a new analytic function for modeling partially penetrating wells a new analytic function is presented to model three dimensional flow near a partially penetrating well the function represents a sink distribution along the well axis whereby equipotential conditions along the well perimeter are approximately satisfied by adjusting several degrees of freedom of the function this procedure is well known and has led to rather accurate solutions provided a sufficient number of free parameters were incorporated the values for these parameters are obtained by solving a system of linear equations the function presented in this paper achieves the same accuracy as past solutions with a significant reduction in the number of degrees of freedom required and hence fewer equations to be solved this increased efficiency is of little consequence when the well is modeled by itself however when combined with the solutions to the many other flow features in a regional aquifer the savings become significant in fact if each of the individual solutions would have many degrees of freedom the resulting system of equations may become unmanageable thus restricting applications to demonstrate the use of the new function a hypothetical groundwater contamination problem is solved whereby contaminants are intercepted by a partially penetrating well

discriminative face alignment this paper proposes a discriminative framework for efficiently aligning images although conventional active appearance models aams based approaches have achieved some success they suffer from the generalization problem i e how to align any image with a generic model we treat the iterative image alignment problem as a process of maximizing the score of a trained two class classifier that is able to distinguish correct alignment positive class from incorrect alignment negative class during the modeling stage given a set of images with ground truth landmarks we train a conventional point distribution model pdm and a boosting based classifier which acts as an appearance model when tested on an image with the initial landmark locations the proposed algorithm iteratively updates the shape parameters of the pdm via the gradient ascent method such that the classification score of the warped image is maximized we use the term boosted appearance models bams to refer to the learned shape and appearance models as well as our specific alignment method the proposed framework is applied to the face alignment problem using extensive experimentation we show that compared to the aam based approach this framework greatly improves the robustness accuracy and efficiency of face alignment by a large margin especially for unseen data

domination by product measures we consider families of 0 1 valued random variables indexed by the vertices of countable graphs with bounded degree first we show that if these random variables satisfy the property that conditioned on what happens outside of the neighborhood of each given site the probability of seeing a 1 at this site is at least a value p which is large enough then this random field dominates a product measure with positive density moreover the density of this dominated product measure can be made arbitrarily close to 1 provided that p is close enough to 1 next we address the issue of obtaining the critical value of p defined as the threshold above which the domination by positive density product measures is assured for the graphs which have as vertices the integers and edges connecting vertices which are separated by no more than k units this critical value is shown to be 1 k k k 1 k 1 and a discontinuous transition is shown to occur similar critical values of p are found for other classes of probability measures on 0 1 z for the class of k dependent measures the critical value is again 1 k k k 1 k 1 with a discontinuous transition for the class of two block factors the critical value is shown to be 1 2 and a continuous transition is shown to take place in this case thus both the critical value and the nature of the transition are different in the two block factor and 1 dependent cases

feature adaptive co segmentation by complexity awareness in this paper we propose a novel feature adaptive co segmentation method that can learn adaptive features of different image groups for accurate common objects segmentation we also propose image complexity awareness for adaptive feature learning in the proposed method the original images are first ranked according to the image complexities that are measured by superpixel changing cue and object detection cue then the unsupervised segments of the simple images are used to learn the adaptive features which are achieved using an expectation minimization algorithm combining l 1 regularized least squares optimization with the consideration of the confidence of the simple image segmentation accuracies and the fitness of the learned model the error rate of the final co segmentation is tested by the experiments on different image groups and verified to be lower than the existing state of the art co segmentation methods

critical percolation and the minimal spanning tree in slabs the minimal spanning forest on d is known to consist of a single tree for d 2 and is conjectured to consist of infinitely many trees for large d in this paper we prove that there is a single tree for quasi planar graphs such as 2 0 k d 2 our method relies on generalizations of the gluing lemma of duminil copin sidoravicius and tassion a related result is that critical bernoulli percolation on a slab satisfies the box crossing property its proof is based on a new russo seymour welsh type theorem for quasi planar graphs thus at criticality the probability of an open path from 0 of diameter n decays polynomially in n this strengthens the result of duminil copin et al where the absence of an infinite cluster at criticality was first established 2017 wiley periodicals inc

