Finding Shortest Paths Research Articles

Computerized image analysis: Texture‐field orientation method for pectoral muscle identification on MLO‐view mammograms

To develop a new texture-field orientation (TFO) method that combines a priori knowledge, local and global information for the automated identification of pectoral muscle on mammograms. The authors designed a gradient-based directional kernel (GDK) filter to enhance the linear texture structures, and a gradient-based texture analysis to extract a texture orientation image that represented the dominant texture orientation at each pixel. The texture orientation image was enhanced by a second GDK filter for ridge point extraction. The extracted ridge points were validated and the ridges that were less likely to lie on the pectoral boundary were removed automatically. A shortest-path finding method was used to generate a probability image that represented the likelihood that each remaining ridge point lay on the true pectoral boundary. Finally, the pectoral boundary was tracked by searching for the ridge points with the highest probability lying on the pectoral boundary. A data set of 130 MLO-view digitized film mammograms (DFMs) from 65 patients was used to train the TFO algorithm. An independent data set of 637 MLO-view DFMs from 562 patients was used to evaluate its performance. Another independent data set of 92 MLO-view full field digital mammograms (FFDMs) from 92 patients was used to assess the adaptability of the TFO algorithm to FFDMs. The pectoral boundary detection accuracy of the TFO method was quantified by comparison with an experienced radiologist's manually drawn pectoral boundary using three performance metrics: The percent overlap area (POA), the Hausdorff distance (Hdist), and the average distance (AvgDist). The mean and standard deviation of POA, Hdist, and AvgDist were 95.0 +/- 3.6%, 3.45 +/- 2.16 mm, and 1.12 +/- 0.82 mm, respectively. For the POA measure, 91.5%, 97.3%, and 98.9% of the computer detected pectoral muscles had POA larger than 90%, 85%, and 80%, respectively. For the distance measures, 85.4% and 98.0% of the computer detected pectoral boundaries had Hdist within 5 and 10 mm, respectively, and 99.4% of computer detected pectoral muscle boundaries had AvgDist within 5 mm from the radiologist's manually drawn boundaries. The pectoral muscle on DFMs can be detected accurately by the automated TFO method. The preliminary study of applying the same pectoral muscle identification algorithm to FFDMs without retraining demonstrates that the TFO method is reasonably robust against the differences in the image properties between the digitized and digital mammograms.

Neuroptikon: a customizable tool for dynamic, multi-scale visualization of complex neural circuits

Event Abstract Back to Event Neuroptikon: a customizable tool for dynamic, multi-scale visualization of complex neural circuits Frank Midgley1*, Donald J. Olbris1, Dmitri Chklovskii1 and Vivek Jayaraman1 1 HHMI, Janelia Farm Research Campus, United States Groups around the world are using electron and light microscopy, optogenetics and physiology to map neural connectivity in a variety of brain regions and species. Having the circuit diagram for a brain region is potentially very useful, but how should such information be represented? The visualization of neural circuits becomes difficult as the density of both a circuit’s connections and the data associated with the components of the circuit increases. Visualizing the entire circuit causes fine detail to be lost, while focusing on specific components hides their context within the larger circuit. We have developed an open-source, Python-based, abstract circuit visualization package, Neuroptikon, which overcomes these problems with an expandable suite of interactive tools. Circuits are represented in Neuroptikon at both a biological and a visual level. A simple biological model allows the construction of neural circuits from regions, neurons and/or neurites and can be extended by user-defined attributes. A NetworkX (Hagberg et al. 2008) version of the circuit is maintained which allows graph-theoretic analysis. A flexible visualization layer sits above the model and allows any biological attributes (built-in or user-defined parameter-value pairs) to control the display of some or all of the circuit’s components. Circuit components can be positioned in two or three dimensions either manually or automatically by one of the included layout algorithms. Visualizations can be managed independently of circuits allowing multiple styles of visualization for the same circuit (say, an anatomically accurate layout of neurons versus a layout based on wiring optimization or one chosen for maximum clarity) and re-use of the same visualization for different circuits. Neuroptikon allows interaction with circuits through its graphical and scripting interfaces. A basic set of interactive tools including local connectivity highlighting and shortest path finding are provided by the graphical interface. Both the biological model and visualization layer can be queried and modified via the scripting interface. Script commands can be executed interactively or via saved scripts. The scripting interface also allows expansion of the user interface via new layout algorithms, custom inspectors, etc. We have developed a software package that enables an abstracted representation of neural circuits suitable for conceptual analysis and experimental design. This tool can also serve as a useful front-end for repositories of neuroanatomical and neurophysiological data, and citation databases indexed by neuroanatomical features. Neuroptikon has been used to model and visualize synapse level connectivity in C. elegans, compartmental arborizations in Drosophila and region level connectivity in the primate visual cortex, and we will present these test cases as part of a demonstration of the tool.

