exclusion and persistence in deterministic and stochastic chemostat models abstract we first introduce and analyze a variant of the deterministic single substrate chemostat model in this model microbe removal and growth rates depend on biomass concentration with removal terms increasing faster than growth terms using a comparison principle we show that persistence of all species is possible in this scenario then we turn to modelling the influence of random fluctuations by setting up and analyzing a stochastic differential equation in particular we show that random effects may lead to extinction in scenarios where the deterministic model predicts persistence on the other hand we also establish some stochastic persistence results

on a system of reaction diffusion equations arising from competition with internal storage in an unstirred chemostat abstract in this paper we study a system of reaction diffusion equations arising from competition of two microbial populations for a single limited nutrient with internal storage in an unstirred chemostat the conservation principle is used to reduce the dimension of the system by eliminating the equation for the nutrient the reduced system limiting system generates a strongly monotone dynamical system in its feasible domain under a partial order we construct suitable upper lower solutions to establish the existence of positive steady state solutions given the parameters of the reduced system we answer the basic questions as to which species survives and which does not in the spatial environment and determine the global behaviors the primary conclusion is that the survival of species depends on species s intrinsic biological characteristics the external environment forces and the principal eigenvalues of some scalar partial differential equations we also lift the dynamics of the limiting system to the full system

ends of maps ii versions of the finiteness obstruction and simple homotopy theory within e overx are developed this provides a setting for obstructions to the map analogs of the end ands cobordism theorems for manifolds these are applied to study equivariant mapping cylinder neighborhoods in topological group actions triangulations of locally triangulable spaces and block bundle structures on approximate fibrations

a mathematical model of competition for two essential resources in the unstirred chemostat a mathematical model of competition between two species for two growth limiting essential complementary resources in the unstirred chemostat is considered the existence of a positive steady state solution and some of its properties are established analytically techniques include the maximum principle the fixed point index and numerical simulations the simulations also seem to indicate that there are regions in parameter space for which a globally stable positive equilibrium occurs and that there are other regions for which the model admits bistability and even multiple positive equilibria

on the unification of line processes outlier rejection and robust statistics with applications in early vision the modeling of spatial discontinuities for problems such as surface recovery segmentation image reconstruction and optical flow has been intensely studied in computer vision while line process models of discontinuities have received a great deal of attention there has been recent interest in the use of robust statistical techniques to account for discontinuities this paper unifies the two approaches to achieve this we generalize the notion of a line process to that of an analog outlier process and show how a problem formulated in terms of outlier processes can be viewed in terms of robust statistics we also characterize a class of robust statistical problems for which an equivalent outlier process formulation exists and give a straightforward method for converting a robust estimation problem into an outlier process formulation we show how prior assumptions about the spatial structure of outliers can be expressed as constraints on the recovered analog outlier processes and how traditional continuation methods can be extended to the explicit outlier process formulation these results indicate that the outlier process approach provides a general framework which subsumes the traditional line process approaches as well as a wide class of robust estimation problems examples in surface reconstruction image segmentation and optical flow are presented to illustrate the use of outlier processes and to show how the relationship between outlier processes and robust statistics can be exploited an appendix provides a catalog of common robust error norms and their equivalent outlier process formulations

pattern formation in the brusselator system in the paper we deal with a reaction diffusion system well known as the brusselator model and some improved results for the steady states of this model are presented we first give an a priori estimates positive upper and lower bounds of positive steady states then we obtain the non existence and existence of positive non constant steady states as the parameters and b are varied which means some certain conditions under which the pattern formation occurs or not

soft color segmentation and its applications we propose an automatic approach to soft color segmentation which produces soft color segments with an appropriate amount of overlapping and transparency essential to synthesizing natural images for a wide range of image based applications although many state of the art and complex techniques are excellent at partitioning an input image to facilitate deriving a semantic description of the scene to achieve seamless image synthesis we advocate a segmentation approach designed to maintain spatial and color coherence among soft segments while preserving discontinuities by assigning to each pixel a set of soft labels corresponding to their respective color distributions we optimize a global objective function which simultaneously exploits the reliability given by global color statistics and flexibility of local image compositing leading to an image model where the global color statistics of an image is represented by a gaussian mixture model gmm whereas the color of a pixel is explained by a local color mixture model where the weights are defined by the soft labels to the elements of the converged gmm transparency is naturally introduced in our probabilistic framework which infers an optimal mixture of colors at an image pixel to adequately consider global and local information in the same framework an alternating optimization scheme is proposed to iteratively solve for the global and local model parameters our method is fully automatic and is shown to converge to a good optimal solution we perform extensive evaluation and comparison and demonstrate that our method achieves good image synthesis results for image based applications such as image matting color transfer image deblurring and image colorization

