on the problem of evaluating quasistationary distributions for open reaction schemes a number of recent papers have been concerned with the stochastic modeling of autocatalytic reactions in some instances the birth and death model has been criticized for its apparent inadequacy in being able to describe the long term behavior of the catalyst in particular the fluctuations in the concentration of the catalyst about its macroscopically stable state this criticism has been answered to some extent with the introduction of the notion of a quasistationary distribution a number of authors have established the existence of limiting conditional distributions that can adequately describe these fluctuations however much of the work appears only to be appropriate for dealing with closed systems for attention is usually restricted to finite state birth and death processes for open systems it is more appropriate to consider infinite state processes and from the point of view of establishing conditions for the existence of quasistationary distributions extending the results for closed systems is far from straightforward here simple conditions are given for the existence of quasistationary distributions for markov processes with a denumerable infinity of states these can be applied to any open autocatalytic system the results also extend to explosive processes and to processes that terminate with probability less than 1

optic flow based on multi scale anchor point movement and discontinuity preserving regularization we introduce a new method to determine the flow field of an image sequence using multi scale anchor points these anchor points manifest themselves in the scale space representation of an image the novelty of our method lies largely in the fact that the relation between the scale space anchor points and the flow field is formulated in terms of soft constraints in a variational method this leads to an algorithm for the computation of the flow field that differs fundamentally from previously proposed ones based on hard constraints we show a significant performance increase when our method is applied to the yosemite image sequence a standard and well established benchmark sequence in optic flow research also it is shown that this performance is not sensitive to slight changes in the two parameters used and that with the same parameter values our method yields very good results in the rubber whale image sequence as well

feature based image analysis according to marr s paradigm of computational vision the first process is an extraction of relevant features the goal of this paper is to quantify and characterize the information carried by features using image structure measured at feature points to reconstruct images in this way we indirectly evaluate the concept of feature based image analysis the main conclusions are that i a reasonably low number of features characterize the image to such a high degree that visually appealing reconstructions are possible ii different feature types complement each other and all carry important information the strategy is to define metamery classes of images and examine the information content of a canonical least informative representative of this class algorithms for identifying these are given finally feature detectors localizing the most informative points relative to different complexity measures derived from models of natural image statistics are given

on the estimation of optical flow relations between different approaches and some new results abstract a common basis is suggested for the optical flow estimation approaches of nagel 1983 haralick and lee 1983 and tretiak and pastor 1984 based on a discussion of these approaches an exact solution for the system of partial differential equations proposed by horn and schunck 1981 is given at gray value corners and extrema the insight gained by this solution results in a modification of the oriented smoothness approach of nagel 1983 which thereby becomes considerably simpler in addition the optical flow estimation approach of hildreth 1983 1984 can be shown to represent a kind of special case of this modified oriented smoothness approach in a more direct manner than discussed in nagel 1984

a combined post filtering method to improve accuracy of variational optical flow estimation we present a novel combined post filtering cpf method to improve the accuracy of optical flow estimation its attractive advantages are that outliers reduction is attained while discontinuities are well preserved and occlusions are partially handled major contributions are the following first the structure tensor st based edge detection is introduced to extract flow edges moreover we improve the detection performance by extending the traditional 2d spatial edge detector into spatial scale 3d space and also using a gradient bilateral filter gbf to replace the linear gaussian filter to construct a multi scale nonlinear st gbf is useful to preserve discontinuity but it is computationally expensive a hybrid gbf and gaussian filter hgbgf approach is proposed by means of a spatial scale gradient signal to noise ratio snr measure to solve the low efficiency issue additionally a piecewise occlusion detection method is used to extract occlusions second we apply a cpf method which uses a weighted median filter wmf a bilateral filter bf and a fast median filter mf to post smooth the detected edges and occlusions and the other flat regions of the flow field respectively benchmark tests on both synthetic and real sequences demonstrate the effectiveness of our method

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

the calabi metric for the space of kahler metrics given any closed kahler manifold we define following an idea by calabi bull am math soc 60 167 168 1954 a riemannian metric on the space of kahler metrics regarded as an infinite dimensional manifold we prove several geometrical features of the resulting space some of which we think were already known to calabi in particular the space is a portion of an infinite dimensional sphere and explicit unique smooth solutions for the cauchy and the dirichlet problems for the geodesic equation are given

