Showing papers on "Maxima and minima published in 2013"
TL;DR: Six new transfer functions divided into two families, s-shaped and v-shaped, are introduced and evaluated and prove that the new introduced v- shaped family of transfer functions significantly improves the performance of the original binary PSO.
Abstract: Particle Swarm Optimization (PSO) is one of the most widely used heuristic algorithms. The simplicity and inexpensive computational cost makes this algorithm very popular and powerful in solving a wide range of problems. The binary version of this algorithm has been introduced for solving binary problems. The main part of the binary version is a transfer function which is responsible to map a continuous search space to a discrete search space. Currently there appears to be insufficient focus on the transfer function in the literature despite its apparent importance. In this study six new transfer functions divided into two families, s-shaped and v-shaped, are introduced and evaluated. Twenty-five benchmark optimization functions provided by CEC 2005 special session are employed to evaluate these transfer functions and select the best one in terms of avoiding local minima and convergence speed. In order to validate the performance of the best transfer function, a comparative study with six recent modifications of BPSO is provided as well. The results prove that the new introduced v-shaped family of transfer functions significantly improves the performance of the original binary PSO.
766 citations
TL;DR: In this article, the authors developed a procedure extending stochastic gradient descent to the case where the function is defined on a Riemannian manifold and proved that the gradient descent algorithm converges to a critical point of the cost function.
Abstract: Stochastic gradient descent is a simple approach to find the local minima of a cost function whose evaluations are corrupted by noise. In this paper, we develop a procedure extending stochastic gradient descent algorithms to the case where the function is defined on a Riemannian manifold. We prove that, as in the Euclidian case, the gradient descent algorithm converges to a critical point of the cost function. The algorithm has numerous potential applications, and is illustrated here by four examples. In particular a novel gossip algorithm on the set of covariance matrices is derived and tested numerically.
397 citations
TL;DR: This work presents an alternative formulation for SfM based on finding a coarse initial solution using a hybrid discrete-continuous optimization, and then improving that solution using bundle adjustment, and shows that it can produce models that are similar to or better than those produced with incremental bundles adjustment, but more robustly and in a fraction of the time.
Abstract: Recent work in structure from motion (SfM) has built 3D models from large collections of images downloaded from the Internet. Many approaches to this problem use incremental algorithms that solve progressively larger bundle adjustment problems. These incremental techniques scale poorly as the image collection grows, and can suffer from drift or local minima. We present an alternative framework for SfM based on finding a coarse initial solution using hybrid discrete-continuous optimization and then improving that solution using bundle adjustment. The initial optimization step uses a discrete Markov random field (MRF) formulation, coupled with a continuous Levenberg-Marquardt refinement. The formulation naturally incorporates various sources of information about both the cameras and points, including noisy geotags and vanishing point (VP) estimates. We test our method on several large-scale photo collections, including one with measured camera positions, and show that it produces models that are similar to or better than those produced by incremental bundle adjustment, but more robustly and in a fraction of the time.
389 citations
TL;DR: In this paper, the objective function consists of a data-misfit term and a penalty term, which measures how accurately the wavefields satisfy the wave-equation, and the solution is forced to solve the waveequation and fit the observed data, which leads to significant computational savings.
Abstract: Wave-equation based inversions, such as full-waveform inversion, are challenging because of their computational costs, memory requirements, and reliance on accurate initial models. To confront these issues, we propose a novel formulation of full-waveform inversion based on a penalty method. In this formulation, the objective function consists of a data-misfit term and a penalty term which measures how accurately the wavefields satisfy the wave-equation. Because we carry out the inversion over a larger search space, including both the model and synthetic wavefields, our approach suffers less from local minima. Our main contribution is the development of an efficient optimization scheme that avoids having to store and update the wavefields by explicit elimination. Compared to existing optimization strategies for full-waveform inversion, our method differers in two main aspects; i) The wavefields are solved from an augmented wave-equation, where the solution is forced to solve the wave-equation and fit the observed data, ii) no adjoint wavefields are required to update the model, which leads to significant computational savings. We demonstrate the validity of our approach by carefully selected examples and discuss possible extensions and future research.
