guided image completion by confidence propagation this paper presents a new guided image completion method which fills any missing values by considering information from a guidance image we develop a confidence propagation scheme that allows the filling process to be carried out simultaneously without the need of deciding the filling order we conduct experiments in several applications where the problem can be formulated into a guided image completion problem such as interactive segmentation and colorization the experimental results show that our method provides good results and succeeds in situations where conventional methods fail in addition as all building blocks are parallel processes our method is much suitable for hardware acceleration highlightswe proposed an image completion method based on a new formulation filling process was carried out simultaneously without deciding the filling order good results were obtained in a variety of applications

structure selective depth superresolution for rgb d cameras this paper describes a method for high quality depth superresolution the standard formulations of image guided depth upsampling using simple joint filtering or quadratic optimization lead to texture copying and depth bleeding artifacts these artifacts are caused by inherent discrepancy of structures in data from different sensors although there exists some correlation between depth and intensity discontinuities they are different in distribution and formation to tackle this problem we formulate an optimization model using a nonconvex regularizer a nonlocal affinity established in a high dimensional feature space is used to offer precisely localized depth boundaries we show that the proposed method iteratively handles differences in structure between depth and intensity images this property enables reducing texture copying and depth bleeding artifacts significantly on a variety of range data sets we also propose a fast alternating direction method of multipliers algorithm to solve our optimization problem our solver shows a noticeable speed up compared with the conventional majorize minimize algorithm extensive experiments with synthetic and real world data sets demonstrate that the proposed method is superior to the existing methods

genetic algorithm approach on multi criteria minimum spanning tree problem minimum spanning tree mst problem is of high importance in network optimization the multi criteria mst mc mst is a more realistic representation of the practical problem in the real world but it is difficult for the traditional network optimization technique to deal with in this paper a genetic algorithm ga approach is developed to deal with this problem without neglecting its network topology the proposed method adopts the prufer number as the tree encoding and applies the multiple criteria decision making mcdm technique and nondominated sorting technique to make the ga search give out all pareto optimal solutions either focused on the region near the ideal point or distributed all along the pareto frontier compared with the enumeration method of pareto optimal solution the numerical analysis shows the efficiency and effectiveness of the ga approach on the mc mst problem

adaptive support weight approach for correspondence search we present a new window based method for correspondence search using varying support weights we adjust the support weights of the pixels in a given support window based on color similarity and geometric proximity to reduce the image ambiguity our method outperforms other local methods on standard stereo benchmarks

regional bit allocation and rate distortion optimization for multiview depth video coding with view synthesis distortion model in this paper we propose a view synthesis distortion model vsdm that establishes the relationship between depth distortion and view synthesis distortion for the regions with different characteristics color texture area corresponding depth ctad region and color smooth area corresponding depth csad respectively with this vsdm we propose regional bit allocation rba and rate distortion optimization rdo algorithms for multiview depth video coding mdvc by allocating more bits on ctad for rendering quality and fewer bits on csad for compression efficiency experimental results show that the proposed vsdm based rba and rdo can improve the coding efficiency significantly for the test sequences in addition for the proposed overall mdvc algorithm that integrates vsdm based rba and rdo it achieves 9 99 and 14 51 bit rate reduction on average for the high and low bit rate respectively it can improve virtual view image quality 0 22 and 0 24 db on average at the high and low bit rate respectively when compared with the original joint multiview video coding model the rd performance comparisons using five different metrics also validate the effectiveness of the proposed overall algorithm in addition the proposed algorithms can be applied to both intra and inter frames

the inverse mean curvature flow and the riemannian penrose inequality let m be an asymptotically flat 3 manifold of nonnegative scalar curvature the riemannian penrose inequality states that the area of an outermost minimal surface n in m is bounded by the adm mass m according to the formula n 16 m 2 we develop a theory of weak solutions of the inverse mean curvature flow and employ it to prove this inequality for each connected component of n using geroch s monotonicity formula for the adm mass our method also proves positivity of bartnik s gravitational capacity by computing a positive lower bound for the mass purely in terms of local geometry

shape from focus the shape from focus method presented here uses different focus levels to obtain a sequence of object images the sum modified laplacian sml operator is developed to provide local measures of the quality of image focus the operator is applied to the image sequence to determine a set of focus measures at each image point a depth estimation algorithm interpolates a small number of focus measure values to obtain accurate depth estimates a fully automated shape from focus system has been implemented using an optical microscope and tested on a variety of industrial samples experimental results are presented that demonstrate the accuracy and robustness of the proposed method these results suggest shape from focus to be an effective approach for a variety of challenging visual inspection tasks

measure of image sharpness using eigenvalues this paper deals with the design and implementation of a novel image sharpness metric based on the statistical approach this sharpness metric is derived by modelling the image sharpness problem as a generalized eigenvalues problem this problem is solved using rayleigh quotient optimization where relevant statistical information of an image is extracted and then represented through a series of eigenvalues the novelty of this paper comes from the application of eigenvalues in image sharpness metric formulation to provide robust assessment with the presence of various blur and noisy conditions firstly the input image is normalized by its energy to minimize the effects caused by image contrast secondly the covariance matrix is computed from this normalized image before it is diagonalized using singular values decomposition svd to obtain a series of eigenvalues finally the image sharpness of the normalized image is determined by the trace of the first several eigenvalues the performance of the proposed metric is gauged by comparing with several objective image sharpness metrics experimental results using synthetic and real images with known and unknown distortion conditions show the robustness and feasibility of the proposed metric in providing relative image sharpness in particular the proposed metric provides wider working range and more precise prediction consistency under all tested deformation conditions although it is slightly expensive in terms of computation than other metrics

using dynamic programming for solving variational problems in vision dynamic programming is discussed as an approach to solving variational problems in vision dynamic programming ensures global optimality of the solution is numerically stable and allows for hard constraints to be enforced on the behavior of the solution within a natural and straightforward structure as a specific example of the approach s efficacy applying dynamic programming to the energy minimizing active contours is described the optimization problem is set up as a discrete multistage decision process and is solved by a time delayed discrete dynamic programming algorithm a parallel procedure for decreasing computational costs is discussed