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

long time existence of minimizing movement solutions of calabi flow abstract we recast the calabi flow in degiorgi s language of minimizing movements we establish the long time existence of minimizing movements for k energy with arbitrary initial condition furthermore we establish some a priori regularity results for these solutions and that sufficiently regular minimizing movements are smooth solutions to calabi flow

motion estimation using the correlation transform the zero mean normalized cross correlation is shown to improve the accuracy of optical flow but its analytical form is quite complicated for the variational framework this paper addresses this issue and presents a new direct approach to this matching measure our approach uses the correlation transform to define very discriminative descriptors that are pre computed and that have to be matched in the target frame it is equivalent to the computation of the optical flow for the correlation transforms of the images the smoothness energy is non local and uses a robust penalty in order to preserve motion discontinuities the model is associated with a fast and parallelizable minimization procedure based on the projected proximal point algorithm the experiments confirm the strength of this model and implicitly demonstrate the correctness of our solution the results demonstrate that the involved data term is very robust with respect to changes in illumination especially where large illumination exists

a decoupled approach to illumination robust optical flow estimation despite continuous improvements in optical flow in the last three decades the ability for optical flow algorithms to handle illumination variation is still an unsolved challenge to improve the ability to interpret apparent object motion in video containing illumination variation an illumination robust optical flow method is designed this method decouples brightness into reflectance and illumination components using a stochastic technique reflectance is given higher weight to ensure robustness against illumination which is suppressed illumination experiments using the middlebury and university of oulu databases demonstrate the decoupled method s improvement when compared with state of the art in addition a novel technique is implemented to visualize optical flow output which is especially useful to compare different optical flow methods in the absence of the ground truth

the space of kahler metrics this paper the second of a series deals with the function space mathcal h of all smooth kahler metrics in any given n dimensional closed complex manifold v these metrics being restricted to a given fixed real cohomology class called a polarization of v this function space is equipped with a pre hilbert metric structure introduced by t mabuchi 10 who also showed that formally this metric has nonpositive curvature in the first paper of this series 4 the second author showed that the same space is a path length space he also proved that mathcal h is geodesically convex in the sense that for any two points of mathcal h there is a unique geodesic path joining them which is always length minimizing and of class c1 1 this partially verifies two conjectures of donaldson 8 on the subject in the present paper we show first of all that the space is as expected a path length space of nonpositive curvature in the sense of a d aleksandrov a second result is related to the theory of extremal kahler metrics namely that the gradient flow in mathcal h of the k energy of v has the property that it strictly decreases the length of all paths in mathcal h except those induced by one parameter families of holomorphic automorphisms of m

optimal lower bounds for donaldson s j functional abstract in this paper we provide an explicit formula for the optimal lower bound of donaldson s j functional in the sense of finding explicitly the optimal constant in the definition of coercivity which always exists and takes negative values in general this constant is positive precisely if the j equation admits a solution and the explicit formula has a number of applications first this leads to new existence criteria for constant scalar curvature kahler csck metrics in terms of tian s alpha invariant moreover we use the above formula to discuss calabi dream manifolds and an analogous notion for the j equation and show that for surfaces the optimal bound is an explicitly computable rational function which typically tends to minus infinity as the underlying class approaches the boundary of the kahler cone even when the underlying kahler classes admit csck metrics as a final application we show that if the lejmi szekelyhidi conjecture holds then the optimal bound coincides with its algebraic counterpart the set of j semistable classes equals the closure of the set of uniformly j stable classes in the kahler cone and there exists an optimal degeneration for uniform j stability

morphologically invariant matching of structures with the complete rank transform invariances are one of the key concepts to render computer vision algorithms robust against severe illumination changes however there is no free lunch with any invariance comes an unavoidable loss of information the goal of our paper is to introduce two novel descriptors which minimise this loss the complete rank transform and the complete census transform they are invariant under monotonically increasing intensity rescalings while containing a maximum possible amount of information to analyse our descriptors we embed them as constancy assumptions into a variational framework for optic flow computation as a suitable regularisation term we choose total generalised variation that favours piecewise affine solutions our experiments focus on the kitti benchmark where robustness w r t illumination changes is one of the main issues the results demonstrate that our descriptors yield state of the art accuracy