A Border Line-Based Pruning Scheme for Shortest Path Computations

With the progress of IT and mobile positioning technologies, various types of location-based services (LBS) have been proposed and implemented. Finding a shortest path between two nodes is one of the most fundamental tasks in many LBS related applications. So far, there have been many research efforts on the shortest path finding problem. For instance, A * algorithm estimates neighboring nodes using a heuristic function and selects minimum cost node as the closest one to the destination. Pruning method, which is known to outperform the A * algorithm, improves its routing performance by avoiding unnecessary exploration in the search space. For pruning, shortest paths for all node pairs in a map need to be pre-computed, from which a shortest path container is generated for each edge. The container for an edge consists of all the destination nodes whose shortest path passes through the edge and possibly some unnecessary nodes. These containers are used during routing to prune unnecessary node visits. However, this method shows poor performance as the number of unnecessary nodes included in the container increases. In this paper, we focus on this problem and propose a new border line-based pruning scheme for path routing which can reduce the number of unnecessary node visits significantly. Through extensive experiments on randomly-generated, various complexity of maps, we empirically find out optimal number of border lines for clipping containers and compare its performance with other methods.

Dynamic shortest path problems with time-varying costs

This paper concerns the problem of finding shortest paths from one node to all other nodes in networks for which arc costs can vary with time, each arc has a transit time, and parking with a corresponding time-varying cost is allowed at the nodes. The transit times can also take negative values. A general labeling method, as well as several implementations, are presented for finding shortest paths and detecting negative cycles under the assumption that arc traversal costs are piecewise linear and node parking costs are piecewise constant.

A self-organizing shortest path finding strategy on complex networks

The shortcomings of traditional methods to find the shortest path are revealed, and a strategy of finding the self-organizing shortest path based on thermal flux diffusion on complex networks is presented. In our method, the shortest paths between the source node and the other nodes are found to be self-organized by comparing node temperatures. The computation complexity of the method scales linearly with the number of edges on underlying networks. The effects of the method on several networks, including a regular network proposed by Ravasz and Barabási which is called the RB network, a real network, a random network proposed by Ravasz and Barabási which is called the ER network and a scale-free network, are also demonstrated. Analytic and simulation results show that the method has a higher accuracy and lower computational complexity than the conventional methods.

A quick estimate of the strength of uniaxially tied framed structures

A quick direct limit analysis method to estimate the strength of structures consisting of beam and cable-type members is proposed. The method is based on the kinematic theorem of plasticity and uses equilibrium arguments only. The influence of tension members is accounted for separately, using a shortest path finding technique between the two ends of each such member. The same technique also handles the effect of the indeterminacy for the rest of the structure and the equilibrium with the applied loads. The efficiency of the method is shown through its application to three different structures of increased complexity.

The theory and application of tolerance relations

We present four different but equivalent statements of tolerance relations. Based on the connection among tolerance relation, covering and approximation, we introduce the concept of maximal covering network and apply it to complex network analysis. A new algorithm for the shortest path finding of networks is given.

COMBING MULTILEVEL GREEN'S FUNCTION INTERPOLATION METHOD WITH VOLUME LOOP BASES FOR INDUCTANCE EXTRACTION PROBLEMS

In this paper,a fast integral equation method is developed for extracting the inductances in RF ICs,RF MEMs,IC packages,and deep submicron ICs etc. This method combines a recently developed Multilevel Green's Function Interpolation Method (MLGFIM) (1,2) with the volume integral equation discretized using Volume Loop (VL) basis functions. In it,instead of using the filaments model to simulate the currents flowing in the inductors,we use the conventional SWG basis functions for this kind of basis functions is flexible for problems with complex geometries. The shortest path finding algorithm is also used to find the source loop basis functions. The inductance extractions from the straight line,the spiral inductors,the bump,and the parallel buses in this paper demonstrate the validity and efficiency of this hybrid method.

The shortest path finding method for MIMD controlled MX Core

The shortest path finding method for MIMD controlled MX Core

Distance and nearest neighbor transforms on gray-level surfaces

This article presents an efficient priority pixel queue algorithm for calculating the distance transform on curved space (DTOCS), the corresponding nearest neighbor transform, and the new projection DTOCS (PDTOCS). The transforms provide tools for approximating distances and finding shortest paths on gray-level surfaces. Surface variation, or roughness, can also be measured.

