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Detection of Calcification from Abdominal Aortic Aneurysm
Published in Ayman El-Baz, Jasjit S. Suri, Cardiovascular Imaging and Image Analysis, 2018
Safa Salahat, Ahmed Soliman, Harish Bhaskar, Tim McGloughlin, Ayman El-Baz, Naoufel Werghi
In [43], a semi-automatic graph cut based 3D segmentation method that works both for CT and MR was developed. This method segments the lumen and aortic wall, and was tested on patients with and without AAA, and synthetic images. This method doesn't over segment, nor does it require prior information on the shape. This segmentation method is based on graph cut, in which the graph consists of nodes and undirected edges of weighted capacity, and a source and a sink nodes, in order to find the minimum cut. The graph cut method classifies the nodes into two subsets that either exist inside or outside the segmented area. The other nodes used to separate the two sets represent the edges. The volume consists of L images of N × M pixels each, and the user needs to manually initialize the region of interest, which would result in inside, outside, and neutral volumes.
A Self-Organizing Map-Based Spectral Clustering on Shortest Path of a Graph
Published in Siddhartha Bhattacharyya, Anirban Mukherjee, Indrajit Pan, Paramartha Dutta, Arup Kumar Bhaumik, Hybrid Intelligent Techniques for Pattern Analysis and Understanding, 2017
Parthajit Roy, Swati Adhikari, J. K. Mandal
In the problem of graph partitioning, the entire dataset is expressed as a graph G=(V,E), where V is the set of vertices and E is the set of edges. Then the vertex set V is divided into a number of smaller components K, with some specific properties. Graph clustering algorithms are mostly based on the graph partitioning problems. The partition in which the number of edges connecting two separate components is small, i.e., a minimum cut can be obtained, is considered as a good partition. There are various methods like ratio cut and normalized cut available to find the minimum cut which are NP-hard problems. In the proposed method, a shortest path based planar graph cut method is used. For this, planar decomposition of the original graph representing the input vectors is made. This is also known as Delaunay triangulation. For planar graph, Delaunay triangulation, and shortest path see Appendix 13.A. The spectral properties of the graph matrices are used to solve the graph cut problems. Actually, through the use of spectral clustering methods these NP-hard graphs cut problems can be solved more easily. Spectral clustering represents data in lower-dimensional space which can be clustered easily. In spectral clustering, a similarity graph is used. A similarity graph is a weighted graph in which each data object is expressed as a node of the graph and the connection between two data objects is made if the similarity between the corresponding data objects is positive or exceeds a certain amount of threshold value. The weight of any edge is assigned with the amount of similarity between two data objects. As distance decreases, the similarity increases. Now, if this graph is partitioned, the weight of an edge connecting two data objects, each one from two different groups has very low weight. When two data objects are chosen from the same group, the edge between them has high weight. Figure 13.B.3b shows a similarity graph.
Optimizing pushback design considering minimum mining width for open pit strategic planning
Published in Engineering Optimization, 2022
Pierre Nancel-Penard, Nelson Morales
The fundamental problem in mine design consists of determining the pushbacks, for which planners rely on a parametrization of (UP) to determine nested pits. (UP) was introduced together with an algorithm for its solution by Lerchs and Grossman (1965). Picard (1976) demonstrated that (UP) is equivalent to the maximum closure problem, which can be formulated as a minimum cut problem. Hochbaum proposed an efficient polynomial algorithm based on a maximum pseudo-flow approach solving large minimum cut problems fast (Hochbaum 2008).