is transverse macrodispersivity in three dimensional groundwater transport equal to zero a counterexample 1 in advective transport through weakly heterogeneous aquifers of random stationary and isotropic three dimensional permeability distribution transverse macrodispersivity t is found to be zero this was determined in the past by solving the transport equation at first order in the log conductivity variance 2 y however field findings indicate the presence of small but finite t the aim of the paper is to determine t for highly heterogeneous formations using a model that contains inclusions of conductivity k submerged in a matrix of conductivity k 0 for large k k 0 in the dilute medium approximation valid for small volume fraction n but arbitrary and for spherical inclusions it is found that t 0 because of the axisymmetry of flow past a sphere a medium made up of rotational ellipsoids of arbitrary random orientation macroscopically isotropic and of the same and n is devised as a counterexample it is found that because of the intertwining of streamlines t 0 being of order 1 4 for 1 these findings are confirmed by accurate numerical simulations of flow through a large number of interacting inclusions for 10 and n 0 2 jamming limit the large value t l 0 15 is attained the numerical simulations display the strong permanent deformation of stream tubes responsible for this phenomenon coined as advective mixing the two point covariance used in practice in order to characterize the aquifer structure is not able to detect the structures that produce advective mixing nevertheless the presence of high conductivity lenses inclined with respect to the mean flow may explain the occurrence of finite t in field applications

uniqueness of the infinite cluster and continuity of connectivity functions for short and long range percolation for independent translation invariant irreducible percolation models it is proved that the infinite cluster when it exists must be unique the proof is based on the convexity or almost convexity and differentiability of the mean number of clusters per site which is the percolation analogue of the free energy the analysis applies to both site and bond models in arbitrary dimension including long range bond percolation in particular uniqueness is valid at the critical point of one dimensional 1 x y 2 models in spite of the discontinuity of the percolation density there corollaries of uniqueness and its proof are continuity of the connectivity functions and except possibly at the critical point of the percolation density related to differentiability of the free energy are inequalities which bound the specific heat critical exponent in terms of the mean cluster size exponent and the critical cluster size distribution exponent e g 1 2 1 1

percolation of level sets for two dimensional random fields with lattice symmetry let x x 2 be a random field which may be viewed as the potential of an incompressible flow for which the trajectories follow the level lines of percolation methods are used to analyze the sizes of the connected components of level sets x x h and sets x x h in several classes of random fields with lattice symmetry in typical cases there is a sharp transition at a critical value ofh from exponential boundedness for such components to the existence of an unbounded component in some examples however there is a nondegenerate interval of values ofh where components are bounded but not exponentially so and in other cases each level set may be a single infinite line which visits every region of the lattice

dynamic affine invariant shape appearance handshape features and classification in sign language videos we propose the novel approach of dynamic affine invariant shape appearance model aff sam and employ it for handshape classification and sign recognition in sign language sl videos aff sam offers a compact and descriptive representation of hand configurations as well as regularized model fitting assisting hand tracking and extracting handshape features we construct sa images representing the hand s shape and appearance without landmark points we model the variation of the images by linear combinations of eigenimages followed by affine transformations accounting for 3d hand pose changes and improving model s compactness we also incorporate static and dynamic handshape priors offering robustness in occlusions which occur often in signing the approach includes an affine signer adaptation component at the visual level without requiring training from scratch a new singer specific model we rather employ a short development data set to adapt the models for a new signer experiments on the boston university 400 continuous sl corpus demonstrate improvements on handshape classification when compared to other feature extraction approaches supplementary evaluations of sign recognition experiments are conducted on a multi signer 100 sign data set from the greek sign language lemmas corpus these explore the fusion with movement cues as well as signer adaptation of aff sam to multiple signers providing promising results

discriminative deep face shape model for facial point detection facial point detection is an active area in computer vision due to its relevance to many applications it is a nontrivial task since facial shapes vary significantly with facial expressions poses or occlusion in this paper we address this problem by proposing a discriminative deep face shape model that is constructed based on an augmented factorized three way restricted boltzmann machines model specifically the discriminative deep model combines the top down information from the embedded face shape patterns and the bottom up measurements from local point detectors in a unified framework in addition along with the model effective algorithms are proposed to perform model learning and to infer the true facial point locations from their measurements based on the discriminative deep face shape model 68 facial points are detected on facial images in both controlled and in the wild conditions experiments on benchmark data sets show the effectiveness of the proposed facial point detection algorithm against state of the art methods