Navigation in small-world networks: a scale-free continuum model

The small-world phenomenon, the principle that we are all linked by a short chain of intermediate acquaintances, has been investigated in mathematics and social sciences. It has been shown to be pervasive both in nature and in engineering systems like the World Wide Web. Work of Jon Kleinberg has shown that people, using only local information, are very effective at finding short paths in a network of social contacts. In this paper we argue that the underlying key to finding short paths is scale invariance. In order to appreciate scale invariance we suggest a continuum setting, since true scale invariance happens at all scales, something which cannot be observed in a discrete model. We introduce a random-connection model that is related to continuum percolation, and we prove the existence of a unique scale-free model, among a large class of models, that allows the construction, with high probability, of short paths between pairs of points separated by any distance.

Navigation in small-world networks: a scale-free continuum model

The small-world phenomenon, the principle that we are all linked by a short chain of intermediate acquaintances, has been investigated in mathematics and social sciences. It has been shown to be pervasive both in nature and in engineering systems like the World Wide Web. Work of Jon Kleinberg has shown that people, using only local information, are very effective at finding short paths in a network of social contacts. In this paper we argue that the underlying key to finding short paths is scale invariance. In order to appreciate scale invariance we suggest a continuum setting, since true scale invariance happens at all scales, something which cannot be observed in a discrete model. We introduce a random-connection model that is related to continuum percolation, and we prove the existence of a unique scale-free model, among a large class of models, that allows the construction, with high probability, of short paths between pairs of points separated by any distance.

Curve Matching, Time Warping, and Light Fields: New Algorithms for Computing Similarity between Curves

The problem of curve matching appears in many application domains, like time series analysis, shape matching, speech recognition, and signature verification, among others. Curve matching has been studied extensively by computational geometers, and many measures of similarity have been examined, among them being the Frechet distance (sometimes referred in folklore as the "dog-man" distance). A measure that is very closely related to the Frechet distance but has never been studied in a geometric context is the Dynamic Time Warping measure (DTW), first used in the context of speech recognition. This measure is ubiquitous across different domains, a surprising fact because notions of similarity usually vary significantly depending on the application. However, this measure suffers from some drawbacks, most importantly the fact that it is defined between sequences of points rather than curves. Thus, the way in which a curve is sampled to yield such a sequence can dramatically affect the quality of the result. Some attempts have been made to generalize the DTW to continuous domains, but the resulting algorithms have exponential complexity. In this paper we propose similarity measures that attempt to capture the "spirit" of dynamic time warping while being defined over continuous domains, and present efficient algorithms for computing them. Our formulation leads to a very interesting connection with finding short paths in a combinatorial manifold defined on the input chains, and in a deeper sense relates to the way light travels in a medium of variable refractivity.

An efficient fault-containing self-stabilizing algorithm for the shortest path problem

Shortest path finding has a variety of applications in transportation and communication. In this paper, we propose a fault-containing self-stabilizing algorithm for the shortest path problem in a distributed system. The improvement made by the proposed algorithm in stabilization times for single-fault situations can demonstrate the desirability of an efficient fault-containing self-stabilizing algorithm. For single-fault situations, the worst-case stabilization time of the proposed algorithm is O(Δ), where Δ is the maximum node degree in the system, and the contamination number of the proposed algorithm is 1.

Finding Shortest Paths Under Time-Bandwidth Constraints by Using Elliptical Minimal Search Area

Although many studies on shortest-path algorithms have been conducted, few of them have taken advantage of the added characteristics of highway networks and, thus, have failed to become more efficient in finding shortest paths, or lowest-cost paths, for transportation problems. A new concept is proposed for enhancing most existing shortest-path algorithms. Taking advantage of the geographical nature of most transportation networks, the new concept uses a minimal search area to reduce the amount of computations that must be performed by existing algorithms. To simplify the analysis, a hypothetical network in an L1 metric was used to approximate two-dimensional roadways. Empirical results from thousands of shortest paths between arbitrary origin-destination pairs suggested that an elliptical shape is most suitable for confining the search area when seeking a shortest path. Further analysis established the formulation of the ellipse, which becomes rounder when the origin is close to the destination and more ...

Finding Shortest Paths under Time–Bandwidth Constraints by using Elliptical Minimal Search Area

Although many studies on shortest-path algorithms have been conducted, few of them have taken advantage of the added characteristics of highway networks and, thus, have failed to become more efficient in finding shortest paths, or lowest-cost paths, for transportation problems. A new concept is proposed for enhancing most existing shortest-path algorithms. Taking advantage of the geographical nature of most transportation networks, the new concept uses a minimal search area to reduce the amount of computations that must be performed by existing algorithms. To simplify the analysis, a hypothetical network in an L1 metric was used to approximate two-dimensional roadways. Empirical results from thousands of shortest paths between arbitrary origin–destination pairs suggested that an elliptical shape is most suitable for confining the search area when seeking a shortest path. Further analysis established the formulation of the ellipse, which becomes rounder when the origin is close to the destination and more elongated when the two points are far apart. The elliptical minimal search area is stable and has a high level of confidence in containing the true shortest path, even if the cost function for each link is dynamic or stochastic. A list of future tasks is presented to further the promising findings of this research. The algorithm, which is not in itself a shortest algorithm per se, can enhance other shortest-path algorithms for transportation roadway networks.