a brunn minkowski type inequality for fano manifolds and some uniqueness theorems in kahler geometry for phi a metric on the anticanonical bundle k x of a fano manifold x we consider the volume of x begin aligned int x e phi end aligned in earlier papers we have proved that the logarithm of the volume is concave along geodesics in the space of positively curved metrics on k x our main result here is that the concavity is strict unless the geodesic comes from the flow of a holomorphic vector field on x even with very low regularity assumptions on the geodesic as a consequence we get a simplified proof of the bando mabuchi uniqueness theorem for kahler einstein metrics a generalization of this theorem to twisted kahler einstein metrics and some classes of manifolds that satisfy weaker hypotheses than being fano is also given we moreover discuss a generalization of the main result to other bundles than k x and finally use the same method to give a new proof of the theorem of tian and zhu on uniqueness of kahler ricci solitons

scene segmentation from visual motion using global optimization this paper presents results from computer experiments with an algorithm to perform scene disposition and motion segmentation from visual motion or optic flow the maximum a posteriori map criterion is used to formulate what the best segmentation or interpretation of the scene should be where the scene is assumed to be made up of some fixed number of moving planar surface patches the bayesian approach requires first specification of prior expectations for the optic flow field which here is modeled as spatial and temporal markov random fields and secondly a way of measuring how well the segmentation predicts the measured flow field the markov random fields incorporate the physical constraints that objects and their images are probably spatially continuous and that their images are likely to move quite smoothly across the image plane to compute the flow predicted by the segmentation a recent method for reconstructing the motion and orientation of planar surface facets is used the search for the globally optimal segmentation is performed using simulated annealing

variational method for joint optical flow estimation and edge aware image restoration the most popular optical flow algorithms rely on optimizing the energy function that integrates a data term and a smoothness term in contrast to this traditional framework we derive a new objective function that couples optical flow estimation and image restoration our method is inspired by the recent successes of edge aware constraints eac in preserving edges in general gradient domain image filtering by incorporating an eac image fidelity term ift in the conventional variational model the new energy function can simultaneously estimate optical flow and restore images with preserved edges in a bidirectional manner for the energy minimization we rewrite the eac into gradient form and optimize the ift with euler lagrange equations we can thus apply the image restoration by analytically solving a system of linear equations our eac combined ift is easy to implement and can be seamlessly integrated into various optical flow functions suggested in literature extensive experiments on public optical flow benchmarks demonstrate that our method outperforms the current state of the art in optical flow estimation and image restoration highlightsincorporating an eac added ift to the variational model to form a new energy function which can estimate optical flow and restore images jointly the eac can be rewritten into the first order gradient form and is beneficial for preserving edges and minimization input images can be fast restored by optimizing the euler lagrange equations of the eac integrated ift

monge ampere equations in big cohomology classes we define non pluripolar products of an arbitrary number of closed positive 1 1 currents on a compact kahler manifold x given a big 1 1 cohomology class on x i e a class that can be represented by a strictly positive current and a positive measure on x of total mass equal to the volume of and putting no mass on pluripolar sets we show that can be written in a unique way as the top degree self intersection in the non pluripolar sense of a closed positive current in we then extend kolodziedj s approach to sup norm estimates to show that the solution has minimal singularities in the sense of demailly if has l 1 e density with respect to lebesgue measure if is smooth and positive everywhere we prove that t is smooth on the ample locus of provided is nef using a fixed point theorem we finally explain how to construct singular kahler einstein volume forms with minimal singularities on varieties of general type

weighted local intensity fusion method for variational optical flow estimation estimating a dense motion field of successive video frames is a fundamental problem in image processing the multi scale variational optical flow method is a critical technique that addresses this issue despite the considerable progress over the past decades there are still some challenges such as dealing with large displacements and estimating the smoothness parameter we present a local intensity fusion lif method to tackle these difficulties by evaluating the local interpolation error in terms of l1 block match on the corresponding set of images we fuse flow proposals which are obtained from different methods and from different parameter settings integrally under a unified lif this approach has two benefits 1 the incorporated matching information is helpful to recover large displacements and 2 the obtained optimal fusion solution gives a tradeoff between the data term and the smoothness term in addition a selective gradient based weight is introduced to improve the performance of the lif finally we propose a corrected weighted median filter cwmf which applies the motion information to correct errors of the color distance weight to denoise the intermediate flow fields during optimization experiments demonstrate the effectiveness of our method highlightsa lif is proposed to handle both large and small motion and to estimate smoothness parameter a selective gradient is introduced to the lif to reduce errors that are caused by outliers a cwmf is designed to overcome the defect of traditional wmf