feature augmentation for learning confidence measure in stereo matching confidence estimation is essential for refining stereo matching results through a post processing step this problem has recently been studied using a learning based approach which demonstrates a substantial improvement on conventional simple non learning based methods however the formulation of learning based methods that individually estimates the confidence of each pixel disregards spatial coherency that might exist in the confidence map thus providing a limited performance under challenging conditions our key observation is that the confidence features and resulting confidence maps are smoothly varying in the spatial domain and highly correlated within the local regions of an image we present a new approach that imposes spatial consistency on the confidence estimation specifically a set of robust confidence features is extracted from each superpixel decomposed using the gaussian mixture model and then these features are concatenated with pixel level confidence features the features are then enhanced through adaptive filtering in the feature domain in addition the resulting confidence map estimated using the confidence features with a random regression forest is further improved through k nearest neighbor based aggregation scheme on both pixel and superpixel level to validate the proposed confidence estimation scheme we employ cost modulation or ground control points based optimization in stereo matching experimental results demonstrate that the proposed method outperforms state of the art approaches on various benchmarks including challenging outdoor scenes

coexistence and stability of an unstirred chemostat model with beddington deangelis function this paper deals with an unstirred chemostat model with the beddington deangelis functional response first a sufficient condition to the existence of positive steady state solutions is established second the effect of the parameter b 1 in the beddington deangelis functional response which models mutual interference between species u is considered the result shows that if b 1 is sufficiently large the solution of this model is determined by a limiting equation the main tool used here includes the fixed point index theory the perturbation technique and the bifurcation theory

asymptotic behavior of an unstirred chemostat model with internal inhibitor this paper deals with a chemostat model with an internal inhibitor first the elementary stability and asymptotic behavior of solutions of the system are determined second the effects of the inhibitor are considered it turns out that the parameter which measures the effect of the inhibitor plays a very important role in deciding the stability and longtime behavior of solutions of the system the results show that if is sufficiently large this model has no coexistence solution and one of the semitrivial equilibria is a global attractor when the maximal growth rate a of the species u lies in certain range but when a belongs to another range all positive solutions of this model are governed by a limit problem and two semitrivial equilibria are bistable the main tools used here include monotone system theory degree theory bifurcation theory and perturbation technique

stereo using monocular cues within the tensor voting framework we address the fundamental problem of matching in two static images the remaining challenges are related to occlusion and lack of texture our approach addresses these difficulties within a perceptual organization framework considering both binocular and monocular cues initially matching candidates for all pixels are generated by a combination of matching techniques the matching candidates are then embedded in disparity space where perceptual organization takes place in 3d neighborhoods and thus does not suffer from problems associated with scanline or image neighborhoods the assumption is that correct matches produce salient coherent surfaces while wrong ones do not matching candidates that are consistent with the surfaces are kept and grouped into smooth layers thus we achieve surface segmentation based on geometric and not photometric properties surface overextensions which are due to occlusion can be corrected by removing matches whose projections are not consistent in color with their neighbors of the same surface in both images finally the projections of the refined surfaces on both images are used to obtain disparity hypotheses for unmatched pixels the final disparities are selected after a second tensor voting stage during which information is propagated from more reliable pixels to less reliable ones we present results on widely used benchmark stereo pairs