287 citations
TL;DR: Vevacious as discussed by the authors takes a generic expression for a one-loop effective potential energy function and finds all the tree-level extrema, which are then used as the starting points for gradient-based minimization of the 1-loop energy function.
Abstract: Several extensions of the Standard Model of particle physics contain additional scalars implying a more complex scalar potential compared to that of the Standard Model. In general these potentials allow for charge- and/or color-breaking minima besides the desired one with correctly broken SU(2)
L
×U(1)
Y
. Even if one assumes that a metastable local minimum is realized, one has to ensure that its lifetime exceeds that of our universe. We introduce a new program called Vevacious which takes a generic expression for a one-loop effective potential energy function and finds all the tree-level extrema, which are then used as the starting points for gradient-based minimization of the one-loop effective potential. The tunneling time from a given input vacuum to the deepest minimum, if different from the input vacuum, can be calculated. The parameter points are given as files in the SLHA format (though is not restricted to supersymmetric models), and new model files can be easily generated automatically by the Mathematica package SARAH. This code uses HOM4PS2 to find all the minima of the tree-level potential, PyMinuit to follow gradients to the minima of the one-loop potential, and CosmoTransitions to calculate tunneling times.
159 citations
TL;DR: This work proposes a method to plan optimal whole-body dynamic motion in multi-contact non-gaited transitions using a B-spline time parameterization for the active joints and addresses the problem of the balance within the optimization problem.
Abstract: We propose a method to plan optimal whole-body dynamic motion in multi-contact non-gaited transitions. Using a B-spline time parameterization for the active joints, we turn the motion-planning problem into a semi-infinite programming formulation that is solved by nonlinear optimization techniques. Our main contribution lies in producing constraint-satisfaction guaranteed motions for any time grid. Indeed, we use Taylor series expansion to approximate the dynamic and kinematic models over fixed successive time intervals, and transform the problem (constraints and cost functions) into time polynomials which coefficients are function of the optimization variables. The evaluation of the constraints turns then into computation of extrema (over each time interval) that are given to the solver. We also account for collisions and self-collisions constraints that have not a closed-form expression over the time. We address the problem of the balance within the optimization problem and demonstrate that generating whole-body multi-contact dynamic motion for complex tasks is possible and can be tractable, although still time consuming. We discuss thoroughly the planning of a sitting motion with the HRP-2 humanoid robot and assess our method with several other complex scenarios.
146 citations
TL;DR: In this paper, an easy-to-calculculate calibrated CCCP algorithm produces a consistent solution path which contains the oracle estimator with probability approaching one, and a high-dimensional BIC criterion is proposed to select the optimal tuning parameter which asymptotically identifies the estimator.
Abstract: We investigate high-dimensional non-convex penalized regression, where the number of covariates may grow at an exponential rate. Although recent asymptotic theory established that there exists a local minimum possessing the oracle property under general conditions, it is still largely an open problem how to identify the oracle estimator among potentially multiple local minima. There are two main obstacles: (1) due to the presence of multiple minima, the solution path is nonunique and is not guaranteed to contain the oracle estimator; (2) even if a solution path is known to contain the oracle estimator, the optimal tuning parameter depends on many unknown factors and is hard to estimate. To address these two challenging issues, we first prove that an easy-to-calculate calibrated CCCP algorithm produces a consistent solution path which contains the oracle estimator with probability approaching one. Furthermore, we propose a high-dimensional BIC criterion and show that it can be applied to the solution path to select the optimal tuning parameter which asymptotically identifies the oracle estimator. The theory for a general class of non-convex penalties in the ultra-high dimensional setup is established when the random errors follow the sub-Gaussian distribution. Monte Carlo studies confirm that the calibrated CCCP algorithm combined with the proposed high-dimensional BIC has desirable performance in identifying the underlying sparsity pattern for high-dimensional data analysis.
125 citations
TL;DR: In this paper, the stability of parameter points in the constrained minimal supersymmetric standard model was investigated and it was shown that allowed regions of the parameter space with light staus or with light stops are seriously constrained by the requirement that there are no deeper minima, even with the less strict requirement that the tunneling time out of the normal electroweak-symmetry-breaking vacuum is more than a fifth of the age of the known universe.