a theoretical framework for convex regularizers in pde based computation of image motion many differential methods for the recovery of the optic flow field from an image sequence can be expressed in terms of a variational problem where the optic flow minimizes some energy typically these energy functionals consist of two terms a data term which requires e g that a brightness constancy assumption holds and a regularizer that encourages global or piecewise smoothness of the flow field in this paper we present a systematic classification of rotation invariant convex regularizers by exploring their connection to diffusion filters for multichannel images this taxonomy provides a unifying framework for data driven and flow driven isotropic and anisotropic as well as spatial and spatio temporal regularizers while some of these techniques are classic methods from the literature others are derived here for the first time we prove that all these methods are well posed they posses a unique solution that depends in a continuous way on the initial data an interesting structural relation between isotropic and anisotropic flow driven regularizers is identified and a design criterion is proposed for constructing anisotropic flow driven regularizers in a simple and direct way from isotropic ones its use is illustrated by several examples

reliable estimation of dense optical flow fields with large displacements in this paper we show that a classic optical flow technique by nagel and enkelmann 1986 ieee trans pattern anal mach intell vol 8 pp 565 593 can be regarded as an early anisotropic diffusion method with a diffusion tensor we introduce three improvements into the model formulation that i avoid inconsistencies caused by centering the brightness term and the smoothness term in different images ii use a linear scale space focusing strategy from coarse to fine scales for avoiding convergence to physically irrelevant local minima and iii create an energy functional that is invariant under linear brightness changes applying a gradient descent method to the resulting energy functional leads to a system of diffusion reaction equations we prove that this system has a unique solution under realistic assumptions on the initial data and we present an efficient linear implicit numerical scheme in detail our method creates flow fields with 100 density over the entire image domain it is robust under a large range of parameter variations and it can recover displacement fields that are far beyond the typical one pixel limits which are characteristic for many differential methods for determining optical flow we show that it performs better than the optical flow methods with 100 density that are evaluated by barron et al 1994 int j comput vision vol 12 pp 43 47 our software is available from the internet

a gradient estimate in the calabi yau theorem we prove a c 1 estimate for the complex monge ampere equation on a compact kahler manifold directly from the c 0 estimate without using a c 2 estimate this was earlier done only under additional assumption of non negative bisectional curvature

ricci flow and the metric completion of the space of kahler metrics we consider the space of kahler metrics as a riemannian submanifold of the space of riemannian metrics and study the associated submanifold geometry in particular we show that the intrinsic and extrinsic distance functions are equivalent we also determine the metric completion of the space of kahler metrics making contact with recent generalizations of the calabi yau theorem due to dinew and guedj zeriahi as an application we obtain a new analytic stability criterion for the existence of a kahler einstein metric on a fano manifold in terms of the ricci flow and the distance function we also prove that the kahler ricci flow converges as soon as it converges in the metric sense

piecewise smooth dense optical flow via level sets we propose a new algorithm for dense optical flow computation dense optical flow schemes are challenged by the presence of motion discontinuities in state of the art optical flow methods over smoothing of flow discontinuities accounts for most of the error a breakthrough in the performance of optical flow computation has recently been achieved by brox et al our algorithm embeds their functional within a two phase active contour segmentation framework piecewise smooth flow fields are accommodated and flow boundaries are crisp experimental results show the superiority of our algorithm with respect to alternative techniques we also study a special case of optical flow computation in which the camera is static in this case we utilize a known background image to separate the moving elements in the sequence from the static elements tests with challenging real world sequences demonstrate the performance gains made possible by incorporating the static camera assumption in our algorithm

robust non local tv l 1 optical flow estimation with occlusion detection in this paper we propose a robust non local tv l 1 optical flow method with occlusion detection to address the problem of weak robustness of optical flow estimation with motion occlusion first a tv l 1 form for flow estimation is defined using a combination of the brightness constancy and gradient constancy assumptions in the data term and by varying the weight under the charbonnier function in the smoothing term second to handle the potential risk of the outlier in the flow field a general non local term is added in the tv l 1 optical flow model to engender the typical non local tv l 1 form third an occlusion detection method based on triangulation is presented to detect the occlusion regions of the sequence the proposed non local tv l 1 optical flow model is performed in a linearizing iterative scheme using improved median filtering and a coarse to fine computing strategy the results of the complex experiment indicate that the proposed method can overcome the significant influence of non rigid motion motion occlusion and large displacement motion results of experiments comparing the proposed method and existing state of the art methods by respectively using middlebury and mpi sintel database test sequences show that the proposed method has higher accuracy and better robustness