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

an o 1 disparity refinement method for stereo matching disparity refinement is the final step but also the timing bottleneck of stereo matching due to its high computational complexity weighted media filter refinement method and non local refinement method are two typical refinement methods with o n computational complexity for each pixel where n indicates the maximum disparity this paper presents an o 1 disparity refinement method based on belief aggregation and belief propagation the aggregated belief which means the possibility of correct disparity value is efficiently computed on a minimum spanning tree first and then the belief aggregation is fast performed on another minimum spanning tree in two sequential passes first from leaf nodes to root then from root to leaf nodes only 2 additions and 4 multiplications are required for each pixel at all disparity levels so the computational complexity is o 1 performance evaluation on middlebury data sets shows that the proposed method has good performances both in accuracy and speed we proposed an o 1 disparity refinement method for each pixel speed evaluation shows constant result due to o 1 computational complexity accuracy evaluation shows better performance than 2 typical refinement methods

stereo matching with color weighted correlation hierarchical belief propagation and occlusion handling in this paper we formulate a stereo matching algorithm with careful handling of disparity discontinuity and occlusion the algorithm works with a global matching stereo model based on an energy minimization framework the global energy contains two terms the data term and the smoothness term the data term is first approximated by a color weighted correlation then refined in occluded and low texture areas in a repeated application of a hierarchical loopy belief propagation algorithm the experimental results are evaluated on the middlebury data sets showing that our algorithm is the top performer among all the algorithms listed there

a nonlinear boundary value problem arising from competition in the chemostat a boundary value problem with two parameters for two coupled second order nonlinear ordinary differential equations is considered this problem arises in a study of chemostats without a well mixing hypothesis the existence of a solution in the interior of the positive cone is established via two bifurcations some open questions are pointed out

positive solutions of a competition model for two resources in the unstirred chemostat this paper deals with a competition model between two species for two growth limiting and perfectly complementary resources in the unstirred chemostat the main purpose is to determine the exact range of the parameters of two species so that the system possesses positive solutions and to investigate multiple positive steady states of the system the main tools used here include the monotone methods and the topological fixed point theory developed by amann

stereo matching using epipolar distance transform in this paper we propose a simple but effective image transform called the epipolar distance transform for matching low texture regions it converts image intensity values to a relative location inside a planar segment along the epipolar line such that pixels in the low texture regions become distinguishable we theoretically prove that the transform is affine invariant thus the transformed images can be directly used for stereo matching any existing stereo algorithms can be directly used with the transformed images to improve reconstruction accuracy for low texture regions results on real indoor and outdoor images demonstrate the effectiveness of the proposed transform for matching low texture regions keypoint detection and description for low texture scenes our experimental results on middlebury images also demonstrate the robustness of our transform for highly textured scenes the proposed transform has a great advantage its low computational complexity it was tested on a macbook air laptop computer with a 1 8 ghz core i7 processor with a speed of about 9 frames per second for a video graphics array sized image

differential geometric inference in surface stereo many traditional two view stereo algorithms explicitly or implicitly use the frontal parallel plane assumption when exploiting contextual information since e g the smoothness prior biases toward constant disparity depth over a neighborhood this introduces systematic errors to the matching process for slanted or curved surfaces these errors are nonnegligible for detailed geometric modeling of natural objects such as a human face we show how to use contextual information geometrically to avoid such errors a differential geometric study of smooth surfaces allows contextual information to be encoded in cartan s moving frame model over local quadratic approximations providing a framework of geometric consistency for both depth and surface normals the accuracy of our reconstructions argues for the sufficiency of the approximation in effect cartan s model provides the additional constraint necessary to move beyond the frontal parallel plane assumption in stereo reconstruction it also suggests how geometry can extend surfaces to account for unmatched points due to partial occlusion

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

linear scale and rotation invariant matching matching visual patterns that appear scaled rotated and deformed with respect to each other is a challenging problem we propose a linear formulation that simultaneously matches feature points and estimates global geometrical transformation in a constrained linear space the linear scheme enables search space reduction based on the lower convex hull property so that the problem size is largely decoupled from the original hard combinatorial problem our method therefore can be used to solve large scale problems that involve a very large number of candidate feature points without using prepruning in the search this method is more robust in dealing with weak features and clutter we apply the proposed method to action detection and image matching our results on a variety of images and videos demonstrate that our method is accurate efficient and robust