Abstract: The recent discovery of a Higgs boson by the LHC experiments has pro-found implications for supersymmetric models. In particular, in the context of restricted models, such as the supergravity-inspired constrained minimal supersymmetric standard model, one finds that preferred regions in parameter space have large soft supersymmetry-breaking trilinear couplings. This potentially gives rise to charge- and/or color-breaking minima besides those with the correct breaking of SU(2)L × U(1)Y. We investigate the stability of parameter points in this model against tunneling to possible deeper color- and/or charge-breaking minima of the one-loop effective potential. We find that allowed regions of the parameter space with light staus or with light stops are seriously constrained by the requirement that there are no deeper minima, and the parameter space is still quite constrained even by the less strict requirement that the tunneling time out of the normal electroweak-symmetry-breaking vacuum is more than a fifth of the age of the known Universe. We also find that “thumb rule” conditions on Lagrangian parameters based on specific directions in the tree-level potential are of limited use.
115 citations
TL;DR: The types of radial basis functions that fit in this analysis show global convergence to first-order critical points for the ORBIT algorithm and the use of ORBIT in finding local minima on a computationally expensive environmental engineering problem involving remediation of contaminated groundwater.
Abstract: We analyze globally convergent, derivative-free trust-region algorithms relying on radial basis function interpolation models. Our results extend the recent work of Conn, Scheinberg, and Vicente [SIAM J. Optim., 20 (2009), pp. 387--415] to fully linear models that have a nonlinear term. We characterize the types of radial basis functions that fit in our analysis and thus show global convergence to first-order critical points for the ORBIT algorithm of Wild, Regis, and Shoemaker [SIAM J. Sci. Comput., 30 (2008), pp. 3197--3219]. Using ORBIT, we present numerical results for different types of radial basis functions on a series of test problems. We also demonstrate the use of ORBIT in finding local minima on a computationally expensive environmental engineering problem involving remediation of contaminated groundwater.
88 citations
01 Nov 2013
TL;DR: This paper model the robust loop-closure pose-graph SLAM problem as a Bayesian network and shows that it can be solved with the Classification Expectation-Maximization (EM) algorithm, and shows proofs of the conceptual similarity between the EM algorithm and the M-Estimator.
Abstract: In this paper, we model the robust loop-closure pose-graph SLAM problem as a Bayesian network and show that it can be solved with the Classification Expectation-Maximization (EM) algorithm. In particular, we express our robust pose-graph SLAM as a Bayesian network where the robot poses and constraints are latent and observed variables. An additional set of latent variables is introduced as weights for the loop-constraints. We show that the weights can be chosen as the Cauchy function, which are iteratively computed from the errors between the predicted robot poses and observed loop-closure constraints in the Expectation step, and used to weigh the cost functions from the pose-graph loop-closure constraints in the Maximization step. As a result, outlier loop-closure constraints are assigned low weights and exert less influences in the pose-graph optimization within the EM iterations. To prevent the EM algorithm from getting stuck at local minima, we perform the EM algorithm multiple times where the loop constraints with very low weights are removed after each EM process. This is repeated until there are no more changes to the weights. We show proofs of the conceptual similarity between our EM algorithm and the M-Estimator. Specifically, we show that the weight function in our EM algorithm is equivalent to the robust residual function in the M-Estimator. We verify our proposed algorithm with experimental results from multiple simulated and real-world datasets, and comparisons with other existing works.
87 citations
TL;DR: This work applies the double-ended surface walking method to a model PES, a large set of gas phase Baker reactions, and complex surface catalytic reactions, which demonstrates that the DESW method can establish a low energy pathway linking two minima even without iterative optimization of the pathway.
Abstract: Toward the activity prediction with large-scale computations, here a double-ended surface walking (DESW) method is developed for connecting two minima on a potential energy surface (PES) and locating the associated transition state (TS) using only the first derivatives. The method operates two images starting from the initial and the final states, respectively, to walk in a stepwise manner toward each other. The surface walking involves repeated bias potential addition and local relaxation with the constrained Broyden dimer method to correct the walking direction. We apply the method to a model PES, a large set of gas phase Baker reactions, and complex surface catalytic reactions, which demonstrates that the DESW method can establish a low energy pathway linking two minima even without iterative optimization of the pathway, from which the TS can be located readily. By comparing the efficiency of the new method with the existing methods, we show that the DESW method is much less computationally demanding a...