highly accurate optic flow computation with theoretically justified warping in this paper we suggest a variational model for optic flow computation based on non linearised and higher order constancy assumptions besides the common grey value constancy assumption also gradient constancy as well as the constancy of the hessian and the laplacian are proposed since the model strictly refrains from a linearisation of these assumptions it is also capable to deal with large displacements for the minimisation of the rather complex energy functional we present an efficient numerical scheme employing two nested fixed point iterations following a coarse to fine strategy it turns out that there is a theoretical foundation of so called warping techniques hitherto justified only on an experimental basis since our algorithm consists of the integration of various concepts ranging from different constancy assumptions to numerical implementation issues a detailed account of the effect of each of these concepts is included in the experimental section the superior performance of the proposed method shows up by significantly smaller estimation errors when compared to previous techniques further experiments also confirm excellent robustness under noise and insensitivity to parameter variations

on functionals with greyvalue controlled smoothness terms for determining optical flow the modification by h h nagel 1987 of the approach developed by b k p horn and b g schunck 1981 for determining optical flow is generalized to the case where local motion information is given by more than one constraint equation applying this scheme to three constraint equations reported in the literature as a special case a generalization of nagel s approach is obtained an existence and uniqueness result of solutions under very general conditions that in turn ensures the applicability of standard techniques to compute an approximate solution is presented

uniqueness in e x ω abstract we prove uniqueness for the dirichlet problem for the complex monge ampere equation on compact kahler manifolds in the case of probability measures vanishing on pluripolar sets the proof uses the mass concentration technique due to kolodziej coupled with inequalities for mixed monge ampere measures and the comparison principle

the weighted monge ampere energy of quasiplurisubharmonic functions abstract we study degenerate complex monge ampere equations on a compact kahler manifold x we show that the complex monge ampere operator d d c n is well defined on the class e x of plurisubharmonic functions with finite weighted monge ampere energy the class e x is the largest class of psh functions on which the monge ampere operator is well defined and the comparison principle is valid it contains several functions whose gradient is not square integrable we give a complete description of the range of the operator d d c n on e x as well as on some of its subclasses we also study uniqueness properties extending calabi s result to this unbounded and degenerate situation and we give applications to complex dynamics and to the existence of singular kahler einstein metrics

regularization strategies for discontinuity preserving optical flow methods the aim of this paper is to study several strategies for the preservation of flow discontinuities in variational optical flow methods we analyze the combination of robust functionals and diffusion tensors in the smoothness assumption our study includes the use of tensors based on decreasing functions which has shown to provide good results however it presents several limitations and usually does not perform better than other basic approaches it typically introduces instabilities in the computed motion fields in the form of independent blobs of vectors with large magnitude we propose two alternatives to overcome these drawbacks first a simple approach that combines the decreasing function with a minimum isotropic smoothing and second a method that looks for the best parameter configuration that preserves the important motion contours and avoid instabilities it relies on the input images and the regularization parameter it is fully automatic providing a near optimal value for many sequences as shown in the experiments both proposals allow to detect the contours of the motion field and produce more stable solutions for a large range of parameters in the experimental results we present a detailed study and comparison of the different strategies

quasi stationary distributions for discrete state models this paper contains a survey of results related to quasi stationary distributions which arise in the setting of stochastic dynamical systems that eventually evanesce and which may be useful in describing the long term behaviour of such systems before evanescence we are concerned mainly with continuous time markov chains over a finite or countably infinite state space since these processes most often arise in applications but will make reference to results for other processes where appropriate next to giving an historical account of the subject we review the most important results on the existence and identification of quasi stationary distributions for general markov chains and give special attention to birth death processes and related models the question of under what circumstances a quasi stationary distribution given its existence is indeed a good descriptor of the long term behaviour of a system before evanescence is addressed as well we conclude with a discussion of computational aspects with more details given in a web appendix accompanying this paper