modeling three dimensional flow about ellipsoidal inhomogeneities with application to flow to a gravel packed well and flow through lens shaped inhomogeneities analytic functions are superimposed to model three dimensional steady groundwater flow in regions containing one or more inhomogeneities shaped like prolate or oblate ellipsoids of revolution each function and the sum of such functions are solutions of laplace s equation the governing differential equation for steady groundwater flow the functions are implemented in a manner that provides exact continuity of flow across the entire boundary of each inhomogeneity in general continuity of head is provided at specified control points on the boundary and is approximated between control points for the case of one inhomogeneity in a uniform flow field it turns out that there is exact continuity of head across the entire surface of the inhomogeneity the method is implemented in a computer program written by the author two applications are demonstrated 1 flow to a gravel packed well and 2 flow through a series of lens shaped inhomogeneities the examples demonstrate that the approximation of continuity of head can be made acceptable for many problems a possible application of the technique would be testing various theories regarding contaminant migration and dispersion by simulating flow and chemical diffusion through large numbers of lens shaped inhomogeneities

global propagation of affine invariant features for robust matching local invariant features have been successfully used in image matching to cope with viewpoint change partial occlusion and clutters however when these factors become too strong there will be a lot of mismatches due to the limited repeatability and discriminative power of features in this paper we present an efficient approach to remove the false matches and propagate the correct ones for the affine invariant features which represent the state of the art local invariance first a pair wise affine consistency measure is proposed to evaluate the consensus of the matches of affine invariant regions the measure takes into account both the keypoint location and the region shape size and orientation based on this measure a geometric filter is then presented which can efficiently remove the outliers from the initial matches and is robust to severe clutters and non rigid deformation to increase the correct matches we propose a global match refinement and propagation method that simultaneously finds a optimal group of local affine transforms to relate the features in two images the global method is capable of producing a quasi dense set of matches even for the weakly textured surfaces that suffer strong rigid transformation or non rigid deformation the strong capability of the proposed method in dealing with significant viewpoint change non rigid deformation and low texture objects is demonstrated in experiments of image matching object recognition and image based rendering

modeling three dimensional flow in confined aquifers by superposition of both two and three dimensional analytic functions a technique is presented to incorporate three dimensional flow in a dupuit forchheimer model the method is based on superposition of approximate analytic solutions to both two and three dimensional flow features in a confined aquifer of infinite extent three dimensional solutions are used in the domain of interest while farfield conditions are represented by two dimensional solutions approximate three dimensional solutions have been derived for a partially penetrating well and a shallow creek each of these solutions satisfies the condition that no flow occurs across the confining layers of the aquifer because of this condition the flow at some distance of a three dimensional feature becomes nearly horizontal consequently remotely from a three dimensional feature its three dimensional solution is replaced by a corresponding two dimensional one the latter solution is trivial as compared to its three dimensional counterpart and its use greatly enhances the computational efficiency of the model as an example the flow is modeled between a partially penetrating well and a shallow creek that occur in a regional aquifer system

graph based construction of textured large field of view mosaics for bladder cancer diagnosis large field of view panoramic images greatly facilitate bladder cancer diagnosis and follow up such 2d mosaics can be obtained by registering the images of a video sequence acquired during cystoscopic examinations the scientific challenge in the registration process lies in the strong inter and intra patient texture variability of the images from which primitives cannot be robustly extracted state of the art registration methods are not at the same time robust and accurate especially for image pairs with a small amount of overlap less than 90 or strong perspective transformations moreover no previous contribution to cystoscopy mosaicing presents panoramic images created from multiple overlapping sequences e g zigzags or loop trajectories we show how such overlapping sections can be automatically detected and present a novel registration algorithm that robustly superimposes non consecutive image pairs which are related by stronger perspective transformations and share less overlap than consecutive images less than 50 globally coherent panoramic images are constructed using a non linear optimization and a novel contrast enhancing stitching method results on both phantom and patient data are obtained using constant algorithm parameters which demonstrate the robustness of the proposed method while the methods presented in this contribution are specifically designed for cystoscopy mosaicing they can also be applied to more general mosaicing problems we demonstrate this on a traditional stitching application where a set of pictures of a building are stitched into a seamless globally coherent panoramic image

