An approach to image segmentation based on shortest paths in graphs

Reconfiguring two shortest paths in a graph means modifying one shortest path to the other by changing one vertex at a time, so that all the intermediate paths are also shortest paths. This problem has several natural applications, namely: (a) revamping road networks, (b) rerouting data packets in a synchronous multiprocessing setting, (c) the shipping container stowage problem, and (d) the train marshalling problem. When modelled as graph problems, (a) is the most general case while (b), (c) and (d) are restrictions to different graph classes. We show that (a) is intractable, even for relaxed variants of the problem. For (b), (c) and (d), we present efficient algorithms to solve the respective problems. We also generalise the problem to when at most k (for some k >= 2) contiguous vertices on a shortest path can be changed at a time.

In various applications where the problem domain can be modeled into graphs, the shortest path computation in the graph is an indispensable challenge. In applications like online social networks and shortest route computation problems, the size of the graph is so large; the number of nodes have become close to hundreds of billions. Shortest path graph algorithms like SSSP (Single Source Shortest Path) and APSP (All Pairs Shortest Path) have low arithmetic intensity and irregular memory access patterns. The GPU implementation of many arithmetic and logical problems exceed the performance of the CPU system implementations. There is an increasing need for faster computation of shortest path in graphs for various applications. The objective of the work is to demonstrate that GPUs can efficiently perform shortest path computations on undirected weighted graphs considering space efficiency. For the implementation, GPUs supporting CUDA (Compute Unified Device Architecture) programming have been used. Additionally a space efficient approach called Triangular Matrix Method has been used.

This paper introduces the definition of maximum entropy,the principle of onedimensional and 2-D maximum entropy.This paper solves the image segmentation problem by using the maximum entropy algorithm.The image gray value is divided into two regions of the background and the object.The key problem associated with this method is to find the optimal parameter extracting objects from background, the proposed method is used to segment image and ideal segmentation results can be obtained with less computation cost.Experimental simulation shows that the algorithm has a higher accuracy while preserving the edge infomation,and maximum entropy has been proven to be an efficient method for image segmentation.

The radius-stepping algorithm is an efficient, parallelixable algorithm for finding the shortest paths in graphs. It solved the problem in Δ-Stepping algorithm, which has no known theoretical bounds fur general graphs. 1" this paper, we describe a parallel privacy-preserving method for finding SingleSource Shortest Paths (SSSP). Our optimized method is based on the Radius-Stepping algorithm. The method is implemented on iop of the Secure Multiparty Computation (SMC) Sharemiiid platform. We have reshaped the radius-stepping algorithm to work on vectors representing the graph in a SIMD manner, in order to enable a fast execution using the secret-sharing based SMC protocol set of Sharemind. The results of the real implementation show an efficient method that reduced the execution time hundreds of times iii comparison with a standard case of the privacy-preserving radius-stepping and Δ-Stepping algorithms.

We present the buffer heap , a cache-oblivious priority queue that supports Delete-Min , Delete , and a hybrid Insert / Decrease-Key operation in O (1/ B log 2 N / M ) amortized block transfers from main memory, where M and B are the (unknown) cache size and block size, respectively, and N is the number of elements in the queue. We introduce the notion of a slim data structure that captures the situation when only a limited portion of the cache, which we call a slim cache , is available to the data structure to retain data between data structural operations. We show that a buffer heap automatically adapts to such an environment and supports all operations in O (1/λ + 1/ B log 2 N /λ) amortized block transfers each when the size of the slim cache is λ. Our results provide substantial improvements over known trivial cache performance bounds for cache-oblivious priority queues with Decrease-Keys . Using the buffer heap, we present cache-oblivious implementations of Dijkstra’s algorithm for undirected and directed single-source shortest path (SSSP) problems for graphs with non-negative real edge-weights. On a graph with n vertices and m edges, our algorithm for the undirected case performs O ( n + m / B log 2 n / M ) block transfers and for the directed case performs O (( n + m / B ) ċ log 2 n / B ) block transfers. These results give the first non-trivial cache-oblivious bounds for the SSSP problem on general graphs. For the all-pairs shortest path (APSP) problem on weighted undirected graphs, we incorporate slim buffer heaps into multi-buffer-buffer-heaps and use these to improve the cache-aware cache complexity. We also present a simple cache-oblivious APSP algorithm for unweighted undirected graphs that performs O ( mn / B log M / B n / B ) block transfers. This matches the cache-aware bound and is a substantial improvement over the previous cache-oblivious bound for the problem.

We consider the shortest paths between all pairs of nodes in a directed or undirected complete graph with edge lengths which are uniformly and independently distributed in [0, 1]. We show that die longest of these paths is bounded by c log n/n almost surely, where c is a constant and n is the number of nodes. Our bound is the best possible up to a constant. We apply this result to some well-known problems and obtain several algorithmic improvements over existing results. Our results hold with obvious modifications to random (as opposed to complete) graphs and to any distribution of weights whose density is positive and bounded from below at a neighborhood of zero. As a corollary of our proof we get a new result concerning the diameter of random graphs.

We present Skil, an imperative language enhanced with higher order functions and currying, as well as with a polymorphic type system. The high level of Skil allows the integration of algorithmic skeletons, i.e. of higher order functions representing parallel computation patterns. At the same time, the language can be efficiently implemented. After describing a series of skeletons which work with distributed arrays, we give two examples of parallel programs implemented on the basis of skeletons, namely shortest paths in graphs and Gaussian elimination. Run time measurements show that we approach the efficiency of message passing C up to a factor between 1 and 2.5.