an investigation of smoothness constraints for the estimation of displacement vector fields from image sequences a mapping between one frame from an image sequence and the preceding or following frame can be represented as a displacement vector field in most situations the mere gray value variations do not provide sufficient information in order to estimate such a displacement vector field supplementary constraints are necessary for example the postulate that a displacement vector field varies smoothly as a function of the image position taken as a general requirement this creates difficulties at gray value transitions which correspond to occluding contours nagel therefore introduced the oriented smoothness requirement which restricts variations of the displacement vector field only in directions with small or no variation of gray values this contribution reports results of an investigation about how such an oriented smoothness constraint may be formulated and evaluated

over parameterized variational optical flow a novel optical flow estimation process based on a spatio temporal model with varying coefficients multiplying a set of basis functions at each pixel is introduced previous optical flow estimation methodologies did not use such an over parameterized representation of the flow field as the problem is ill posed even without introducing any additional parameters neighborhood based methods of the lucas kanade type determine the flow at each pixel by constraining the flow to be described by a few parameters in small neighborhoods modern variational methods represent the optic flow directly via the flow field components at each pixel the benefit of over parametrization becomes evident in the smoothness term which instead of directly penalizing for changes in the optic flow accumulates a cost of deviating from the assumed optic flow model our proposed method is very general and the classical variational optical flow techniques are special cases of it when used in conjunction with constant basis functions experimental results with the novel flow estimation process yield significant improvements with respect to the best results published so far

variational optical flow estimation based on stick tensor voting variational optical flow techniques allow the estimation of flow fields from spatio temporal derivatives they are based on minimizing a functional that contains a data term and a regularization term recently numerous approaches have been presented for improving the accuracy of the estimated flow fields among them tensor voting has been shown to be particularly effective in the preservation of flow discontinuities this paper presents an adaptation of the data term by using anisotropic stick tensor voting in order to gain robustness against noise and outliers with significantly lower computational cost than full tensor voting in addition an anisotropic complementary smoothness term depending on directional information estimated through stick tensor voting is utilized in order to preserve discontinuity capabilities of the estimated flow fields finally a weighted non local term that depends on both the estimated directional information and the occlusion state of pixels is integrated during the optimization process in order to denoise the final flow field the proposed approach yields state of the art results on the middlebury benchmark

reliable and efficient computation of optical flow in this paper we present two very efficient and accurate algorithms for computing optical flow the first is a modified gradient based regularization method and the other is an ssd based regularization method for the gradient based method to amend the errors in the discrete image flow equation caused by numerical differentiation as well as temporal and spatial aliasing in the brightness function we propose to selectively combine the image flow constraint and a contour based flow constraint into the data constraint by using a reliability measure each data constraint is appropriately normalized to obtain an approximate minimum distance of the data point to the linear flow equation constraint instead of the conventional linear flow constraint these modifications lead to robust and accurate optical flow estimation we propose an incomplete cholesky preconditioned conjugate gradient algorithm to solve the resulting large and sparse linear system efficiently our ssd based regularization method uses a normalized ssd measure based on a similar reasoning as in the gradient based scheme as the data constraint in a regularization framework the nonlinear conjugate gradient algorithm in conjunction with an incomplete cholesky preconditioning is developed to solve the resulting nonlinear minimization problem experimental results on synthetic and real image sequences for these two algorithms are given to demonstrate their performance in comparison with competing methods reported in literature

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

the mabuchi geometry of finite energy classes abstract we introduce different finsler metrics on the space of smooth kahler potentials that will induce a natural geometry on various finite energy classes e x motivated by questions raised by r berman v guedj and y rubinstein we characterize the underlying topology of these spaces in terms of convergence in energy and give applications of our results to existence of kahler einstein metrics on fano manifolds

a computational framework and an algorithm for the measurement of visual the robust measurement of visual motion from digitized image sequences has been an important but difficult problem in computer vision this paper describes a hierarchical computational framework for the determination of dense displacement fields from a pair of images and an algorithm consist ent with that framework our framework is based on the separation of the image intensity information as well as the process of measuring motion according to scale the large scale intensity information is first used to obtain rough estimates of image motion which are then refined by using intensity information at smaller scales the estimates are in the form of displacement or velocity vectors for pixels and are accompanied by a direction dependent confidence measure a smoothness constraint is employed to propagate the measurements with high confidence to their neigboring areas where the confidences are low at all levels the computations are pixel parallel uniform across the image and based on information from a small neighborhood of a pixel for our algorithm the local displacement vectors are determind by mini mizing the sum of squared differences ssd of intensities the confidence measures are derived from the shape of the ssd surface and the smoothness constraint is cast in the form of energy minimization results of applying our algorithm to pairs of real images are included in addition to our own