an analytic approximate method for modeling steady three dimensional flow to partially penetrating wells an analytic approximate solution is derived for the modeling of three dimensional flow to partially penetrating wells the solution is written in terms of a correction on the solution for a fully penetrating well and is obtained by dividing the aquifer up locally in a number of aquifer layers the resulting system of differential equations is solved by application of the theory for multiaquifer flow the presented approach has three major benefits first the solution may be applied to any groundwater model that can simulate flow to a fully penetrating well the solution may be superimposed onto the solution for the fully penetrating well to simulate the local three dimensional drawdown and flow field second the approach is applicable to isotropic anisotropic and stratified aquifers and to both confined and unconfined flow third the solution extends over a small area around the well only outside this area the three dimensional effect of the partially penetrating well is negligible and no correction to the fully penetrating well is needed a number of comparisons are made to existing three dimensional analytic solutions including radial confined and unconfined flow and a well in a uniform flow field it is shown that a subdivision in three layers is accurate for many practical cases very accurate solutions are obtained with more layers

absence of infinite cluster for critical bernoulli percolation on slabs we prove that for bernoulli percolation on a graph 2 0 k k 0 there is no infinite cluster at criticality almost surely the proof extends to finite range bernoulli percolation models on 2 that are invariant under 2 rotation and reflection 2016 wiley periodicals inc

consistent image registration presents a new method for image registration based on jointly estimating the forward and reverse transformations between two images while constraining these transforms to be inverses of one another this approach produces a consistent set of transformations that have less pairwise registration error i e better correspondence than traditional methods that estimate the forward and reverse transformations independently the transformations are estimated iteratively and are restricted to preserve topology by constraining them to obey the laws of continuum mechanics the transformations are parameterized by a fourier series to diagonalize the covariance structure imposed by the continuum mechanics constraints and to provide a computationally efficient numerical implementation results using a linear elastic material constraint are presented using both magnetic resonance and x ray computed tomography image data the results show that the joint estimation of a consistent set of forward and reverse transformations constrained by linear elasticity give better registration results than using either constraint alone or none at all

metric learning for image alignment image alignment has been a long standing problem in computer vision parameterized appearance models pams such as the lucas kanade method eigentracking and active appearance models are commonly used to align images with respect to a template or to a previously learned model while pams have numerous advantages relative to alternate approaches they have at least two drawbacks first they are especially prone to local minima in the registration process second often few if any of the local minima of the cost function correspond to acceptable solutions to overcome these problems this paper proposes a method to learn a metric for pams that explicitly optimizes that local minima occur at and only at the places corresponding to the correct fitting parameters to the best of our knowledge this is the first paper to address the problem of learning a metric to explicitly model local properties of the pams error surface synthetic and real examples show improvement in alignment performance in comparison with traditional approaches in addition we show how the proposed criteria for a good metric can be used to select good features to track

anisotropic motion estimation on edge preserving riesz wavelets for robust video mosaicing image mosaicing is a technique widely used for extending the field of view of industrial medical outdoor or indoor scenes however image registration can be very challenging e g due to large texture variability illumination changes image blur and camera perspective changes in this paper a total variational optical flow approach is investigated to estimate dense point correspondences between image pairs an edge preserving riesz wavelet scale space combined with a novel tv regularizer is proposed for preserving motion discontinuities along the edges of weak textures and for handling strong in plane rotations present in image sequences an anisotropic weighted median filtering is implemented for minimizing outliers quantitative evaluation of the method on the middlebury image database and simulated sequences with known ground truth demonstrates high accuracy of the proposed method in comparison with other state of the art methods including a robust graph cut method and a patch matching approach qualitative results on video sequences of difficult real scenes demonstrate the robustness of the proposed method highlightsmosaicing of images with strong texture and illumination variability fast robust and accurate optical flow computation tv l1 method on a second order riesz wavelet basis for preserving texture discontinuities novel anisotropic tv regularizer accurate results for both the middlebury data set and various complicated scenes

active appearance models revisited active appearance models aams and the closely related concepts of morphable models and active blobs are generative models of a certain visual phenomenon although linear in both shape and appearance overall aams are nonlinear parametric models in terms of the pixel intensities fitting an aam to an image consists of minimising the error between the input image and the closest model instances i e solving a nonlinear optimisation problem we propose an efficient fitting algorithm for aams based on the inverse compositional image alignment algorithm we show that the effects of appearance variation during fitting can be precomputed projected out using this algorithm and how it can be extended to include a global shape normalising warp typically a 2d similarity transformation we evaluate our algorithm to determine which of its novel aspects improve aam fitting performance