analytic and geometric background of recurrence and non explosion of the brownian motion on riemannian manifolds we provide an overview of such properties of the brownian motion on complete non compact riemannian manifolds as recurrence and non explosion it is shown that both properties have various analytic characterizations in terms of the heat kernel green function liouville properties etc on the other hand we consider a number of geometric conditions such as the volume growth isoperimetric inequalities curvature bounds etc which are related to recurrence and non explosion

analytic network process for pattern classification problems using genetic algorithms the analytic network process anp is a useful technique for multi attribute decision analysis mcda that employs a network representation to describe interrelationships between diverse attributes owing to effectiveness of the anp in allowing for complex interrelationships between attributes this paper develops an anp based classifier for pattern classification problems with interdependence or independence among attributes to deal with interdependence this study employs genetic algorithms gas to automatically determine elements in the supermatrix that are not easily user specified to find degrees of importance of respective attributes then with the relative importance for each attribute in the limiting supermatrix the current work determines the class label of a pattern by its synthetic evaluation experimental results obtained by the proposed anp based classifier are comparable to those obtained by other fuzzy or non fuzzy classification methods

shape from focus using multilayer feedforward neural networks the conventional shape from focus sff methods have inaccuracies because of piecewise constant approximation of the focused image surface fis we propose a scheme for sff based on representation of three dimensional 3 d fis in terms of neural network weights the neural networks are trained to learn the shape of the fis that maximizes the focus measure

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

biharmonic hypersurfaces of the 4 dimensional semi euclidean space es4 abstract a submanifold m r n of a semi euclidean space e s m is said to have harmonic mean curvature vector field if h 0 where h denotes the mean curvature vector submanifolds with harmonic mean curvature vector are also known as biharmonic submanifolds in this paper we prove that every nondegenerate hypersurface of e s 4 the shape operator of which is diagonalizable with harmonic mean curvature vector field is minimal

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

quasi minimal surfaces of pseudo riemannian space forms with positive relative nullity abstract in this paper we consider surfaces in 4 dimensional pseudo riemannian space forms with index 2 first we obtain some of geometrical properties of such surfaces considering their relative null space then we get classifications of quasi minimal surfaces with positive relative nullity

robust guided image filtering using nonconvex potentials filtering images using a guidance signal a process called guided or joint image filtering has been used in various tasks in computer vision and computational photography particularly for noise reduction and joint upsampling this uses an additional guidance signal as a structure prior and transfers the structure of the guidance signal to an input image restoring noisy or altered image structure the main drawbacks of such a data dependent framework are that it does not consider structural differences between guidance and input images and that it is not robust to outliers we propose a novel sd for static dynamic filter to address these problems in a unified framework and jointly leverage structural information from guidance and input images guided image filtering is formulated as a nonconvex optimization problem which is solved by the majorize minimization algorithm the proposed algorithm converges quickly while guaranteeing a local minimum the sd filter effectively controls the underlying image structure at different scales and can handle a variety of types of data from different sensors it is robust to outliers and other artifacts such as gradient reversal and global intensity shift and has good edge preserving smoothing properties we demonstrate the flexibility and effectiveness of the proposed sd filter in a variety of applications including depth upsampling scale space filtering texture removal flash non flash denoising and rgb nir denoising

improvements in shape from focus for holographic reconstructions with regard to focus operators neighborhood size and height value interpolation this paper presents a shape from focus method which is improved with regard to the mathematical operator used for contrast measurement the selection of the neighborhood size surface refinement through interpolation and surface postprocessing three dimensional models of living human faces are presented with such a high resolution that single hairs are visible

evolving estimators of the pointwise holder exponent with genetic programming the regularity of a signal can be numerically expressed using holder exponents which characterize the singular structures a signal contains in particular within the domains of image processing and image understanding regularity based analysis can be used to describe local image shape and appearance however estimating the holder exponent is not a trivial task and current methods tend to be computationally slow and complex this work presents an approach to automatically synthesize estimators of the pointwise holder exponent for digital images this task is formulated as an optimization problem and genetic programming gp is used to search for operators that can approximate a traditional estimator the oscillations method experimental results show that gp can generate estimators that achieve a low error and a high correlation with the ground truth estimation furthermore most of the gp estimators are faster than traditional approaches in some cases their runtime is orders of magnitude smaller this result allowed us to implement a real time estimation of the holder exponent on a live video signal the first such implementation in current literature moreover the evolved estimators are used to generate local descriptors of salient image regions a task for which a stable and robust matching is achieved comparable with state of the art methods in conclusion the evolved estimators produced by gp could help expand the application domain of holder regularity within the fields of image analysis and signal processing

on a global existence theorem of small amplitude solutions for nonlinear wave equations in an exterior domain soit un domaine non borne dans un espace euclidien a n dimensions r n a frontiere compacte et c on considere le probleme mixte u u f t x d 1 d 1 u f t x dans 0 u 0 sur 0 u 0 x u 0 x t u 0 x u 1 x dans f est une fonction non lineaire a valeur reelle et d 1 d 1 u t j x u 1 j 2

stereo matching using tree filtering matching cost aggregation is one of the oldest and still popular methods for stereo correspondence while effective and efficient cost aggregation methods typically aggregate the matching cost by summing averaging over a user specified local support region this is obviously only locally optimal and the computational complexity of the full kernel implementation usually depends on the region size in this paper the cost aggregation problem is re examined and a non local solution is proposed the matching cost values are aggregated adaptively based on pixel similarity on a tree structure derived from the stereo image pair to preserve depth edges the nodes of this tree are all the image pixels and the edges are all the edges between the nearest neighboring pixels the similarity between any two pixels is decided by their shortest distance on the tree the proposed method is non local as every node receives supports from all other nodes on the tree the proposed method can be naturally extended to the time domain for enforcing temporal coherence unlike previous methods the non local property guarantees that the depth edges will be preserved when the temporal coherency between all the video frames are considered a non local weighted median filter is also proposed based on the non local cost aggregation algorithm it has been demonstrated to outperform all local weighted median filters on disparity depth upsampling and refinement