TL;DR: The results show that the AQUARS methods generally use fewer function evaluations to identify the global minimum or to reach a target value compared to the alternatives, and are much better than EGO and MLSL coupled to MADS with kriging on the watershed calibration problem and on 15 of the test problems.
Abstract: We present the AQUARS (A QUAsi-multistart Response Surface) framework for finding the global minimum of a computationally expensive black-box function subject to bound constraints. In a traditional multistart approach, the local search method is blind to the trajectories of the previous local searches. Hence, the algorithm might find the same local minima even if the searches are initiated from points that are far apart. In contrast, AQUARS is a novel approach that locates the promising local minima of the objective function by performing local searches near the local minima of a response surface (RS) model of the objective function. It ignores neighborhoods of fully explored local minima of the RS model and it bounces between the best partially explored local minimum and the least explored local minimum of the RS model. We implement two AQUARS algorithms that use a radial basis function model and compare them with alternative global optimization methods on an 8-dimensional watershed model calibration problem and on 18 test problems. The alternatives include EGO, GLOBALm, MLMSRBF (Regis and Shoemaker in INFORMS J Comput 19(4):497---509, 2007), CGRBF-Restart (Regis and Shoemaker in J Global Optim 37(1):113---135 2007), and multi level single linkage (MLSL) coupled with two types of local solvers: SQP and Mesh Adaptive Direct Search (MADS) combined with kriging. The results show that the AQUARS methods generally use fewer function evaluations to identify the global minimum or to reach a target value compared to the alternatives. In particular, they are much better than EGO and MLSL coupled to MADS with kriging on the watershed calibration problem and on 15 of the test problems.
TL;DR: This paper proposes a data-adapted iterative method which minimizes in each iteration step a smoothness functional subject to inequality constraints involving the extrema and presents an optimization based normalization to extract instantaneous frequencies from the analytic function approach.
TL;DR: In this article, the authors extend Berge's theorem to set-valued mappings with possible non-compact image sets and study relevant properties of minima, assuming that the image sets are compact.
TL;DR: In this article, approximate point group symmetry is exploited to reduce the mean time of finding the global minima of atomic and molecular clusters by up to two orders of magnitude, with smaller improvements in efficiency for simpler single-funnel energy landscapes.
Abstract: Locating the global minima of atomic and molecular clusters can be a difficult optimisation problem. Here we report benchmarks for procedures that exploit approximate symmetry. This strategy was implemented in the GMIN program following a theoretical analysis, which explained why high-symmetry structures are more likely to have particularly high or particularly low energy. The analysis, and the corresponding algorithms, allow for approximate point group symmetry, and can be combined with basin-hopping and genetic algorithms. We report results for 38-, 75-, and 98-atom Lennard-Jones clusters, which are all multiple-funnel systems. Exploiting approximate symmetry reduces the mean time taken to locate the global minimum by up to two orders of magnitude, with smaller improvements in efficiency for LJ55 and LJ74, which correspond to simpler single-funnel energy landscapes.
TL;DR: The analysis shows that semi-global practical convergence (in the initial states) to the global extremum can be achieved in presence of local extrema if compact sets of inputs are considered.
TL;DR: This paper presents a fully complex-valued relaxation network (FCRN) with its projection-based learning algorithm and demonstrates the superior classification/approximation performance of the FCRN.
Abstract: This paper presents a fully complex-valued relaxation network (FCRN) with its projection-based learning algorithm. The FCRN is a single hidden layer network with a Gaussian-like sech activation function in the hidden layer and an exponential activation function in the output layer. For a given number of hidden neurons, the input weights are assigned randomly and the output weights are estimated by minimizing a nonlinear logarithmic function (called as an energy function) which explicitly contains both the magnitude and phase errors. A projection-based learning algorithm determines the optimal output weights corresponding to the minima of the energy function by converting the nonlinear programming problem into that of solving a set of simultaneous linear algebraic equations. The resultant FCRN approximates the desired output more accurately with a lower computational effort. The classification ability of FCRN is evaluated using a set of real-valued benchmark classification problems from the University of California, Irvine machine learning repository. Here, a circular transformation is used to transform the real-valued input features to the complex domain. Next, the FCRN is used to solve three practical problems: a quadrature amplitude modulation channel equalization, an adaptive beamforming, and a mammogram classification. Performance results from this paper clearly indicate the superior classification/approximation performance of the FCRN.