simple analytic functions for modeling three dimensional flow in layered aquifers analytic functions are presented for modeling three dimensional steady groundwater flow in stratified aquifers the functions create discontinuity in the potential across an infinite plane while maintaining continuity of the potential gradient across the plane these functions may be superimposed with other analytic functions to model three dimensional flow in stratified aquifers under a variety of boundary conditions an interface between two layers of different hydraulic conductivity an impermeable boundary or a thin leaky layer may be modeled using such functions these functions are simple compared to functions for doublet distributions over finite plane panels and are suitable for efficient modeling

rationalizing efficient compositional image alignment we study the issue of computational efficiency for gauss newton gn non linear least squares optimization in the context of image alignment we introduce the constant jacobian gauss newton cjgn optimization a gn scheme with constant jacobian and hessian matrices and the equivalence and independence conditions as the necessary requirements that any function of residuals must satisfy to be optimized with this efficient approach we prove that the inverse compositional ic image alignment algorithm is an instance of a cjgn scheme and formally derive the compositional and extended brightness constancy assumptions as the necessary requirements that must be satisfied by any image alignment problem so it can be solved with an efficient compositional scheme moreover in contradiction with previous results we also prove that the forward and inverse compositional algorithms are not equivalent they are equivalent however when the extended brightness constancy assumption is satisfied to analyze the impact of the satisfaction of these requirements we introduce a new image alignment evaluation framework and the concepts of short and wide baseline jacobian in wide baseline jacobian problems the optimization will diverge if the requirements are not satisfied however with a good initialization a short baseline jacobian problem may converge even if the requirements are not satisfied

flow and transport in highly heterogeneous formations 1 conceptual framework and validity of first order approximations 1 flow of uniform mean velocity u takes place in a formation of spatially variable random conductivity k x advective transport of a plume of an inert solute is investigated by the lagrangean approach the aim of the study is to determine the spatial moments of the plume i e of fluid particle trajectories for highly heterogeneous aquifers for which y 1 where y ln k a multi indicator model of the permeability structure which is different from the common multi gaussian one is proposed the formation is modeled as a collection of n blocks of different k j the structure is defined by the distribution of k j the blocks shape and the coordinates of their centroids the following simplifications are adopted the blocks are inclusions of a regular shape circles spheres for isotropic media investigated here defined by the radius a and the inclusions are not overlapping and their centroids are distributed uniformly and independently in space at the continuous limit the model is characterized by the joint pdf f y a the model is shown to be quite general and to comprise binary bimodal indicator variograms and unimodal distributions of y as particular cases the study is focused on the latter case with y normal n y y2 and stationary covariance of given integral scale iy these are the parameters commonly estimated for sedimentary formations this leaves still freedom in selecting the pdf f a the simple model selected for semianalytical and numerical analysis is that of inclusions of radius r and volume fraction n submerged in a matrix of effective conductivity kef the latter represents the effect of inclusions of much smaller radius which appear as a nugget in the log conductivity two point covariance an approximate analytical solution of the flow is obtained by using a self consistent approximation while a fully numerical one is derived in part 3 jankovic et al 2003a transport is solved by particle tracking and the time dependent spatial moments trajectories variance skewness kurtosis are presented in part 2 fiori et al 2003 in the self consistent approximation the asymptotic longitudinal macrodispersivity l which is a function of y shows strong nonlinear effects inclusions of large positive y lead to a finite l whereas l grows unbounded for those of negative y this effect is not captured by the common first order approximation in y which is symmetrical and overestimates l for y 0 and underestimates it for y 0 as a result the second spatial moment is predicted accurately by the first order approximation by cancellation of errors provided that f y is symmetrical however the transient regime and higher order moments are not captured by the first order approximation