whom to befriend to influence people alice wants to join a new social network and influence its members to adopt a new product or idea each person v in the network has a certain threshold t v for activation i e adoption of the product or idea if v has at least t v activated neighbors then v will also become activated if alice wants to activate the entire social network whom should she befriend we study the problem of finding the minimum number of links that alice should form to people in the network in order to activate the entire social network this minimum links problem has applications in viral marketing and the study of epidemics we show that the solution can be quite different from the related and widely studied target set selection problem we prove that the minimum links problem is np complete in fact it is hard to approximate to within an epsilon ln n factor for some constant epsilon even for graphs with degree 3 and with threshold at most 2 in contrast we give linear time algorithms to solve the problem for trees cycles and cliques and give precise bounds on the number of links needed

fast domain decomposition for global image smoothing edge preserving smoothing eps can be formulated as minimizing an objective function that consists of data and regularization terms at the price of high computational cost this global eps approach is more robust and versatile than a local one that typically has a form of weighted averaging in this paper we introduce an efficient decomposition based method for global eps that minimizes the objective function of l 2 data and possibly non smooth and non convex regularization terms in linear time different from previous decomposition based methods which require solving a large linear system our approach solves an equivalent constrained optimization problem resulting in a sequence of 1 d sub problems this enables applying fast linear time solver for weighted least squares and l 1 smoothing problems an alternating direction method of multipliers algorithm is adopted to guarantee fast convergence our method is fully parallelizable and its runtime is even comparable to the state of the art local eps approaches we also propose a family of fast majorization minimization algorithms that minimize an objective with non convex regularization terms experimental results demonstrate the effectiveness and flexibility of our approach in a range of image processing and computational photography applications

a novel algorithm for estimation of depth map using image focus for 3d shape recovery in the presence of noise three dimensional shape recovery from one or multiple observations is a challenging problem of computer vision in this paper we present a new focus measure for the estimation of a depth map using image focus this depth map can subsequently be used in techniques and algorithms leading to the recovery of a three dimensional structure of the object a requirement of a number of high level vision applications the proposed focus measure has shown robustness in the presence of noise as compared to the earlier focus measures this new focus measure is based on an optical transfer function implemented in the fourier domain the results of the proposed focus measure have shown drastic improvements in estimation of a depth map with respect to the earlier focus measures in the presence of various types of noise including gaussian shot and speckle noises the results of a range of focus measures are compared using root mean square error and correlation metric measures

fgsn fuzzy granular social networks model and applications abstract social network data has been modeled with several approaches including sociogram and sociomatrices which are popular and comprehensive similar to these we have developed here a novel modeling technique based on granular computing theory and fuzzy neighborhood systems which provides a uniform framework to represent social networks in this model a social network is represented with a collection of granules fuzzy sets are used for defining the granules the model is named fuzzy granular social network fgsn familiar measures of networks viz degree betweenness embeddedness and clustering coefficient are redefined in the context of this new framework two measures namely entropy of fgsn and energy of granules are defined to quantify the uncertainty involved in fgsn arising from fuzziness in the relationships of actors experimental results demonstrate the applicability of the model in two well known problems of social networks namely target set selection and community detection with comparative studies

boundary detection by constrained optimization a statistical framework is used for finding boundaries and for partitioning scenes into homogeneous regions the model is a joint probability distribution for the array of pixel gray levels and an array of labels in boundary finding the labels are binary zero or one representing the absence or presence of boundary elements in partitioning the label values are generic two labels are the same when the corresponding scene locations are considered to belong to the same region the distribution incorporates a measure of disparity between certain spatial features of block pairs of pixel gray levels using the kolmogorov smirnov nonparametric measures of difference between the distributions of these features the number of model parameters is minimized by forbidding label configurations which are assigned probability zero the maximum a posteriori estimator of boundary placements and partitionings is examined the forbidden states introduce constraints into the calculation of these configurations stochastic relaxation methods are extended to accommodate constrained optimization

depth superresolution by transduction this paper presents a depth superresolution sr method that uses both of a low resolution lr depth image and a high resolution hr intensity image we formulate depth sr as a graph based transduction problem in particular the hr intensity image is represented as an undirected graph in which pixels are characterized as vertices and their relations are encoded as an affinity function when the vertices initially labeled with certain depth hypotheses from the lr depth image are regarded as input queries all the vertices are scored with respect to the relevances to these queries by a classifying function each vertex is then labeled with the depth hypothesis that receives the highest relevance score we design the classifying function by considering the local and global structures of the hr intensity image this approach enables us to address a depth bleeding problem that typically appears in current depth sr methods furthermore input queries are assigned in a probabilistic manner making depth sr robust to noisy depth measurements we also analyze existing depth sr methods in the context of transduction and discuss their theoretic relations intensive experiments demonstrate the superiority of the proposed method over state of the art methods both qualitatively and quantitatively

classification of spatial surfaces with parallel mean curvature vector in pseudo euclidean spaces of arbitrary dimension spatial surfaces with parallel mean curvature vector play some important roles in general relativity theory of harmonic maps as well as in differential geometry recently spatial surfaces in four dimensional minkowski space time with parallel mean curvature vector were classified by chen and van der veken complete classification of parallel surfaces in 4 dimensional lorentzian space forms tohoku math j 61 1 2009 in this article we completely classify spatial surfaces with parallel mean curvature vector in pseudo euclidean spaces of arbitrary dimension the main result states that there exist 16 families of such surfaces as by product we achieve the complete classification of spatial surfaces with parallel mean curvature vector in minkowski space times of arbitrary dimension