accurate stereo matching by two step energy minimization in stereo matching cost filtering methods and energy minimization algorithms are considered as two different techniques due to their global extent energy minimization methods obtain good stereo matching results however they tend to fail in occluded regions in which cost filtering approaches obtain better results in this paper we intend to combine both the approaches with the aim to improve overall stereo matching results we show that a global optimization with a fully connected model can be solved by cost filtering methods based on this observation we propose to perform stereo matching as a two step energy minimization algorithm we consider two markov random field mrf models 1 a fully connected model defined on the complete set of pixels in an image and 2 a conventional locally connected model we solve the energy minimization problem for the fully connected model after which the marginal function of the solution is used as the unary potential in the locally connected mrf model experiments on the middlebury stereo data sets show that the proposed method achieves the state of the arts results

subgroups of bianchi groups and arithmetic quotients of hyperbolic 3 space let o be the ring of integers in an imaginary quadratic number field the group psl 2 o acts discontinuously on hyperbolic 3 space h if psl 2 o is a torsionfree subgroup of finite index then the manifold h can be compactified to a manifold m so that the inclusion h m is a homotopy equivalence m is a compact with boundary the boundary being a union of finitely many 2 tori this paper contains a computer aided study of subgroups of low index in psl 2 o for various o the explicit description of these subgroups leads to a study of the homeomorphism types of the m

on learning conditional random fields for stereo until recently the lack of ground truth data has hindered the application of discriminative structured prediction techniques to the stereo problem in this paper we use ground truth data sets that we have recently constructed to explore different model structures and parameter learning techniques to estimate parameters in markov random fields mrfs via maximum likelihood one usually needs to perform approximate probabilistic inference conditional random fields crfs are discriminative versions of traditional mrfs we explore a number of novel crf model structures including a crf for stereo matching with an explicit occlusion model crfs require expensive inference steps for each iteration of optimization and inference is particularly slow when there are many discrete states we explore belief propagation variational message passing and graph cuts as inference methods during learning and compare with learning via pseudolikelihood to accelerate approximate inference we have developed a new method called sparse variational message passing which can reduce inference time by an order of magnitude with negligible loss in quality learning using sparse variational message passing improves upon previous approaches using graph cuts and allows efficient learning over large data sets when energy functions violate the constraints imposed by graph cuts

stereo correspondence with compact windows via minimum ratio cycle one of the earliest and still widely used methods for dense stereo correspondence is based on matching windows of pixels the main difficulty of this method is choosing a window of appropriate size and shape small windows may lack sufficient intensity variation for reliable matching while large windows smooth out disparity discontinuities we propose an algorithm to choose a window size and shape by optimizing over a large class of compact windows the word compact is used informally to reflect the fact that the ratio of perimeter to area of our windows is small we believe that this is the first area based method which efficiently constructs nonrectangular windows fast optimization over compact windows is achieved via the minimum ratio cycle algorithm for graphs the algorithm has only a few parameters which are easy to fix

orientation guided geodesic weighting for patchmatch based stereo matching we propose an orientation guided geodesic weighting oggw strategy for local stereo matching we propose a method of cost volume filtering combining a multipoint lpa method with our oggw strategy we propose a patchmatch filter with curved surface fitting pmf cs to obtain a disparity map with sub pixel accuracy recently patchmatch based methods for local stereo matching are experiencing great progress with the use of compact and over segmented regions that have similar intensities or colors using patches as support regions this paper proposes an orientation guided geodesic weighting oggw strategy to search for an approximate shortest path from a support pixel in the patch to a pixel of interest along a guided orientation the oggw is computed by accumulating intensity differences or color dissimilarities between connected pixels along the path after obtaining matching cost updates by model fitting the oggw is used for weighted averaging on the updated costs to obtain a filtered cost volume in addition a new filtering method that combines the patchmatch filter with curved surface fitting pmf cs is presented in this paper curved surface fitting along with outliers removal is carried out to seek for a reliable regression model for estimating the disparities on a patch and to achieve a disparity map with sub pixel accuracy we conduct a number of experiments to evaluate the performances of oggw and pmf cs on cost volume filtering and disparity estimation experimental results show that our algorithm produces accurate stereo matching results and outperforms the current state of the art patchmatch based methods