TL;DR: In this article, a geometric way of minimizing highly symmetric Higgs potentials is proposed, which, surprisingly, is often much more efficient than the usual method, and it gives the global minimum for any set of free parameters of the potential, thus offering an intuitive understanding of how they affect the vacuum expectation values.
Abstract: In non-minimal Higgs mechanisms, one often needs to minimize highly symmetric Higgs potentials. Here we propose a geometric way of doing it, which, surprisingly, is often much more efficient than the usual method. By construction, it gives the global minimum for any set of free parameters of the potential, thus offering an intuitive understanding of how they affect the vacuum expectation values. For illustration, we apply this method to the S
4 and A
4-symmetric three-Higgs-doublet models. We find that at least three recent phenomenological analyses of the A
4-symmetric model used a local, not the global minimum. We discuss coexistence of minima of different types, and comment on the mathematical origin of geometrical CP-violation and on a new symmetry linking different minima.
TL;DR: This work develops R-SPLINE---a Retrospective-search algorithm that alternates between a continuous Search using Piecewise-Linear Interpolation and a discrete Neighborhood Enumeration, to asymptotically identify a local minimum.
Abstract: We consider simulation-optimization (SO) models where the decision variables are integer ordered and the objective function is defined implicitly via a simulation oracle, which for any feasible solution can be called to compute a point estimate of the objective-function value. We develop R-SPLINE---a Retrospective-search algorithm that alternates between a continuous Search using Piecewise-Linear Interpolation and a discrete Neighborhood Enumeration, to asymptotically identify a local minimum. R-SPLINE appears to be among the first few gradient-based search algorithms tailored for solving integer-ordered local SO problems. In addition to proving the almost-sure convergence of R-SPLINE’s iterates to the set of local minima, we demonstrate that the probability of R-SPLINE returning a solution outside the set of true local minima decays exponentially in a certain precise sense. R-SPLINE, with no parameter tuning, compares favorably with popular existing algorithms.
TL;DR: It is shown that f^* is an almost-optimal controller (in a worst-case sense), and the closed-loop stability is guaranteed for a set of trajectories of interest, when the number of data used for control design tends to infinity and these data are dense in the controller domain.
TL;DR: In this article, the authors perform a visibility graph analysis on both the daily and monthly sunspot series and propose two ways to construct the network: one is from the original observable measurements and the other is from a negative-inverse transformed series.
Abstract: Complex network approaches have been recently developed as an alternative framework to study the statistical features of time-series data. We perform a visibility-graph analysis on both the daily and monthly sunspot series. Based on the data, we propose two ways to construct the network: one is from the original observable measurements and the other is from a negative-inverse-transformed series. The degree distribution of the derived networks for the strong maxima has clear non-Gaussian properties, while the degree distribution for minima is bimodal. The long-term variation of the cycles is reflected by hubs in the network which span relatively large time intervals. Based on standard network structural measures, we propose to characterize the long-term correlations by waiting times between two subsequent events. The persistence range of the solar cycles has been identified over 15\,--\,1000 days by a power-law regime with scaling exponent $\gamma = 2.04$ of the occurrence time of the two subsequent and successive strong minima. In contrast, a persistent trend is not present in the maximal numbers, although maxima do have significant deviations from an exponential form. Our results suggest some new insights for evaluating existing models. The power-law regime suggested by the waiting times does indicate that there are some level of predictable patterns in the minima.
02 Aug 2013
TL;DR: An effective improved artificial potential field-based regression search (improved APF-based RS) method that can obtain a better and shorter path efficiently without local minima and oscillations in an environment including known, partially known or unknown, static, and dynamic environments is presented.