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

a global optimization algorithm for target set selection problems our study concerns the target set selection problem which involves discovering a subset of influential players in a given social network performing a task of information diffusion to maximize the number of nodes influenced in the network we are motivated by the facts that the well known algorithms for target set selection problems are heuristic and the best heuristic algorithm only ensures that the spread is within 63 of the optimal influence spread based on the submodular assumption we propose a set based coding genetic algorithm sga which converges in probability to the optimal solution of target set selection problems computational experiments on four synthetically generated graphs and five real world data sets are carried out to compare the performance of the proposed sga with those well known algorithms in the literature statistical significance tests indicate that the proposed sga outperforms the state of the art algorithms for target set selection problems significantly

fundamental relationship between bilateral filtering adaptive smoothing and the nonlinear diffusion equation in this paper the relationship between bilateral filtering and anisotropic diffusion is examined the bilateral filtering approach represents a large class of nonlinear digital image filters we first explore the connection between anisotropic diffusion and adaptive smoothing and then the connection between adaptive smoothing and bilateral filtering previously adaptive smoothing was considered to be an inconsistent approximation to the nonlinear diffusion equation we extend adaptive smoothing to make it consistent thus enabling a unified viewpoint that relates nonlinear digital image filters and the nonlinear diffusion equation

regularization of inverse visual problems involving discontinuities inverse problems such as the reconstruction problems that arise in early vision tend to be mathematically ill posed through regularization they may be reformulated as well posed variational principles whose solutions are computable standard regularization theory employs quadratic stabilizing functionals that impose global smoothness constraints on possible solutions discontinuities present serious difficulties to standard regularization however since their reconstruction requires a precise spatial control over the smoothing properties of stabilizers this paper proposes a general class of controlled continuity stabilizers which provide the necessary control over smoothness these nonquadratic stabilizing functionals comprise multiple generalized spline kernels combined with noncontinuous continuity control functions in the context of computational vision they may be thought of as controlled continuity constraints these generic constraints are applicable to visual reconstruction problems that involve both continuous regions and discontinuities for which global smoothness constraints fail

remarks on global existence for nonlinear parabolic equations on considere le probleme suivant u t u f u d x u d x 2 u u t 0 x avec l hypothese que f 0 p pres de 0 si p 2 et f ne contient pas u alors ce probleme pour tout n 1 admet une solution unique globale lisse pourvu que la donnee initiale soit suffisamment petite

a classification of biconservative hypersurfaces in a pseudo euclidean space abstract in this paper we study biconservative hypersurfaces of index 2 in e 2 5 we give the complete classification of biconservative hypersurfaces with diagonalizable shape operator with exactly three distinct principal curvatures we also give an explicit example of biconservative hypersurfaces with four distinct principal curvatures

optimal depth estimation by combining focus measures using genetic programming three dimensional 3d shape reconstruction is a fundamental problem in machine vision applications shape from focus sff is one of the passive optical methods for 3d shape recovery that uses degree of focus as a cue to estimate 3d shape in this approach usually a single focus measure operator is applied to measure the focus quality of each pixel in the image sequence however the applicability of a single focus measure is limited to estimate accurately the depth map for diverse type of real objects to address this problem we develop optimal composite depth ocd function through genetic programming gp for accurate depth estimation the ocd function is constructed by optimally combining the primary information extracted using one or more focus measures the genetically developed composite function is then used to compute the optimal depth map of objects the performance of the developed nonlinear function is investigated using both the synthetic and the real world image sequences experimental results demonstrate that the proposed estimator is more useful in computing accurate depth maps as compared to the existing sff methods moreover it is found that the heterogeneous function is more effective than homogeneous function

nonlocal image and movie denoising neighborhood filters are nonlocal image and movie filters which reduce the noise by averaging similar pixels the first object of the paper is to present a unified theory of these filters and reliable criteria to compare them to other filter classes a ccd noise model will be presented justifying the involvement of neighborhood filters a classification of neighborhood filters will be proposed including classical image and movie denoising methods and discussing further a recently introduced neighborhood filter nl means in order to compare denoising methods three principles will be discussed the first principle method noise specifies that only noise must be removed from an image a second principle will be introduced noise to noise according to which a denoising method must transform a white noise into a white noise contrarily to method noise this principle which characterizes artifact free methods eliminates any subjectivity and can be checked by mathematical arguments and fourier analysis noise to noise will be proven to rule out most denoising methods with the exception of neighborhood filters this is why a third and new comparison principle the statistical optimality is needed and will be introduced to compare the performance of all neighborhood filters the three principles will be applied to compare ten different image and movie denoising methods it will be first shown that only wavelet thresholding methods and nl means give an acceptable method noise second that neighborhood filters are the only ones to satisfy the noise to noise principle third that among them nl means is closest to statistical optimality a particular attention will be paid to the application of the statistical optimality criterion for movie denoising methods it will be pointed out that current movie denoising methods are motion compensated neighborhood filters this amounts to say that they are neighborhood filters and that the ideal neighborhood of a pixel is its trajectory unfortunately the aperture problem makes it impossible to estimate ground true trajectories it will be demonstrated that computing trajectories and restricting the neighborhood to them is harmful for denoising purposes and that space time nl means preserves more movie details

ensemble strategies with adaptive evolutionary programming mutation operators such as gaussian levy and cauchy have been used with evolutionary programming ep according to the no free lunch theorem it is impossible for ep with a single mutation operator to outperform always for example classical ep cep with gaussian mutation is better at searching in a local neighborhood while the fast ep fep with the cauchy mutation performs better over a larger neighborhood motivated by these observations we propose an ensemble approach where each mutation operator has its associated population and every population benefits from every function call this approach enables us to benefit from different mutation operators with different parameter values whenever they are effective during different stages of the search process in addition the recently proposed adaptive ep aep using gaussian acep and cauchy afep mutations is also evaluated in the aep the strategy parameter values are adapted based on the search performance in the previous few generations the performance of ensemble is compared with a mixed mutation strategy which integrates several mutation operators into a single algorithm as well as against the aep with a single mutation operator improved performance of the ensemble over the single mutation based algorithms and mixed mutation algorithm is verified using statistical tests

