P. Javaheri, J. P. Lowman · Journal of Geophysical Research Solid Earth · 2026
Abstract As spherical shell mantle convection models become increasingly commonplace, understanding how plates are generated has raised the issue of how to recognize whether rigid plates are present in model output. Tectonocists have long recognized that intraplate regions are not rigid without exception. Specifically, lithospheric deformation, widely evident on the continents, also occurs within oceanic regions and additionally results in tectonic plate boundaries having varying widths. These, non‐rigid, diffuse regions comprise roughly 15% of the terrestrial surface and identification of their analogs in models is an important step in recognizing progress on the goal of modeling plate generation. We describe a new plate detection tool, platerecipy , that utilizes the Random Walker segmentation algorithm to identify candidate plates in both mantle convection model output and global geophysical data sets. The method produces a set of probabilities for each surface data point that can be used to both assess confidence in the association of each location with a distinct rigid plate, and identify diffuse regions across the surface. Verification of the rigidity of each region identified as a distinct plate can be obtained by inverting the associated data for the candidate plate's Euler vector. We demonstrate the method's sensitivity to the three controlling parameters used by platerecipy 's algorithm and how the method can be used to determine the Euler vectors of plates identified in a mantle convection model. We also present promising results found by inverting for the Euler vectors of the Earth's major plates through applying platerecipy to a global strain‐rate field.
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Heinrich Matzinger, Angelica Pachon Pinzon · 2009
Abstract. In this article we consider a simple random walker moving on a random media. Whilst doing so, the random walker observes at each point of time the “color ” of the location he is at. This process creates a sequence of observations. We consider the problem of determining when the walker is close to the origin. For this we are only given, the observations made by the walker as well as a small portion of the media close to the origin. With that information alone, we show that we can typically construct an exponential number of stopping times, which all occur whilst the walker is on the small piece of media available to us. The number is exponential in the size of that small piece of media. So far this problem could only be solved when the media contained 5 colors. In the present article, we use a subtle entropy argument on the set of possible observations given the point where the walker starts and given the media in that neighborhood. This allows us to achieve our goal when the media contains 4 equiprobable colors. The random media is often called “scenery”. An important area of research is Scenery Reconstruction, in which one tries to retrieve the scenery based on the observations made by the random walker alone. Finding times when the random walker is close to the origin is the main hurdle for building a scenery reconstruction algorithm. Our present result, implies that the Scenery Reconstruction result in Hart et al. (2011) also applies with 4 colors as opposed to just 5 colors. The less colors the more difficult these problems become. 1.
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Christos G. Bampis, Petros Maragos, Alan C. Bovik · IEEE Transactions on Image Processing · 2016
We propose graph-driven approaches to image segmentation by developing diffusion processes defined on arbitrary graphs. We formulate a solution to the image segmentation problem modeled as the result of infectious wavefronts propagating on an image-driven graph where pixels correspond to nodes of an arbitrary graph. By relating the popular Susceptible - Infected - Recovered epidemic propagation model to the Random Walker algorithm, we develop the Normalized Random Walker and a lazy random walker variant. The underlying iterative solutions of these methods are derived as the result of infections transmitted on this arbitrary graph. The main idea is to incorporate a degree-aware term into the original Random Walker algorithm in order to account for the node centrality of every neighboring node and to weigh the contribution of every neighbor to the underlying diffusion process. Our lazy random walk variant models the tendency of patients or nodes to resist changes in their infection status. We also show how previous work can be naturally extended to take advantage of this degreeaware term which enables the design of other novel methods. Through an extensive experimental analysis, we demonstrate the reliability of our approach, its small computational burden and the dimensionality reduction capabilities of graph-driven approaches. Without applying any regular grid constraint, the proposed graph clustering scheme allows us to consider pixellevel, node-level approaches and multidimensional input data by naturally integrating the importance of each node to the final clustering or segmentation solution. A software release containing implementations of this work and supplementary material can be found at: http://cvsp.cs.ntua.gr/research/GraphClustering/.