A self-stabilizing algorithm for the shortest path problem assuming the distributed demon

Shortest path finding has a variety of applications in transportation and communication.In this paper, we study a well-known self-stabilizing algorithm for the shortest path problem for the distributed systems. The previous works on this topic had two assumptions that can be relaxed in this paper. First, in the previous works, the systems were assumed to be integral-weighted, whereas in this paper, the systems are real-weighted. Second, and more importantly, the previous works have shown that the algorithm is self-stabilizing under the more restricted central demon model, whereas in this paper, we give a rigorous proof showing that the algorithm is actually self-stabilizing under the more general distributed demon model. The work in this paper is of significance because in the existing literature on self-stabilizing systems, most of the papers regarding the distributed demon are for the ring networks only; there are very few papers that discuss the self-stabilizing algorithms for the general distributed systems assuming the distributed demon model.

A self-stabilizing algorithm for the shortest path problem assuming read/write atomicity

Shortest path finding has a variety of applications in the areas of transportation and communication in distributed systems. In this paper, we design and prove the correctness of a self-stabilizing algorithm that solves the single-source shortest path problem for a distributed system. Unlike all previous works on this topic, the model of computation employed by the system in this paper assumes the separate read/write atomicity introduced by Dolev et al. instead of the commonly used composite read/write atomicity introduced by Dijkstra.

An optimal parallel algorithm for solving all-pairs shortest paths problem on circular-arc graphs

The shortest-paths problem is a fundamental problem in graph theory and finds diverse applications in various fields. This is why shortest path algorithms have been designed more thoroughly than any other algorithm in graph theory. A large number of optimization problems are mathematically equivalent to the problem of finding shortest paths in a graph. The shortest-path between a pair of vertices is defined as the path with shortest length between the pair of vertices. The shortest path from one vertex to another often gives the best way to route a message between the vertices. This paper presents anO(n2) time sequential algorithm and anO(n2/p+logn) time parallel algorithm on EREW PRAM model for solving all pairs shortest paths problem on circular-arc graphs, wherep andn represent respectively the number of processors and the number of vertices of the circular-arc graph.

삼차원 메쉬에 대한 기하학 라이브와이어와 기하학 라이브레인

이차원 영상에서 정의된 에지와 유사하게 삼차원 메쉬에서도 주요 부위의 경계를 표현하는 기하학 특징을 정의할 수 있다. 삼차원 메쉬에서 기하학 특징은 메쉬 단순화, 메쉬 변형과 메쉬 편집 등과 같은 여러 응용에 기본적인 항목으로 사용되고 있다. 본 논문에서는 삼차원 메쉬의 기학적 특징을 효과적으로 찾기 위하여 이차원 영상의 라이브와이어와 라이브레인 기법을 삼차원 메쉬로 확장한 기하학 라이브와이어와 기하학하 라이브레인 기법을 제안한다. 제안된 기법에서는 메쉬의 기하학 특징을 나타내기 위하여 근사곡률을 사용하였고 메쉬 그 자체를 정의된 비용함수를 에지의 가중치고 가지는 가중치 방향그래프로 나타내었다. 그리고 만들어진 가중치 방향그래프에 대해 잘 알려진 최단경로 탐색 알고리즘을 이용하여 사용자에 의해 지정된 점들 사이에 존재하는 삼차원 메쉬에서의 기하학 특징을 추출하였다. 본 논문에서는 사람 얼굴, 소, 신발과 치어 메쉬 모델에 나타나는 기하학 특징을 추출하기 위하여 제안한 기법을 적용하여 얻어진 결과를 가시화한다. Similarly to the edges defined in a 2D image, we can define the geometric features representing the boundary of the distinctive parts appearing on 3D meshes. The geometric features have been used as basic primitives in several applications such as mesh simplification, mesh deformation, and mesh editing. In this paper, we propose geometric livewire and geometric livelane for extracting geometric features in a 3D mesh, which are the extentions of livewire and livelane methods in images. In these methods, approximate curvatures are adopted to represent the geometric features in a 3D mesh and the 3D mesh itself is represented as a weighted directed graph in which cost functions are defined for the weights of edges. Using a well-known shortest path finding algorithm in the weighted directed graph, we extracted geometric features in the 3D mesh among points selected by a user. In this paper, we also visualize the results obtained from applying the techniques to extracting geometric features in the general meshes modeled after human faces, cows, shoes, and single teeth.