homothetic and conformal symmetries of solutions to einstein s equations we present several results about the nonexistence of solutions of einstein s equations with homothetic or conformal symmetry we show that the only spatially compact globally hyperbolic spacetimes admitting a hypersurface of constant mean extrinsic curvature and also admitting an infinitesimal proper homothetic symmetry are everywhere locally flat this assumes that the matter fields either obey certain energy conditions or are the yang mills or massless klein gordon fields we find that the only vacuum solutions admitting an infinitesimal proper conformal symmetry are everywhere locally flat spacetimes and certain plane wave solutions we show that if the dominant energy condition is assumed then minkowski spacetime is the only asymptotically flat solution which has an infinitesimal conformal symmetry that is asymptotic to a dilation in other words with the exceptions cited homothetic or conformal killing fields are in fact killing in spatially compact or asymptotically flat spactimes in the conformal procedure for solving the initial value problem we show that data with infinitesimal conformal symmetry evolves to a spacetime with full isometry

screw invariant marginally trapped surfaces in minkowski 4 space a spacelike surface in a lorentzian manifold whose mean curvature vector is lightlike everywhere is called marginally trapped the classification of marginally trapped surfaces in minkowski 4 space which are invariant under a subgroup of the lorentz group that leaves invariant a lightlike direction i e the so called screw invariant surfaces is obtained as corollaries the screw invariant marginally trapped surfaces with harmonic mean curvature vector and with prescribed gaussian curvature are explicitly described

depth analogy data driven approach for single image depth estimation using gradient samples inferring scene depth from a single monocular image is a highly ill posed problem in computer vision this paper presents a new gradient domain approach called depth analogy that makes use of analogy as a means for synthesizing a target depth field when a collection of rgb d image pairs is given as training data specifically the proposed method employs a non parametric learning process that creates an analogous depth field by sampling reliable depth gradients using visual correspondence established on training image pairs unlike existing data driven approaches that directly select depth values from training data our framework transfers depth gradients as reconstruction cues which are then integrated by the poisson reconstruction the performance of most conventional approaches relies heavily on the training rgb d data used in the process and such a dependency severely degenerates the quality of reconstructed depth maps when the desired depth distribution of an input image is quite different from that of the training data e g outdoor versus indoor scenes our key observation is that using depth gradients in the reconstruction is less sensitive to scene characteristics providing better cues for depth recovery thus our gradient domain approach can support a great variety of training range datasets that involve substantial appearance and geometric variations the experimental results demonstrate that our depth gradient domain approach outperforms existing data driven approaches directly working on depth domain even when only uncorrelated training datasets are available

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

on the foundations of relaxation labeling processes a large class of problems can be formulated in terms of the assignment of labels to objects frequently processes are needed which reduce ambiguity and noise and select the best label among several possible choices relaxation labeling processes are just such a class of algorithms they are based on the parallel use of local constraints between labels this paper develops a theory to characterize the goal of relaxation labeling the theory is founded on a definition of con sistency in labelings extending the notion of constraint satisfaction in certain restricted circumstances an explicit functional exists that can be maximized to guide the search for consistent labelings this functional is used to derive a new relaxation labeling operator when the restrictions are not satisfied the theory relies on variational cal culus it is shown that the problem of finding consistent labelings is equivalent to solving a variational inequality a procedure nearly identical to the relaxation operator derived under restricted circum stances serves in the more general setting further a local convergence result is established for this operator the standard relaxation labeling formulas are shown to approximate our new operator which leads us to conjecture that successful applications of the standard methods are explainable by the theory developed here observations about con vergence and generalizations to higher order compatibility relations are described

universal impulse noise filter based on genetic programming in this paper we present a novel method for impulse noise filter construction based on the switching scheme with two cascaded detectors and two corresponding estimators genetic programming as a supervised learning algorithm is employed for building two detectors with complementary characteristics the first detector identifies the majority of noisy pixels the second detector searches for the remaining noise missed by the first detector usually hidden in image details or with amplitudes close to its local neighborhood both detectors are based on the robust estimators of location and scale median and mad the filter made by the proposed method is capable of effectively suppressing all kinds of impulse noise in contrast to many existing filters which are specialized only for a particular noise model in addition we propose the usage of a new impulse noise model the mixed impulse noise which is more realistic and harder to treat than existing impulse noise models the proposed model is the combination of commonly used noise models salt and pepper and uniform impulse noise models simulation results show that the proposed two stage gp filter produces excellent results and outperforms existing state of the art filters

robust color guided depth map restoration one of the most challenging issues in color guided depth map restoration is the inconsistency between color edges in guidance color images and depth discontinuities on depth maps this makes the restored depth map suffer from texture copy artifacts and blurring depth discontinuities to handle this problem most state of the art methods design complex guidance weight based on guidance color images and heuristically make use of the bicubic interpolation of the input depth map in this paper we show that using bicubic interpolated depth map can blur depth discontinuities when the upsampling factor is large and the input depth map contains large holes and heavy noise in contrast we propose a robust optimization framework for color guided depth map restoration by adopting a robust penalty function to model the smoothness term of our model we show that the proposed method is robust against the inconsistency between color edges and depth discontinuities even when we use simple guidance weight to the best of our knowledge we are the first to solve this problem with a principled mathematical formulation rather than previous heuristic weighting schemes the proposed robust method performs well in suppressing texture copy artifacts moreover it can better preserve sharp depth discontinuities than previous heuristic weighting schemes through comprehensive experiments on both simulated data and real data we show promising performance of the proposed method