lucas kanade meets horn schunck combining local and global optic flow methods differential methods belong to the most widely used techniques for optic flow computation in image sequences they can be classified into local methods such as the lucas kanade technique or bigun s structure tensor method and into global methods such as the horn schunck approach and its extensions often local methods are more robust under noise while global techniques yield dense flow fields the goal of this paper is to contribute to a better understanding and the design of novel differential methods in four ways i we juxtapose the role of smoothing regularisation processes that are required in local and global differential methods for optic flow computation ii this discussion motivates us to describe and evaluate a novel method that combines important advantages of local and global approaches it yields dense flow fields that are robust against noise iii spatiotemporal and nonlinear extensions as well as multiresolution frameworks are presented for this hybrid method iv we propose a simple confidence measure for optic flow methods that minimise energy functionals it allows to sparsify a dense flow field gradually depending on the reliability required for the resulting flow comparisons with experiments from the literature demonstrate the favourable performance of the proposed methods and the confidence measure

the cauchy problem for the homogeneous monge ampere equation i toeplitz quantization the cauchy problem for the homogeneous real complex monge ampere equation hrma hcma arises from the initial value problem for geodesics in the space of kahler metrics equipped with the mabuchi metric this cauchy problem is believed to be ill posed and a basic problem is to characterize initial data of weak solutions which exist up to time t in this article we use a quantization method to construct a subsolution of the hcma on a general projective variety and we conjecture that it solves the equation for as long as the unique solution exists the subsolution called the quantum analytic continuation potential is obtained by i toeplitz quantizing the hamiltonian flow determined by the cauchy data ii analytically continuing the quantization and iii taking a certain logarithmic classical limit we then prove that in the case of torus invariant metrics where the hcma reduces to the hrma the quantum analytic continuation potential coincides with the well known legendre transform potential and hence solves the equation as long as it is smooth in the sequel the cauchy problem for the homogeneous monge ampere equation ii legendre transform adv math 228 2011 2989 3025 it is proved that the legendre transform potential ceases to solve the hcma once it ceases to be smooth the results here and in the sequels in particular characterize the initial data of smooth geodesic rays

computation and analysis of image motion a synopsis of current problems and methods the goal of this paper is to offer a structured synopsis of the problems in image motion computation and analysis and of the methods proposed exposing the underlying models and supporting assumptions a sufficient number of pointers to the literature will be given concentrating mostly on recent contributions emphasis will be on the detection measurement and segmentation of image motion tracking and deformable motion issues will be also addressed finally a number of related questions which could require more investigations will be presented

computation of component image velocity from local phase information we present a technique for the computation of 2d component velocity from image sequences initially the image sequence is represented by a family of spatiotemporal velocity tuned linear filters component velocity computed from spatiotemporal responses of identically tuned filters is expressed in terms of the local first order behavior of surfaces of constant phase justification for this definition is discussed from the perspectives of both 2d image translation and deviations from translation that are typical in perspective projections of 3d scenes the resulting technique is predominantly linear efficient and suitable for parallel processing moreover it is local in space time robust with respect to noise and permits multiple estimates within a single neighborhood promising quantiative results are reported from experiments with realistic image sequences including cases with sizeable perspective deformation

note on the stochastic theory of a self catalytic chemical reaction ii abstract the general results of article i on the stochastic representation of the macroscopic stationary state of a self catalytic chemical system are applied to a step by step chemical reaction the relaxation times to the quasi stationary state and to the final stationary state are computed by evaluating the first two non trivial eigenvalues of the transition matrix the previous results of oppenheim shuler and weiss are confirmed precised and extended the critical and subcritical cases are treated by the same method

a multigrid platform for real time motion computation with discontinuity preserving variational methods variational methods are among the most accurate techniques for estimating the optic flow they yield dense flow fields and can be designed such that they preserve discontinuities estimate large displacements correctly and perform well under noise and varying illumination however such adaptations render the minimisation of the underlying energy functional very expensive in terms of computational costs typically one or more large linear or nonlinear equation systems have to be solved in order to obtain the desired solution consequently variational methods are considered to be too slow for real time performance in our paper we address this problem in two ways i we present a numerical framework based on bidirectional multigrid methods for accelerating a broad class of variational optic flow methods with different constancy and smoothness assumptions thereby our work focuses particularly on regularisation strategies that preserve discontinuities ii we show by the examples of five classical and two recent variational techniques that real time performance is possible in all cases even for very complex optic flow models that offer high accuracy experiments show that frame rates up to 63 dense flow fields per second for image sequences of size 160 120 can be achieved on a standard pc compared to classical iterative methods this constitutes a speedup of two to four orders of magnitude