a nonparametric belief propagation method for uncertainty quantification with applications to flow in random porous media a probabilistic graphical model approach to uncertainty quantification for flows in random porous media is introduced model reduction techniques are used locally in the graph to represent the random permeability then the conditional distribution of the multi output responses on the low dimensional representation of the permeability field is factorized into a product of local potential functions an expectation maximization algorithm is used to learn the nonparametric representation of these potentials using the given input output data we develop a nonparametric belief propagation method for uncertainty quantification by employing the loopy belief propagation algorithm the nonparametric nature of our model is able to capture non gaussian features of the response the proposed framework can be used as a surrogate model to predict the responses for new input realizations as well as our confidence on these predictions numerical examples are presented to demonstrate the accuracy and efficiency of the proposed framework for solving uncertainty quantification problems in flows through porous media using stationary and non stationary permeability fields

a reaction diffusion model of harmful algae and zooplankton in an ecosystem abstract this paper is devoted to the investigation of an unstirred chemostat system modeling the interactions of two essential nutrients i e nitrogen and phosphorus harmful algae i e p parvum and cyanobacteria and a small bodied zooplankton in an ecosystem to obtain a weakly repelling property of a compact and invariant set on the boundary we introduce an associated elliptic eigenvalue problem it turns out that the model system admits a coexistence steady state and is uniformly persistent provided that the trivial steady state two semi trivial steady states and a global attractor on the boundary are all weak repellers

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

a food chain model for two resources in un stirred chemostat this paper deals with a multiple food chain model in un stirred chemostat where the prey feeds on two growth limiting nonreproducing resources the conditions for existence of positive steady states are established the global bifurcation of positive solutions is considered also furthermore we obtain the conditions under which the predator possesses uniformly strong persistence or goes to extinction the techniques used in this paper include the degree theory the global bifurcation theory the semigroup theory and the maximum principle

optimal approximations by piecewise smooth functions and associated variational problems abstract this reprint will introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision in computer vision a fundamental problem is to appropriately decompose the domain r of a function g x y of two variables this problem starts by describing the physical situation which produces images assume that a three dimensional world is observed by an eye or camera from some point p and that g1 rho represents the intensity of the light in this world approaching the point sub 1 from a direction rho if one has a lens at p focusing this light on a retina or a film in both cases a plane domain r in which we may introduce coordinates x y then let g x y be the strength of the light signal striking r at a point with coordinates x y g x y is essentially the same as sub 1 rho possibly after a simple transformation given by the geometry of the imaging syste the function g x y defined on the plane domain r will be called an image what sort of function is g the light reflected off the surfaces si of various solid objects o sub i visible from p will strike the domain r in various open subsets r sub i when one object o1 is partially in front of another object o2 as seen from p but some of object o2 appears as the background to the sides of o1 then the open sets r1 and r2 will have a common boundary the edge of object o1 in the image defined on r and one usually expects the image g x y to be discontinuous along this boundary jhd

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

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

isomorphism conjectures in algebraic k theory duff in this paper we are concerned with the four functors y y3 if and which map from the category of topological spaces x to the category diff of q spectra the functor 3 or if maps the space x to the qspectrum of stable topological or smooth pseudoisotopies of x the spaces diff dif 3i x id9 x i 0 are hatcher s deloopings of 970 x yd x cf 29 the functor j maps a path connected space x to the algebraic ktheoretic s2 spectrum for the integral group ring z7r1x the spaces x x i 0 are the gersten wagoner deloopings of z o x cf 27 52 5 x is also defined on a nonpath connected space x to be x1 where xi i e i are the path components of x and ii xi indicates the direct limit of all finite products of the i xi i e i if x is path connected then the functor maps x to the l surgery classifying spaces for oriented surgery problems with fundamental group r i1x identified by their fourfold periodicity k 90 x k 4j x cf 35 39 44 47 in addition if x is not path connected then we set y77 x tiei5 fj xi where xi i e i are the path components of x results obtained by the authors over the past five years cf 15 25 and in particular 19 16 a 1 a 18 together with many earlier results and conjectures which are reviewed in 1 6 1 1 6 6 suggest that for any connected cwcomplex x and for 5 denoting any of the above functors the q spectrum x should be computable in a simple way from the values taken by 9 on covering spaces of x which have very simple fundamental groups in more detail we let 9 x denote the collection of all subgroups h c ir ix which are either finite or virtually infinite cyclic a group h is virtually infinite cyclic if there is a short exact sequence of groups 1 z h f 1 with f equal to a finite group and z equal to the infinite cyclic group for each such group we let xh x denote the covering space projection corresponding to h then the q spectrum 5 x should be computable in a simple way from the q spectra 5 xh h e 9 x the purpose of this paper is to formulate precisely a conjecture along these lines and to verify the conjecture for any x