Cited by 69
Chi‐Ok Hwang, Michael Mascagni · Applied Physics Letters · 2001
A discrete random walk method on grids was proposed and used to solve the linearized Poisson–Boltzmann equation (LPBE) [R. Ettelaie, J. Chem. Phys. 103, 3657 (1995)]. Here, we present an efficient grid-free random walk method. Based on a modified “walk on spheres” algorithm [B. S. Elepov and G. A. Mihailov, Sov. Math. Dokl. 14, 1276 (1973)] for the LPBE, this Monte Carlo algorithm uses a survival probability distribution function for the random walker in a continuous and free diffusion region. This simulation method is illustrated by computing four analytically solvable problems. In all cases, excellent agreement is observed.
Cited by 17Open access
Yang Wei Koh, Adelene Y. L. Sim, Hwee Kuan Lee · Physical Review E · 2015
We study the mechanism behind dynamical trappings experienced during Wang-Landau sampling of continuous systems reported by several authors. Trapping is caused by the random walker coming close to a local energy extremum, although the mechanism is different from that of the critical slowing-down encountered in conventional molecular dynamics or Monte Carlo simulations. When trapped, the random walker misses the entire or even several stages of Wang-Landau modification factor reduction, leading to inadequate sampling of the configuration space and a rough density of states, even though the modification factor has been reduced to very small values. Trapping is dependent on specific systems, the choice of energy bins, and the Monte Carlo step size, making it highly unpredictable. A general, simple, and effective solution is proposed where the configurations of multiple parallel Wang-Landau trajectories are interswapped to prevent trapping. We also explain why swapping frees the random walker from such traps. The efficacy of the proposed algorithm is demonstrated.
Cited by 3Open access
Reza Dorrigiv, Alejandro López-ortiz · 2008
Abstract—We study the performance of several search algorithms on unstructured peer-to-peer networks, both using classic search algorithms such as flooding and random walk, as well as a new hybrid algorithm proposed in this paper. This hybrid algorithm first uses flooding to find sufficient number of nodes and then starts random walks from these nodes. We compare the performance of the search algorithms on several graphs corresponding to common topologies proposed for peerto-peer networks. In particular, we consider binomial random graphs, regular random graphs, power-law graphs, and clustered topologies. Our experiments show that for binomial random graphs and regular random graphs all algorithms have similar performance. For power-law graphs, flooding is effective for small number of messages, but for large number of messages our hybrid algorithm outperforms it. Flooding is ineffective for clustered topologies in which random walk is the best algorithm. For these topologies, our hybrid algorithm provides a compromise between flooding and random walk. We also compare the proposed hybrid algorithm with the k-walker algorithm on power-law and clustered topologies. Our experiments show that while they have close performance on clustered topologies, the hybrid algorithm has much better performance on power-law graphs. We theoretically prove that flooding is effective for regular random graphs which is consistent with our experimental results. I.