Abstract: This paper presents an effective improved artificial potential field-based regression search (improved APF-based RS) method that can obtain a better and shorter path efficiently without local minima and oscillations in an environment including known, partially known or unknown, static, and dynamic environments. We redefine potential functions to eliminate oscillations and local minima problems, and use improved wall-following methods for the robots to escape non-reachable target problems. Meanwhile, we develop a regression search method to optimise the planned path. The optimisation path is calculated by connecting the sequential points produced by improved APF. The simulations demonstrate that the improved APF method easily escapes from local minima, oscillations, and non-reachable target problems. Moreover, the simulation results confirm that our proposed path planning approach can calculate a shorter or more nearly optimal than the general APF can. Results prove our improved APF-based RS method’s feasi...
TL;DR: In this article, the authors consider an optimal control problem of a semi-linear elliptic equation, with bound constraints on the control, and characterize local quadratic growth for the cost function $J$ in the sense of strong solutions.
Abstract: In this article we consider an optimal control problem of a semi-linear elliptic equation, with bound constraints on the control. Our aim is to characterize local quadratic growth for the cost function $J$ in the sense of strong solutions. This means that the function $J$ growths quadratically over all feasible controls whose associated state is close enough to the nominal one, in the uniform topology. The study of strong solutions, classical in the Calculus of Variations, seems to be new in the context of PDE optimization. Our analysis, based on a decomposition result for the variation of the cost, combines Pontryagin's principle and second order conditions. While these two ingredients are known, we use them in such a way that we do not need to assume that the Hessian of Lagrangian of the problem is a Legendre form, or that it is uniformly positive on an extended set of critical directions.
TL;DR: A multipoint potential field method for path planning of autonomous underwater vehicles (AUV) in 3D space is presented in this paper and it is found that the local minima in 2D space can be easily overcome with the MPPF.
Abstract: A multipoint potential field method (MPPF) for path planning of autonomous underwater vehicles (AUV) in 3D space is presented in this paper. The algorithm is developed based on potential field method by incorporating a directed search method for sampling the potential field. In this approach, the analytical gradient of the total potential function is not computed, as it is not essentially required for moving the vehicle to the next position. Rather, a hemispherical region in the direction of motion around the AUV's bow is discretized into equiangular points with center as the current position. By determining the point at which the minimum potential exists, the vehicle can be moved towards that point in 3D space. This method is very simple and applicable for real-time implementation. The problem of local minima is also analyzed and found that the local minima in 2D space can be easily overcome with the MPPF. A simple strategy to avoid the local minima in 3D space is also proposed. The proposed method reduces the burden of fine-tuning the positive scaling factors of potential functions to avoid local minimum. The algorithm development and the simulation results are presented.
TL;DR: In this article, the authors proposed that grand minima in solar activity are caused by simultaneous fluctuations in the meridional circulation and the Babcock-Leighton mechanism for the poloidal field generation in the flux transport dynamo model.
Abstract: We propose that grand minima in solar activity are caused by simultaneous fluctuations in the meridional circulation and the Babcock-Leighton mechanism for the poloidal field generation in the flux transport dynamo model. We present the following results: (a) fluctuations in the meridional circulation are more effective in producing grand minima; (b) both sudden and gradual initiations of grand minima are possible; (c) distributions of durations and waiting times between grand minima seem to be exponential; (d) the coherence time of the meridional circulation has an effect on the number and the average duration of grand minima, a coherence time of about 30 years being consistent with observational data. We also study the occurrence of grand maxima and find that the distributions of durations and waiting times between grand maxima are also exponential, like the grand minima. Finally we address the question whether the Babcock-Leighton mechanism can be operative during grand minima when there are no sunspots. We show that an alpha-effect restricted to the upper portions of the convection zone can pull the dynamo out of the grand minima and can match various observational requirements if the amplitude of this alpha-effect is suitably fine-tuned.
TL;DR: In this paper, the authors analyze some of the main approaches in the literature to the method of adequacy with which Fermat approached the problems of the calculus, as well as its source in the παρισότης of Diophantus, and propose a novel reading thereof.