We consider digit expansions \(n=\sum_{i=0}^l \epsilon_iq^i\) in redundant number systems to base q with \(-(q-1)\le \epsilon_i\le q-1\) and consider such an expansion as minimal, if \(l + \sum\nolimits_{i = 0}^l {|\varepsilon _i |} \) is minimal. We describe an efficient algorithm for determining a minimal representation and give an explicit characterization of optimal representations for odd q.

We present a general toolbox, based on new vertex sparsifiers, for designing data structures to maintain shortest paths in graphs undergoing edge insertions and/or deletions. In particular, we obtain the following results:

The purpose of the research is to develop a universal algorithm for partial texture segmentation of any visual images. The main peculiarity of the proposed segmentation procedure is the extraction of only homogeneous fine-grained texture segments present in the images. At first, an initial seed point is found for the largest and most homogeneous segment of the image. This initial seed point of the segment is expanded using a region growing method. Other texture segments of the image are extracted analogously in turn. At the second stage, the procedure of merging the extracted segments belonging to the same texture class is performed. Then, the detected texture segments are input to a neural network with competitive layers which accomplishes more accurate delineation of the shapes of the extracted texture segments. The proposed segmentation procedure is fully unsupervised, i.e., it does not use any a priori knowledge on either the type of textures or the number of texture segments in the image. The research results in development of the segmentation algorithm realized as a computer program tested in a series of experiments that demonstrate its efficiency on grayscale natural scenes.

A fast computationally efficient method for automatic segmentation and classification of textured images is presented. The method does not necessarily need a-priori information about the textures present in the image, thus avoiding the necessity of a training set of textures. A fast adaptive multichannel technique for autoregressive image model parameter estimation with fast tracking capabilities and a powerful statistical distance measure are appropriately interweaved to form the proposed technique. Specific properties of the estimation part of the algorithm are exploited to reduce greatly the computational complexity of the distance measure. Some interesting extensions of the method are discussed and examples are given which illustrate the performance of the algorithm. >

Image segmentation is the technique of dividing an image into one of kind regions (segments) following some homogeneous criteria. It is an important technique in any image analysis process. Segmentation of medical images like magnetic resonance images, mammogram, cardiac Magnetic resonance (MRIs) images helps in detection and diagnosis of breast tumor, brain tumor, etc. We need a strong and efficient image segmentation method, as most segmentation methods are computationally high priced, and the amount of medical imaging information is growing and very sensitive. In this paper, we delve into different methods available for medical image segmentation with their standpoints. We also compare the two authors’ results based on the parameters True Positive Factor (TPF), True Negative Factor (TNF), and Sum of True Volume Factor (SVTF).

Statistical shape modelling is an efficient and robust method for medical image segmentation in computer-aided diagnosis. The key step in building a statistical shape model is to find corresponding landmarks in each instance of a training set. In this paper, a novel landmark correspondence estimation method that uses edge collapse surface simplification and the sphere registration is proposed. All the landmarks are selected and transformed by spherical conformal mapping from the instances of the training set and the associated correspondence are automatically found on the spheres. We applied our method on 21 cases of 3-D right lung shapes. The results of image segmentation experiment indicate that our method has a positive influence on the accuracy of segmentation result.

The hidden Markov random field (HMRF) model is an efficient method for image segmentation. However, it may not accurately segment a poorly defined image like Magnetic Resonance (MR) brain image. The HMRF model uses an initial estimation for tissue segmentation of MR brain image. The initial estimation of an input image has a large role to play to obtain a robust HMRF model. In general, a hard clustering method is used for initial estimation. However, it is not an efficient technique for the segmentation of a complex and irregular shape image like MR brain image. The method of clustering acts as a preprocessing step in improving the performance of HMRF. It aims at producing a set of concise data in the segmentation of brain tissues. In this paper, we propose a new approach to HMRF model, which incorporates the fuzzy C-means (FCM) clustering for the initial estimation of the brain image, which is not found in the literature. This results in efficient segmentation of brain tissues. The results are compared with the spatial FCM clustering algorithm and HMRF model with K-means clustering, using different segmentation evaluation indices. It is seen that the results are better than the other methods.

This paper presents the first Learning Automaton-based solution to the dynamic single source shortest path problem. It involves finding the shortest path in a single-source stochastic graph topology where there are continuous probabilistic updates in the edge-weights. The algorithm is significantly more efficient than the existing solutions, and can be used to find the "statistical" shortest path tree in the "average" graph topology. It converges to this solution irrespective of whether there are new changes in edge-weights taking place or not. In such random settings, the proposed learning automata solution converges to the set of shortest paths. On the other hand, the existing algorithms will fail to exhibit such a behavior, and would recalculate the affected shortest paths after each weight-change. The important contribution of the proposed algorithm is that all the edges in a stochastic graph are not probed, and even if they are, they are not all probed equally often. Indeed, the algorithm attempts to almost always probe only those edges that will be included in the shortest path graph, while probing the other edges minimally. This increases the performance of the proposed algorithm. All the algorithms were tested in environments where edge-weights change stochastically, and where the graph topologies undergo multiple simultaneous edge-weight updates. Its superiority in terms of the average number of processed nodes, scanned edges and the time per update operation, when compared with the existing algorithms, was experimentally established. The algorithm can be applicable in domains ranging from ground transportation to aerospace, from civilian applications to military, from spatial database applications to telecommunications networking.