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

addendum to classification of marginally trapped lorentzian flat surfaces in e24 and its application to biharmonic surfaces abstract due to omission an additional family shall be added to the list of marginally trapped lorentzian flat surfaces in e 2 4 given in theorem 4 1 of b y chen classification of marginally trapped lorentzian flat surfaces in e 2 4 and its application to biharmonic surfaces j math anal appl 340 2008 861 875

gradient domain based enhancement of multi view depth video multi view depth is an emerging and attractive 3d representation in recent years which acts a significant role in rendering numerous viewing angles from a small number of given input views the performance of those depth based 3d video applications is strongly dependent on the quality of multi view depth however because of the limitations of depth acquisition and estimation the quality of multi view depth suffers from artifacts in spatial dimension and inconsistency in both the temporal and inter view dimensions in this paper we propose a gradient domain based enhancement method for multi view depth being different from the traditional enhancement methods which intended to process one or two above dimensions our proposal exploits the coherence of both temporal and inter view dimensions in addition of the spatial one it is very challenging to obtain the stable characteristics in multi dimensions to solve this problem we propose to investigate the characteristics in the gradient domain rather than the intensity domain the enhanced multi view depth is obtained through the minimization of energy function under the constraint of a joint gradient field jgf which is estimated from multiple dimensions through motion estimation and geometric mapping therefore the enhanced multi view depth is a global optimization in multiple dimensions that ensures the consistency in temporal inter view and spatial domains furthermore we also propose an enhancement structure to indicate the process order of depth frames the experimental results suggest that the proposed method can enhance multi view depth with desired sharpness and consistency

an optimal graph theoretic approach to data clustering theory and its application to image segmentation a novel graph theoretic approach for data clustering is presented and its application to the image segmentation problem is demonstrated the data to be clustered are represented by an undirected adjacency graph g with arc capacities assigned to reflect the similarity between the linked vertices clustering is achieved by removing arcs of g to form mutually exclusive subgraphs such that the largest inter subgraph maximum flow is minimized for graphs of moderate size approximately 2000 vertices the optimal solution is obtained through partitioning a flow and cut equivalent tree of g which can be efficiently constructed using the gomory hu algorithm 1961 however for larger graphs this approach is impractical new theorems for subgraph condensation are derived and are then used to develop a fast algorithm which hierarchically constructs and partitions a partially equivalent tree of much reduced size this algorithm results in an optimal solution equivalent to that obtained by partitioning the complete equivalent tree and is able to handle very large graphs with several hundred thousand vertices the new clustering algorithm is applied to the image segmentation problem the segmentation is achieved by effectively searching for closed contours of edge elements equivalent to minimum cuts in g which consist mostly of strong edges while rejecting contours containing isolated strong edges this method is able to accurately locate region boundaries and at the same time guarantees the formation of closed edge contours

surfaces of prescribed mean curvature vector in semi riemannian manifolds abstract solving a second order quasilinear initial value problem we prove existence and uniqueness of both space like and time like immersions of prescribed mean curvature vector in general semi riemannian manifolds such surfaces arise for example as critical points of generalized area functionals as well as self similar solutions of the mean curvature flow

a focus fusion framework with anisotropic depth map smoothing focus fusion is the task of combining a set of images focused at different depths into a single image that is entirely in focus the crucial point of all focus fusion methods is the decision about the in focus areas to this end we present a general framework for focus fusion that introduces a modern regularisation strategy on these per pixel decisions we assume that neighbouring pixels in the fused image belong to similar depth layers following this assumption we smooth the depth map with a sophisticated anisotropic diffusion process combined with a robust data fidelity term the experiments with synthetic and real world data demonstrate that our new model yields a better quality than several existing focus fusion methods moreover our methodology is general and can be applied to improve many fusion approaches highlightswe show that depth map regularisation is an important tool for focus fusion we incorporate modern concepts such as a coupled anisotropic diffusion term we substantially improve the runtime with a fast gpu implementation we evaluate different in focus measures we compare the overall performance to several methods from the literature

depth video enhancement based on weighted mode filtering this paper presents a novel approach for depth video enhancement given a high resolution color video and its corresponding low quality depth video we improve the quality of the depth video by increasing its resolution and suppressing noise for that a weighted mode filtering method is proposed based on a joint histogram when the histogram is generated the weight based on color similarity between reference and neighboring pixels on the color image is computed and then used for counting each bin on the joint histogram of the depth map a final solution is determined by seeking a global mode on the histogram we show that the proposed method provides the optimal solution with respect to l1 norm minimization for temporally consistent estimate on depth video we extend this method into temporally neighboring frames simple optical flow estimation and patch similarity measure are used for obtaining the high quality depth video in an efficient manner experimental results show that the proposed method has outstanding performance and is very efficient compared with existing methods we also show that the temporally consistent enhancement of depth video addresses a flickering problem and improves the accuracy of depth video

stereo matching using belief propagation in this paper we formulate the stereo matching problem as a markov network and solve it using bayesian belief propagation the stereo markov network consists of three coupled markov random fields that model the following a smooth field for depth disparity a line process for depth discontinuity and a binary process for occlusion after eliminating the line process and the binary process by introducing two robust functions we apply the belief propagation algorithm to obtain the maximum a posteriori map estimation in the markov network other low level visual cues e g image segmentation can also be easily incorporated in our stereo model to obtain better stereo results experiments demonstrate that our methods are comparable to the state of the art stereo algorithms for many test cases

the theory and practice of bayesian image labeling integrating disparate sources of information has been recognized as one of the keys to the success of general purpose vision systems image clues such as shading texture stereo disparities and image flows provide uncertain local and incomplete information about the three dimensional scene spatial a priori knowledge plays the role of filling in missing information and smoothing out noise this thesis proposes a solution to the longstanding open problem of visual integration it reports a framework based on bayesian probability theory for computing an intermediate representation of the scene from disparate sources of information the computation is formulated as a labeling problem local visual observations for each image entity are reported as label likelihoods they are combined consistently and coherently on hierarchically structured label trees with a new computationally simple procedure the pooled label likelihoods are fused with the a priori spatial knowledge encoded as markov random fields mrf s the a posteriori distribution of the labelings are thus derived in a bayesian formalism a new inference method highest confidence first hcf estimation is used to infer a unique labeling from the a posteriori distribution unlike previous inference methods based on the mrf formalism hcf is computationally efficient and predictable while meeting the principles of graceful degradation and least commitment the results of the inference process are consistent with both observable evidence and a priori knowledge the effectiveness of the approach is demonstrated with experiments on two image analysis problems intensity edge detection and surface reconstruction for edge detection likelihood outputs from a set of local edge operators are integrated with a priori knowledge represented as an mrf probability distribution for surface reconstruction intensity information is integrated with sparse depth measurements and a priori knowledge coupled mrf s provide a unified treatment of surface reconstruction and segmentation and an extension of hcf implements a solution method experiments using real image and depth data yield robust results the framework can also be generalized to higher level vision problems as well as to other domains