two terminal video coding following recent works on the rate region of the quadratic gaussian two terminal source coding problem and limit approaching code designs this paper examines multiterminal source coding of two correlated i e stereo video sequences to save the sum rate over independent coding of both sequences two multiterminal video coding schemes are proposed in the first scheme the left sequence of the stereo pair is coded by h 264 avc and used at the joint decoder to facilitate wyner ziv coding of the right video sequence the first i frame of the right sequence is successively coded by h 264 avc intracoding and wyner ziv coding an efficient stereo matching algorithm based on loopy belief propagation is then adopted at the decoder to produce pixel level disparity maps between the corresponding frames of the two decoded video sequences on the fly based on the disparity maps side information for both motion vectors and motion compensated residual frames of the right sequence are generated at the decoder before wyner ziv encoding in the second scheme source splitting is employed on top of classic and wyner ziv coding for compression of both i frames to allow flexible rate allocation between the two sequences experiments with both schemes on stereo video sequences using h 264 avc ldpc codes for slepian wolf coding of the motion vectors and scalar quantization in conjunction with ldpc codes for wyner ziv coding of the residual coefficients give a slightly lower sum rate than separate h 264 avc coding of both sequences at the same video quality

fusion of median and bilateral filtering for range image upsampling we present a new upsampling method to enhance the spatial resolution of depth images given a low resolution depth image from an active depth sensor and a potentially high resolution color image from a passive rgb camera we formulate it as an adaptive cost aggregation problem and solve it using the bilateral filter the formulation synergistically combines the median and bilateral filters thus it better preserves the depth edges and is more robust to noise numerical and visual evaluations on a total of 37 middlebury data sets demonstrate the effectiveness of our method a real time high resolution depth capturing system is also developed using commercial active depth sensor based on the proposed upsampling method

a system of partial differential equations modeling the competition for two complementary resources in flowing habitats abstract this paper examines a system of reaction diffusion equations arising from a flowing water habitat in this habitat one or two microorganisms grow while consuming two growth limiting complementary essential resources for the single population model the existence and uniqueness of a positive steady state solution is proved furthermore the unique positive solution is globally attracting for the system with regard to nontrivial nonnegative initial values mathematical analysis for the two competing populations is carried out more precisely the long time behavior is determined by using the monotone dynamical system theory when the semi trivial solutions are both unstable it is also shown that coexistence solutions exist by using the fixed point index theory when the semi trivial solutions are both asymptotically stable

a system of resource based growth models with two resources in the unstirred chemostat abstract models of single species growth in the unstirred chemostat on two growth limiting nonreproducing resources are considered for the case of two complementary resources the existence and uniqueness of a positive steady state solution is established it is also proved that the unique positive solution is globally attracting for the system with regard to nontrivial nonnegative initial values for the case of two substitutable resources the existence of a positive steady state solution is determined for a range of the parameter m n techniques include the maximum principle monotone method and global bifurcation theory the longtime behavior of the corresponding limiting system is given for a range of m n in the special case of m n the uniqueness and global attractivity of the positive steady state solution of the original system is established

steady state solutions of a reaction diffusion system arising from intraguild predation and internal storage abstract intraguild predation is added to a mathematical model of competition between two species for a single nutrient with internal storage in the unstirred chemostat at first we established the sharp a priori estimates for nonnegative solutions of the system which assure that all of nonnegative solutions belong to a special cone the selection of this special cone enables us to apply the topological fixed point theorems in cones to establish the existence of positive solutions secondly existence for positive steady state solutions of intraguild prey and intraguild predator is established in terms of the principal eigenvalues of associated nonlinear eigenvalue problems by means of the degree theory in the special cone it turns out that positive steady state solutions exist when the associated principal eigenvalues are both negative or both positive