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Erik Jenner, Enrique Fita Sanmartín, Fred A. Hamprecht · arXiv (Cornell University) · 2021
The minimum graph cut and minimum $s$-$t$-cut problems are important\nprimitives in the modeling of combinatorial problems in computer science,\nincluding in computer vision and machine learning. Some of the most efficient\nalgorithms for finding global minimum cuts are randomized algorithms based on\nKarger's groundbreaking contraction algorithm. Here, we study whether Karger's\nalgorithm can be successfully generalized to other cut problems. We first prove\nthat a wide class of natural generalizations of Karger's algorithm cannot\nefficiently solve the $s$-$t$-mincut or the normalized cut problem to\noptimality. However, we then present a simple new algorithm for seeded\nsegmentation / graph-based semi-supervised learning that is closely based on\nKarger's original algorithm, showing that for these problems, extensions of\nKarger's algorithm can be useful. The new algorithm has linear asymptotic\nruntime and yields a potential that can be interpreted as the posterior\nprobability of a sample belonging to a given seed / class. We clarify its\nrelation to the random walker algorithm / harmonic energy minimization in terms\nof distributions over spanning forests. On classical problems from seeded image\nsegmentation and graph-based semi-supervised learning on image data, the method\nperforms at least as well as the random walker / harmonic energy minimization /\nGaussian processes.\n
Cited by 1Open access
Stellinga, Bram (author) · Research Repository (Delft University of Technology) · 2023
The segmentation of anatomical structures in 3D medical images is crucial for various applications in the field of medical imaging. Fully automated methods often lack accuracy, while manual segmenting requires much time and effort from a user. Due to this, Active Learning approaches are being proposed to solve this by making the method interactive. This is done by iteratively segmenting the image based on user provided input, which can then be added to correct uncertain regions of intermediate segmentation results. We propose a method to improve a Random Walker (RW) algorithm that is used for interactive 3D medical image segmentation, by integrating an ensemble of predicted segmentations obtained by a previously trained Bayesian Deep Neural Network (BDNN). The predictions are used to improve the weight function used by the RW to indicate the similarity of neighbouring voxels. We evaluate our results by combining the weight function originally used by the RW, with two custom approaches, Mean Predictions and Unanimous Votes. Both are combined with the original RW's weights in the form of a weighted sum. Mean Predictions is based on only the mean of all predictions for each voxel, while Unanimous Votes only considers averages of either exactly 1 or 0. Lastly, we will propose a method to combine the original weight function with the mean predictions by summing together the image intensities with the mean predictions while keeping the variance normalized. All results are evaluated using both synthetic data and empirical data from a MICCAI dataset. Lastly, our method shows that the Adaptive Alpha Approach outperforms all other methods including the original RW in terms of average DICE Coeffients for the first two iterations.
Cited by 0Open access
Shawn Andrews, Ghassan Hamarneh, Ahmed Saad · 2010
Abstract. Updating segmentation results in real-time based on repeated user in-put is a reliable way to guarantee accuracy, paramount in medical imaging ap-plications, while making efficient use of an expert’s time. The random walker algorithm with priors is a robust method able to find a globally optimal proba-bilistic segmentation with an intuitive method for user input. However, like many other segmentation algorithms, it can be too slow for real-time user interaction. We propose a speedup to this popular algorithm based on offline precomputation, taking advantage of the time images are stored on servers prior to an analysis session. Our results demonstrate the benefits of our approach. For example, the segmentations found by the original random walker and by our new precomputa-tion method for a given 3D image have a Dice’s similarity coefficient of 0.975, yet our method runs in 1/25th of the time. 1
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Hidekatsu TOKUMARU, Hideaki Sakai · JSME international journal · 1987
Recent trends in random data analysis with parametric and nonparametric approaches are reviewed. First, for nonparametric spectrum analysis, the effectiveness of using data windows is emphasized with an example. Secondly, based on a recursive algorithm by Levinson and Durbin, various autoregressive (AR) spectrum estimation techniques by Yule-Walker, Burg and others are explained together with their specific properties. Also, selection criteria for the order of AR model fitting are briefly discussed. As for autoregressive moving average (ARMA) spectrum estimation, the high order Yule-Walker method and its variants are mentioned. Finally, a periodic AR model is introduced for treating random data with periodic structures. An example of applying this model to real temperature data is also given.
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Mahdi Ghorbani, Mohammad Reza Meybodi, Ali Mohammad Saghiri · 2013
Abstract — One of the most important issues in peer-to-peer networks is locating objects among a lot of data. There have been different search methods to find data with certain advantages and disadvantages. In this paper, we propose a new version of k-random walk algorithm utilizing learning automata. In this distributed method, the value of k for k-random walk is not selected randomly but it is selected in an adaptive manner. It is decided which walker is more useful to be selected in order to keep on the search according to past experience of each node. Simulation results show that the novel search algorithm improves the number of hits per query, success rate, generated messages per query and objects discovery delay in comparison with the k-random walk algorithm. Keywords-peer-t-peer; search; random walk; learning automata theory I.