a pixel dissimilarity measure that is insensitive to image sampling because of image sampling traditional measures of pixel dissimilarity can assign a large value to two corresponding pixels in a stereo pair even in the absence of noise and other degrading effects we propose a measure of dissimilarity that is provably insensitive to sampling because it uses the linearly interpolated intensity functions surrounding the pixels experiments on real images show that our measure alleviates the problem of sampling with little additional computational overhead

selecting the optimal focus measure for autofocusing and depth from focus a method is described for selecting the optimal focus measure with respect to gray level noise from a given set of focus measures in passive autofocusing and depth from focus applications the method is based on two new metrics that have been defined for estimating the noise sensitivity of different focus measures the first metric the autofocusing uncertainty measure aum is useful in understanding the relation between gray level noise and the resulting error in lens position for autofocusing the second metric autofocusing root mean square error arms error is an improved metric closely related to aum aum and arms error metrics are based on a theoretical noise sensitivity analysis of focus measures and they are related by a monotonic expression the theoretical results are validated by actual and simulation experiments for a given camera the optimally accurate focus measure may change from one object to the other depending on their focused images therefore selecting the optimal focus measure from a given set involves computing all focus measures in the set

fast approximate maximum a posteriori restoration of multicolour images we propose a new algorithm for the approximation of the maximum a posteriori map restoration of noisy images the image restoration problem is considered in a bayesian setting we assume as prior distribution multicolour markov random fields on a graph whose main restriction is the presence of only pairwise site interactions the noise is modelled as a bernoulli field computing the mode of the posterior distribution is np complete i e can very likely be done only in a time exponential in the number of sites of the underlying graph our algorithm runs in polynomial time and is based on the coding of the colours it produces an image with the following property either a pixel is coloured with one of the possible colours or it is left blank in the first case we prove that this is the colour of the site in the exact map restoration the quality of the approximation is then measured by the number of sites being left blank we assess the performance of the new algorithm by numerical experiments on the simple three colour potts model more rigorously we present a probabilistic analysis of the algorithm the results indicate that the approximation is quite often sufficiently good for the interpretation of the image

marginally trapped submanifolds in lorentzian space forms and in the lorentzian product of a space form by the real line we give local explicit representation formulas for n dimensional spacelike submanifolds which are marginally trapped in the minkowski space r1n 2 the de sitter space d x1d54a n 2 the anti de sitter space ad x1d54a n 2 and the lorentzian products x1d54a n 1 and n 1 of the sphere and the hyperbolic space by the real line

deprecation based greedy strategy for target set selection in large scale social networks the problem of target set selection for large scale social networks is addressed in the paper we describe a novel deprecation based greedy strategy to be applied over a pre ordered as obtained with any heuristic influence function set of nodes the proposed algorithm runs in iteration and has two stages i estimation where the performance of each node is evaluated and ii marking where the nodes to be deprecated in later iterations are marked we have theoretically proved that for any monotonic and sub modular influence function the algorithm correctly identifies the nodes to be deprecated for any finite set of input nodes it is shown that the algorithm can meet the ending criteria the worst case performance of the algorithm both in terms of time and performance is also analyzed experimental results on seven un weighted as well as weighted social networks show that the proposed strategy improves the ranking of the input seeds in terms of the total number of nodes influenced

parallel surfaces in lorentzian three manifolds admitting a parallel null vector field we classify parallel surfaces in lorentzian three manifolds admitting a parallel null vector field some families of semi parallel surfaces are also described

about the parabolicity of trapped submanifolds in standard static spacetimes abstract in this work we introduce the concept of totally trapped submanifolds immersed in a lorentzian manifold moreover we obtain some uniqueness or non existence results for p parabolic submanifolds immersed in standard static spacetimes ssst in particular we derive some rigidity results for this type of submanifolds which guarantee that under appropriate hypothesis the only ones are those contained in slices in order to obtain these results we study the height function associated to the submanifold using the p laplacian for a function associated to the warping function of the ssst

global existence of small solutions to a class of nonlinear evolution equations on etudie le comportement global des solutions d une classe d equations d evolution non lineaires on considere le probleme aux valeurs initiales pour des equations quasilineaires qui sont des perturbations d equations lineaires dissipatives

intelligent reversible watermarking and authentication hiding depth map information for 3d cameras in this paper we propose an application for 3d cameras by reversibly hiding the depth map in the corresponding 2d images the proposed technique is prospective in cameras capable of capturing simultaneously the 2d image and resultant depth map of an object 3d cameras equipped with self embedding capability can serve two additional purposes protection of the captured image and secure transmission of its depth map the reversible watermarking in addition to other features guarantees the lossless recovery of an original image and separation of its depth map when required for this purpose a reversible watermarking scheme based on genetic algorithm ga has been proposed which computes suitable threshold for each block of coefficients in the wavelet domain thus a tradeoff is made between watermark imperceptibility and capacity using ga the threshold map is embedded in addition to the actual payload and thus the proposed approach does not require histogram pre processing in order to avoid overflow underflow the same threshold map has been used for authentication purpose by correlating it with the low frequency coefficients of the 2d transformed image further to exploit the inherent redundancy in the depth map which is the actual payload in this case lossless compression has been employed before its embedding similarly besides secret key based permutation a cryptographic layer is overlaid on the watermarking layer for security purposes experiments conducted on images and depth maps obtained using a 3d camera and an optical microscopic system validate the proposed concept