Abstract: We analyze some of the main approaches in the literature to the method of ‘adequality’ with which Fermat approached the problems of the calculus, as well as its source in the παρισότης of Diophantus, and propose a novel reading thereof. Adequality is a crucial step in Fermat's method of finding maxima, minima, tangents, and solving other problems that a modern mathematician would solve using infinitesimal calculus. The method is presented in a series of short articles in Fermat's collected works (62, pp. 133–172). We show that at least some of the manifestations of adequality amount to variational techniques exploiting a small, or infinitesimal, variation e. Fermat's treatment of geometric and physical applications suggests that an aspect of approximation is inherent in adequality, as well as an aspect of smallness on the part of e. We question the relevance to understanding Fermat of 19th century dictionary definitions of παρισότης and adaequare, cited by Breger, and take issue with his interpretation of...
TL;DR: In this paper a DE with auto-adaptive control parameters is proposed which includes a new mutation operator to solve stagnation in local minima and, on top of all this, the choice of a control parameters value in a simple way.
TL;DR: A novel statistical active contour model for oil slick segmentation is proposed which combines the smooth function, the level set function, and the constant approximating the true signal from the corresponding object to make the segmentation robust to the initialization oflevel set function.
Abstract: Robust and accurate segmentation of the oil slick from SAR imagery is a key step for the detection and monitoring of oil spills, whose observation is very important for protecting the marine environments. However, intensity inhomogeneity, noise, and weak boundary often exist in the oil slick region in SAR imagery, making the accurate segmentation of oil slick very challenging. In this paper, we propose a novel statistical active contour model for oil slick segmentation. First, we fit the distributions of the inhomogeneous intensity with Gaussian distributions of different means and variances. Then, a moving window is used to map the original image intensity into another domain, where the intensity distributions of inhomogeneous objects are still Gaussian but are better separated. In the transformed domain, the means of the Gaussian distributions can be adaptively estimated by multiplying a smooth function with the signal within the window. Thereafter, for each local region, we define a statistical energy function, which combines the smooth function, the level set function, and the constant approximating the true signal from the corresponding object. In addition, in order to make the final segmentation robust to the initialization of level set function, we present a new energy function which is convex with respect to the level set function, thereby avoiding the local minima. An efficient iterative algorithm is then proposed to minimize the energy function that makes the segmentation robust. Experiments undertaken using some challenging SAR oil slick images demonstrate the superiority of our proposed algorithm with respect to the state-of-the-art representative methods.
TL;DR: This paper proposes a reduction technique for the case that the label space is a continuous product space and the regularizer is separable, i.e., a sum of regularizers for each dimension of thelabel space.
Abstract: Multilabel problems are of fundamental importance in computer vision and image analysis. Yet, finding global minima of the associated energies is typically a hard computational challenge. Recently, progress has been made by reverting to spatially continuous formulations of respective problems and solving the arising convex relaxation globally. In practice this leads to solutions which are either optimal or within an a posteriori bound of the optimum. Unfortunately, in previous methods, both run time and memory requirements scale linearly in the total number of labels, making these methods very inefficient and often not applicable to problems with higher dimensional label spaces. In this paper, we propose a reduction technique for the case that the label space is a continuous product space and the regularizer is separable, i.e., a sum of regularizers for each dimension of the label space. In typical real-world labeling problems, the resulting convex relaxation requires orders of magnitude less memory and c...
TL;DR: In this paper, the authors proposed that grand minima in solar activity are caused by simultaneous fluctuations in the meridional circulation and the Babcock-Leighton mechanism for the poloidal field generation in the flux transport dynamo model.
Abstract: We propose that grand minima in solar activity are caused by simultaneous fluctuations in the meridional circulation and the Babcock–Leighton mechanism for the poloidal field generation in the flux transport dynamo model. We present the following results: (a) fluctuations in the meridional circulation are more effective in producing grand minima; (b) both sudden and gradual initiations of grand minima are possible; (c) distributions of durations and waiting times between grand minima seem to be exponential; (d) the coherence time of the meridional circulation has an effect on the number and the average duration of grand minima, with a coherence time of about 30 yr being consistent with observational data. We also study the occurrence of grand maxima and find that the distributions of durations and waiting times between grand maxima are also exponential, like the grand minima. Finally we address the question of whether the Babcock–Leighton mechanism can be operative during grand minima when there are no sunspots. We show that an α-effect restricted to the upper portions of the convection zone can pull the dynamo out of the grand minima and can match various observational requirements if the amplitude of this α-effect is suitably fine-tuned.