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Guo Peng-fe · 2014
Random walk algorithm only considers the gray similarity of adjacent pixels,ignores neighboring pixels gradient information.This suppresses random walker walking to the seed point along some edges of similar gray to seed point,resulting in misclassification and missing points.This paper presented a segmentation method of brain image.It extracts image gradient information by using wavelet transform,and puts the gradient information into the edge weight.Finally using improved FCM algorithm,combining with the pixel neighborhood information,we obtained a final split brain image.Experimental results show that this method improves segmentation correct rate and the edge of the segmented image is smoother.
Cited by 0
Mehrdad MOGHBEL, Syamsiah MASHOHOR, Rozi MAHMUD et al. · Universiti Putra Malaysia Institutional Repository (Universiti Putra Malaysia) · 2017
Breast and areola boundary detection and segmentation present the biggest challenge in breast segmentation from thermography images, as breast boundaries, especially in the upper quadrants of the breast, are nonexistent. Many segmentation approaches have been proposed for breast segmentation, such as active contours and snakes, circular Hough transforms, and live wires, but these methods often fail to achieve satisfactory results. With recent advances in image processing techniques, new segmentation concepts are being developed, such as random walkers, which have received high interest from the medical imaging community. In this study, 91 images acquired utilizing a FLIR A320 thermal camera are used for developing an automatic breast segmentation from thermography images based on the random walker algorithm. A series of enhancement filters are applied to the image to make areola detection more accurate. Afterwards, the areola is detected using a series of circular Hough transforms. The detected areola region is then utilized for automatic seed placement for the random walker algorithm. Based on expert radiologist evaluation, the proposed segmentation algorithm was able to achieve 81.3% success rate in breast segmentation, while there was a 37.5% increase in the detection of breast cancer-related abnormalities by radiologists utilizing the segmented images, compared to utilizing original images.
Cited by 0
Joseph Farnan, Franklin Kenter · arXiv (Cornell University) · 2021
For a directed graph, the Pagerank algorithm emulates a random walker on the graph that occasionally "jumps" to a random vertex based on a jumping parameter $α$. Upon completion, the algorithm generates a stochastic vector whose entries correspond to the limiting probability that the walker will be at that vertex. This vector is a right eigenvector of a corresponding Markov trasition matrix. Undoubtedly, this vector can drastically change based upon the jumping parameter $α$. In this article, we investigate the maximum possible discrepancy for different Pagerank vectors on the same unweighted directed (perhaps with loops) graph as measured by the 2-norm. We show that the limsup of this discrepancy can be as large as $\sqrt{\frac{67}{50}}$ using a very specific construction. (For contrast, the norm of the difference for any two stochastic vectors is at most $\sqrt{2}$.) Interestingly, on this construction this discrepancy occurs when $α= 1$ and when $α$ is very close to 1.
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Noah Lee, R. Theodore Smith, Andrew F. Laine · Columbia Academic Commons (Columbia University) · 2008
Fundus auto-fluorescence (FAF) imaging is a non-invasive technique for in vivo ophthalmoscopic inspection of age-related macular degeneration (AMD), the most common cause of blindness in developed countries. Geographic atrophy (GA) is an advanced form of AMD and accounts for 12-21% of severe visual loss in this disorder [3]. Automatic quantification of GA is important for determining disease progression and facilitating clinical diagnosis of AMD. The problem of automatic segmentation of pathological images still remains an unsolved problem. In this paper we leverage the watershed transform and generalized non-linear gradient operators for interactive segmentation and present an intuitive and simple approach for geographic atrophy segmentation. We compare our approach with the state of the art random walker [5] algorithm for interactive segmentation using ROC statistics. Quantitative evaluation experiments on 100 FAF images show a mean sensitivity/specificity of 98.3/97.7% for our approach and a mean sensitivity/specificity of 88.2/96.6% for the random walker algorithm.