a competition model for two resources in un stirred chemostat abstract this paper studies a un stirred chemostat with two species competing for two growth limiting non reproducing resources we determine the conditions for positive steady states of the two species and then consider the global attractors of the model in addition we obtain the conditions under which the two populations uniformly strongly persist or go to extinction since the diffusion mechanism with homogeneous boundary conditions inhibits the growth of the organism species it can be understood that the coexistence will be ensured by proportionally smaller diffusions for the two species in particular it is found that both instability and bi stability subcases of the two semitrivial steady states are included in the coexistence region the two populations will go to extinction when both possess large diffusion rates if just one of them spreads faster with the other one diffusing slower then the related semitrivial steady state will be globally attracting the techniques used for the above results consist of the degree theory the semigroup theory and the maximum principle

statistical modeling of 3 d natural scenes with application to bayesian stereopsis we studied the empirical distributions of luminance range and disparity wavelet coefficients using a coregistered database of luminance and range images the marginal distributions of range and disparity are observed to have high peaks and heavy tails similar to the well known properties of luminance wavelet coefficients however we found that the kurtosis of range and disparity coefficients is significantly larger than that of luminance coefficients we used generalized gaussian models to fit the empirical marginal distributions we found that the marginal distribution of luminance coefficients have a shape parameter p between 0 6 and 0 8 while range and disparity coefficients have much smaller parameters p 0 32 corresponding to a much higher peak we also examined the conditional distributions of luminance range and disparity coefficients the magnitudes of luminance and range disparity coefficients show a clear positive correlation which means at a location with larger luminance variation there is a higher probability of a larger range disparity variation we also used generalized gaussians to model the conditional distributions of luminance and range disparity coefficients the values of the two shape parameters p s reflect the observed luminance range disparity dependency as an example of the usefulness of luminance statistics conditioned on range statistics we modified a well known bayesian stereo ranging algorithm using our natural scene statistics models which improved its performance

parallel and deterministic algorithms from mrfs surface reconstruction deterministic approximations to markov random field mrf models are derived one of the models is shown to give in a natural way the graduated nonconvexity gnc algorithm proposed by a blake and a zisserman 1987 this model can be applied to smooth a field preserving its discontinuities a class of more complex models is then proposed in order to deal with a variety of vision problems all the theoretical results are obtained in the framework of statistical mechanics and mean field techniques a parallel iterative algorithm to solve the deterministic equations of the two models is presented together with some experiments on synthetic and real images

large occlusion stereo a method for solving the stereo matching problem in the presence of large occlusion is presented a data structure the disparity space image is defined to facilitate the description of the effects of occlusion on the stereo matching process and in particular on dynamic programming dp solutions that find matches and occlusions simultaneously we significantly improve upon existing dp stereo matching methods by showing that while some cost must be assigned to unmatched pixels sensitivity to occlusion cost and algorithmic complexity can be significantly reduced when highly reliable matches or ground control points are incorporated into the matching process the use of ground control points eliminates both the need for biasing the process towards a smooth solution and the task of selecting critical prior probabilities describing image formation finally we describe how the detection of intensity edges can be used to bias the recovered solution such that occlusion boundaries will tend to be proposed along such edges reflecting the observation that occlusion boundaries usually cause intensity discontinuities

on a system of reaction diffusion equations arising from competition in an unstirred chemostat a system of reaction diffusion equations modeling two species competition in an unstirred chemostat is considered the asymptotic behavior of solutions is given as a function of the parameters and it is determined when neither one or both competing populations survive techniques include the maximum principle theory of uniform persistence in infinite dimensional dynamical systems and the theory of strongly order preserving semidynamical system

