It is shown how the Cell-BE multiprocessor offers a convenient parallel environment for the above solutions.