Cited by 26Open access
2016
Abstract- Fundus auto-fluorescence (FAF) imaging is a non-invasive technique for in vivo ophthalmoscopic inspection of age-related macular degeneration (AMD), the most common cause of blindness in developed countries. Geographic atrophy (GA) is an advanced form of AMD and accounts for 12-21 % of severe visual loss in this disorder [3]. Automatic quantification of GA is important for determining disease progression and facilitating clinical diagnosis of AMD. The problem of automatic segmentation of pathological images still remains an unsolved problem. In this paper we leverage the watershed transform and generalized non-linear gradient operators for interactive segmentation and present an intuitive and simple approach for geographic atrophy segmentation. We compare our approach with the state of the art random walker [5] algorithm for interactive segmentation using ROC statistics. Quantitative evaluation experiments on 100 FAF images show a mean sensitivity / specificity of 98.3 / 97.7 % for our approach and a mean sensitivity / specificity of 88.2 / 96.6 % for the random walker algorithm.
Cited by 0
Hyung-Il Koo · Journal of Electronic Imaging · 2011
This paper proposes a new colorization method based on the chrominance blending. The weights for the blending are computed by using the random walker algorithm, which is a soft segmentation technique that provides sharp probability transition on object boundaries. As a result, the proposed method reduces color bleeding and provides improved colorization performances compared to conventional ones.
Cited by 2Open access
Jurij Šmakov, Kenji Harada, Naoki Kawashima · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 2003
An efficient quantum Monte Carlo algorithm for the simulation of bosonic systems on a lattice in a grand canonical ensemble is proposed. It is based on the mapping of bosonic models to the spin models in the limit of the infinite total spin quantum number. It is demonstrated how this limit may be taken explicitly in the algorithm, eliminating the systematic errors. The efficiency of the algorithm is examined for the noninteracting lattice boson model and compared with the stochastic series expansion method with the heat-bath-type scattering probability of the random walker.
Cited by 4Open access
Smakov, Jurij, Harada, Kenji, Kawashima, Naoki · arXiv (Cornell University) · 2003
An efficient Quantum Monte Carlo algorithm for the simulation of bosonic systems on a lattice in a grand canonical ensemble is proposed. It is based on the mapping of bosonic models to the spin models in the limit of the infinite total spin quantum number. It is demonstrated, how this limit may be taken explicitly in the algorithm, eliminating the systematic errors. The efficiency of the algorithm is examined for the non-interacting lattice boson model and compared with the stochastic series expansion method with the heat-bath type scattering probability of the random walker.
Cited by 0Open access
Annabel L. Davies, Theodoros Papakonstantinou, Adriani Nikolakopoulou et al. · Statistics in Medicine · 2022
Network meta-analysis (NMA) is a central tool for evidence synthesis in clinical research. The results of an NMA depend critically on the quality of evidence being pooled. In assessing the validity of an NMA, it is therefore important to know the proportion contributions of each direct treatment comparison to each network treatment effect. The construction of proportion contributions is based on the observation that each row of the hat matrix represents a so-called "evidence flow network" for each treatment comparison. However, the existing algorithm used to calculate these values is associated with ambiguity according to the selection of paths. In this article, we present a novel analogy between NMA and random walks. We use this analogy to derive closed-form expressions for the proportion contributions. A random walk on a graph is a stochastic process that describes a succession of random "hops" between vertices which are connected by an edge. The weight of an edge relates to the probability that the walker moves along that edge. We use the graph representation of NMA to construct the transition matrix for a random walk on the network of evidence. We show that the net number of times a walker crosses each edge of the network is related to the evidence flow network. By then defining a random walk on the directed evidence flow network, we derive analytically the matrix of proportion contributions. The random-walk approach has none of the associated ambiguity of the existing algorithm.
Cited by 13Open access