multiflash stereopsis depth edge preserving stereo with small baseline illumination traditional stereo matching algorithms are limited in their ability to produce accurate results near depth discontinuities due to partial occlusions and violation of smoothness constraints in this paper we use small baseline multiflash illumination to produce a rich set of feature maps that enable the acquisition of discontinuity preserving point correspondences first from a single multiflash camera we formulate a qualitative depth map using a gradient domain method that encodes object relative distances then in a multiview setup we exploit shadows created by light sources to compute an occlusion map finally we demonstrate the usefulness of these feature maps by incorporating them into two different dense stereo correspondence algorithms the first based on local search and the second based on belief propagation experimental results show that our enhanced stereo algorithms are able to extract high quality discontinuity preserving correspondence maps from scenes that are extremely challenging for conventional stereo methods we also demonstrate that small baseline illumination can be useful to handle specular reflections in stereo imagery different from most existing active illumination techniques our method is simple inexpensive and compact and requires no calibration of light sources

pattern formation of a coupled two cell brusselator model abstract in this paper we study the stationary problems for the coupled two cell brusselator model as follows d 1 u 1 b 1 u b u 2 v c w u in d 2 v u u 2 v in d 1 w 1 b 1 w b w 2 z c u w in d 2 z w w 2 z in u v w z 0 on we first study the stability of the unique positive constant solution u v w z 1 1 1 1 then we give a priori estimate positive upper and lower bounds to the positive solution at last we obtain the non existence and existence of positive non constant solutions as parameters d 1 d 2 and b varied

a reaction advection diffusion system modeling the competition for two complementary resources with seasonality in a flowing habitat abstract in this current paper we investigate a periodic bio reactor model where microorganisms compete for two essential nutrient resource s needed for growth for the single population growth model we show that when the trivial solution is locally asymptotically stable then the single population will be washed out when the trivial solution is unstable there is a unique periodic positive solution which attracts all solutions with nonzero initial data for the two species model we prove that the existence of a periodic coexistence state is possible if each species can invade the semi trivial periodic state established by the other species more precisely if the semi trivial periodic solutions are both unstable there exists at least one periodic coexistence solution numerical work indicates conditions for persistence depend on the flow characteristics advection and diffusivity from our numerical simulations competitive exclusion bistability and coexistence are all observed

the farrell jones isomorphism conjecture for finite covolume hyperbolic actions and the algebraic theory of bianchi groups we prove the farrell jones isomorphism conjecture for groups acting properly discontinuously via isometries on real hyperbolic n space ihin with finite volume orbit space we then apply this result to show that for any bianchi group f wh f ko zr and ki zr vanish for i 1

global stereo reconstruction under second order smoothness priors second order priors on the smoothness of 3d surfaces are a better model of typical scenes than first order priors however stereo reconstruction using global inference algorithms such as graph cuts has not been able to incorporate second order priors because the triple cliques needed to express them yield intractable nonsubmodular optimization problems this paper shows that inference with triple cliques can be effectively performed our optimization strategy is a development of recent extensions to alpha expansion based on the ldquo qpbordquo algorithm the strategy is to repeatedly merge proposal depth maps using a novel extension of qpbo proposal depth maps can come from any source for example frontoparallel planes as in alpha expansion or indeed any existing stereo algorithm with arbitrary parameter settings

near real time stereo matching with slanted surface modeling and sub pixel accuracy this paper presents a new stereo matching algorithm which takes into consideration surface orientation at the per pixel level two disparity calculation passes are used the first pass assumes that surfaces in the scene are fronto parallel and generates an initial disparity map from which the disparity plane orientations of all pixels are estimated and refined in the second pass the matching costs for different pixels are aggregated along the estimated disparity plane orientations using adaptive support weights where the support weights of neighboring pixels are calculated using a combination of four terms a spatial proximity term a color similarity term a disparity similarity term and an occlusion handling term the disparity search space is quantized at sub pixel level to improve the accuracy of the disparity results the algorithm is designed for parallel execution on graphics processing units gpus for near real time processing speed the evaluation using middlebury benchmark shows that the presented approach outperforms existing real time and near real time algorithms in terms of subpixel level accuracy

stereo matching with nonlinear diffusion one of the central problems in stereo matching and other image registration tasks is the selection of optimal window sizes for comparing image regions this paper addresses this problem with some novel algorithms based on iteratively diffusing support at different disparity hypotheses and locally controlling the amount of diffusion based on the current quality of the disparity estimate it also develops a novel bayesian estimation technique which significantly outperforms techniques based on area based matching ssd and regular diffusion we provide experimental results on both synthetic and real stereo image pairs