on the space of kahler potentials we consider the geodesic equation for the generalized kahler potential with only mixed second derivatives bounded we show that given two such generalized kahler potentials there is a unique geodesic segment such that for each point on the geodesic the generalized kahler potential has uniformly bounded mixed second derivatives in manifold directions this generalizes a fundamental theorem of chen 2000 on the space of kahler potentials 2014 wiley periodicals inc

local geodesics for plurisubharmonic functions we study geodesics for plurisubharmonic functions from the cegrell class mathcal f 1 on a bounded hyperconvex domain of mathbb c n and show that as in the case of metrics on kahler compact manifolds they linearize an energy functional as a consequence we get a uniqueness theorem for functions from mathcal f 1 in terms of total masses of certain mixed monge ampere currents geodesics of relative extremal functions are considered and a reverse brunn minkowski inequality is proved for capacities of multiplicative combinations of multi circled compact sets we also show that functions with strong singularities generally cannot be connected by sub geodesic arcs

determining shape and motion from monocular camera determining the spatial motion of a moving camera from a video is a classical problem in computer vision the difficulty of this problem is that the flow pattern directly observable in the video is generally not the complete flow pattern induced by the motion but only the partial information of it which is known as the normal flow in this paper we present a direct method which neither requires the establishment of feature correspondences nor the recovery of optical flow between two image frames but we directly utilize all observable normal flow data to recover the camera motion we propose a two stage iterative algorithm to search the solution in the motion space in a coarse to fine framework the first stage involves the use of the direction part of the normal flow each of these normal flow data can provide a constrained solution space to the direction of motion the intersection of the motion solutions from all the available normal flow data can reduce the motion ambiguity to a certain extent we then use the globality of the rotational magnitude to all image positions to constrain the motion parameters further once the camera motion is determined the depth map of the imaged scene up to an arbitrary scale can be recovered experimental results on synthetic data and real images are provided to reveal the performance of the proposed method highlightswe determine camera motion and shape directly from normal flows our method does not require optical flows or feature correspondences two constraints are developed to determine camera motion experimental results are comparable to the state of the art methods

optic flow in harmony most variational optic flow approaches just consist of three constituents a data term a smoothness term and a smoothness weight in this paper we present an approach that harmonises these three components we start by developing an advanced data term that is robust under outliers and varying illumination conditions this is achieved by using constraint normalisation and an hsv colour representation with higher order constancy assumptions and a separate robust penalisation our novel anisotropic smoothness is designed to work complementary to the data term to this end it incorporates directional information from the data constraints to enable a filling in of information solely in the direction where the data term gives no information yielding an optimal complementary smoothing behaviour this strategy is applied in the spatial as well as in the spatio temporal domain finally we propose a simple method for automatically determining the optimal smoothness weight this method bases on a novel concept that we call optimal prediction principle opp it states that the flow field obtained with the optimal smoothness weight allows for the best prediction of the next frames in the image sequence the benefits of our optic flow in harmony ofh approach are demonstrated by an extensive experimental validation and by a competitive performance at the widely used middlebury optic flow benchmark

multidimensional orientation estimation with applications to texture analysis and optical flow the problem of detection of orientation in finite dimensional euclidean spaces is solved in the least squares sense the theory is developed for the case when such orientation computations are necessary at all local neighborhoods of the n dimensional euclidean space detection of orientation is shown to correspond to fitting an axis or a plane to the fourier transform of an n dimensional structure the solution of this problem is related to the solution of a well known matrix eigenvalue problem the computations can be performed in the spatial domain without actually doing a fourier transformation along with the orientation estimate a certainty measure based on the error of the fit is proposed two applications in image analysis are considered texture segmentation and optical flow the theory is verified by experiments which confirm accurate orientation estimates and reliable certainty measures in the presence of noise the comparative results indicate that the theory produces algorithms computing robust texture features as well as optical flow