fast global image smoothing based on weighted least squares this paper presents an efficient technique for performing a spatially inhomogeneous edge preserving image smoothing called fast global smoother focusing on sparse laplacian matrices consisting of a data term and a prior term typically defined using four or eight neighbors for 2d image our approach efficiently solves such global objective functions in particular we approximate the solution of the memory and computation intensive large linear system defined over a d dimensional spatial domain by solving a sequence of 1d subsystems our separable implementation enables applying a linear time tridiagonal matrix algorithm to solve d three point laplacian matrices iteratively our approach combines the best of two paradigms i e efficient edge preserving filters and optimization based smoothing our method has a comparable runtime to the fast edge preserving filters but its global optimization formulation overcomes many limitations of the local filtering approaches our method also achieves high quality results as the state of the art optimization based techniques but runs 10 30 times faster besides considering the flexibility in defining an objective function we further propose generalized fast algorithms that perform l norm smoothing 0 2 and support an aggregated robust data term for handling imprecise data constraints we demonstrate the effectiveness and efficiency of our techniques in a range of image processing and computer graphics applications

an ensemble of intelligent water drop algorithms and its application to optimization problems the intelligent water drop iwd algorithm is a recent stochastic swarm based method that is useful for solving combinatorial and function optimization problems in this paper we propose an iwd ensemble known as the master river multiple creek iwd mrmc iwd model which serves as an extension of the modified iwd algorithm the mrmc iwd model aims to improve the exploration capability of the modified iwd algorithm it comprises a master river which cooperates with multiple independent creeks to undertake optimization problems based on the divide and conquer strategy a technique to decompose the original problem into a number of sub problems is first devised each sub problem is then assigned to a creek while the overall solution is handled by the master river to empower the exploitation capability a hybrid mrmc iwd model is introduced it integrates the iterative improvement local search method with the mrmc iwd model to allow a local search to be conducted therefore enhancing the quality of solutions provided by the master river to evaluate the effectiveness of the proposed models a series of experiments pertaining to two combinatorial problems i e the travelling salesman problem tsp and rough set feature subset selection rsfs are conducted the results indicate that the mrmc iwd model can satisfactorily solve optimization problems using the divide and conquer strategy by incorporating a local search method the resulting hybrid mrmc iwd model not only is able to balance exploration and exploitation but also to enable convergence towards the optimal solutions by employing a local search method in all seven selected tsplib problems the hybrid mrmc iwd model achieves good results with an average deviation of 0 021 from the best known optimal tour lengths compared with other state of the art methods the hybrid mrmc iwd model produces the best results i e the shortest and uniform reducts of 20 runs for all13 selected rsfs problems

shape from focus by tensor voting in this correspondence we address the task of recovering shape from focus sff as a perceptual organization problem in 3 d using tensor voting depth hypotheses from different focus operators are validated based on their likelihood to be part of a coherent 3 d surface thereby exploiting scene geometry and focus information to generate reliable depth estimates the proposed method is fast and yields significantly better results compared with existing sff methods

one dimensional regularization with discontinuities regularization is equivalent to fitting smoothing splines to the data so that efficient and reliable numerical algorithms exist for finding solutions however the results exhibit poor performance along edges and boundaries to cope with such anomalies a more general class of smoothing splines that preserve corners and discontinuities is studied cubic splines are investigated in detail since they are easy to implement and produce smooth curves near all data points except those marked as discontinuities or creases a discrete regularization method is introduced to locate corners and discontinuities in the data points before the continuous regularization is applied

weakly trapped submanifolds immersed in generalized robertson walker spacetimes abstract we deal with codimension two weakly trapped submanifolds that is the mean curvature vector field is causal immersed in a generalized robertson walker grw spacetime under suitable hypothesis we are able to prove that such a spacelike submanifold is immersed into a slice of the ambient space for this we use three main core concepts the well known generalized maximum principle of omori and yau stochastic completeness and another appropriate maximum principle at infinity due to yau we also construct a nontrivial example of weakly trapped submanifold in the static grw spacetime r h 2 r illustrating the importance of our results

on efficient k optimal location selection query processing in metric spaces this paper studies the problem of k optimal location selection kols retrieval in metric spaces given a set d a of customers a set d b of locations a constrained region r and a critical distance d c a metric kols mkols query retrieves k locations in d b that are outside r but have the maximal optimality scores here the optimality score of a location l d b located outside r is defined as the number of the customers in d a that are inside r and meanwhile have their distances to l bounded by d c according to a certain similarity metric e g l 1 norm l 2 norm etc the existing kols methods are not sufficient because they are applicable only to the euclidean space and are not sensitive to k in this paper for the first time we present an efficient algorithm for kols query processing in metric spaces our solution employs metric index structures i e m trees on the datasets enables several pruning rules utilizes the advantages of reuse technique and optimality score estimation to support a wide range of data types and similarity metrics in addition we extend our techniques to tackle two interesting and useful variants namely mkols queries with multiple or no constrained regions extensive experimental evaluation using both real and synthetic data sets demonstrates the effectiveness of the presented pruning rules and the performance of the proposed algorithms

classification of lorentzian surfaces with parallel mean curvature vector in pseudo euclidean spaces spatial surfaces with parallel mean curvature vector in pseudo euclidean spaces of arbitrary dimension and index were classified by b y chen in this work we give a complete classification of lorentzian surfaces with parallel mean curvature vector in pseudo euclidean spaces of arbitrary dimension and index consequently the problem to classify all the surfaces with parallel mean curvature vector in pseudo euclidean spaces has been solved

spatial and lorentzian surfaces in robertson walker space times let l14 f c i fs gfc be a robertson walker space time which does not contain any open subset of constant curvature in this paper we provide a general study of nondegenerate surfaces in l14 f c first we prove the nonexistence of marginally trapped surfaces with positive relative nullity then we classify totally geodesic submanifolds finally we classify the family of surfaces with parallel second fundamental form and the family of totally umbilical surfaces with parallel mean curvature vector

convergence analysis of canonical genetic algorithms this paper analyzes the convergence properties of the canonical genetic algorithm cga with mutation crossover and proportional reproduction applied to static optimization problems it is proved by means of homogeneous finite markov chain analysis that a cga will never converge to the global optimum regardless of the initialization crossover operator and objective function but variants of cga s that always maintain the best solution in the population either before or after selection are shown to converge to the global optimum due to the irreducibility property of the underlying original nonconvergent cga these results are discussed with respect to the schema theorem