flow and transport in highly heterogeneous formations 3 numerical simulations and comparison with theoretical results 1 in parts 1 dagan et al 2003 and 2 fiori et al 2003 a multi indicator model of heterogeneous formations is devised in order to solve flow and transport in highly heterogeneous formations the isotropic medium is made up from circular 2 d or spherical 3 d inclusions of different conductivities k submerged in a matrix of effective conductivity this structure is different from the multi gaussian one even for equal log conductivity distribution and integral scale a snapshot of a two dimensional plume in a highly heterogeneous medium of lognormal conductivity distribution shows that the model leads to a complex transport picture the present study was limited however to investigating the statistical moments of ergodic plumes two approximate semianalytical solutions based on a self consistent model sc and on a first order perturbation in the log conductivity variance fo are used in parts 1 and 2 in order to compute the statistical moments of flow and transport variables for a lognormal conductivity pdf in this paper an efficient and accurate numerical procedure based on the analytic element method strack 1989 is used in order to validate the approximate results the solution satisfies exactly the continuity equation and at high accuracy the continuity of heads at inclusion boundaries the dimensionless dependent variables depend on two parameters the volume fraction n of inclusions in the medium and the log conductivity variance y2 for inclusions of uniform radius the largest n was 0 9 2 d and 0 7 3 d whereas the largest y2 was equal to 10 the sc approximation underestimates the longitudinal eulerian velocity variance for increasing n and increasing y2 in 2 d and to a lesser extent in 3 d as compared to numerical results the fo approximation overestimates these variances and these effects are larger in the transverse direction the longitudinal velocity pdf is highly skewed and negative velocities are present at high y2 especially in 2 d the main results are in the comparison of the macrodispersivities computed with the aid of the lagrangian velocity covariances as functions of travel time for the longitudinal macrodispersivity the sc approximation yields results close to the numerical ones in 2 d for n 0 4 but underestimates them for n 0 9 the asymptotic large travel time values of macrodispersivities in the sc and fo approximations are close for low to moderate y2 as shown and explained in part 1 however while the slow tendency to fickian behavior is well reproduced by sc it is much quicker in the fo approximation in 3 d the sc approximation is closer to numerical one for the highest n 0 7 and the different y2 2 4 8 and the comparison improves if molecular diffusion is taken into account transverse macrodispersivity for small travel times is underestimated by sc in 2 d and is closer to numerical results in 3 d whereas fo overestimates them transverse macrodispersivity asymptotically tends to zero in 2 d for large travel times in 3 d the numerical simulations lead to a small but persistent transverse macrodispersivity for large travel times whereas it tends to zero in the approximate solutions the results suggest that the self consistent semianalytical approximation provides a valuable tool to model transport in highly heterogeneous isotropic formations of a 3 d structure in terms of trajectories statistical moments it captures effects like slow transition to fickian behavior and to gaussian trajectory distribution which are neglected by the first order approximation

stream surfaces in two dimensional and three dimensional divergence free flows it is demonstrated that two dimensional flows and three dimensional flows have fundamentally different influences on stream surfaces an element that generates a two dimensional flow only can affect the angle of intersection between two stream surfaces locally an element that generates a three dimensional flow may affect this angle regionally one consequence is that stream functions for three dimensional flows may not in general be chosen such that their basis vectors are everywhere mutually orthogonal another consequence is that the deformation of stream surfaces produced by a three dimensional element does not approach that produced by a two dimensional element at large distances from the element a two dimensional model cannot reproduce stream surfaces that occur in a three dimensional flow

active appearance models we describe a new method of matching statistical models of appearance to images a set of model parameters control modes of shape and gray level variation learned from a training set we construct an efficient iterative matching algorithm by learning the relationship between perturbations in the model parameters and the induced image errors

bayesian constrained local models revisited this paper presents a novel bayesian formulation for aligning faces in unseen images our approach revisits the constrained local models clm formulation where an ensemble of local feature detectors are constrained to lie within the subspace spanned by a point distribution model pdm fitting such a model to an image typically involves two main steps a local search using a detector obtaining response maps for each landmark likelihood term and a global optimization that finds the pdm parameters that jointly maximize all the detections at once the so called global optimization can be posed as a bayesian inference problem where the posterior distribution of the shape and pose parameters can be inferred in a maximum a posteriori map sense this work introduces an extended bayesian global optimization strategy that includes two novel additions 1 to perform second order updates of the pdm parameters accounting for their covariance and 2 to model the underlying dynamics of the shape variations encoded in the prior term by using recursive bayesian estimation extensive evaluations were performed against state of the art methods on several standard datasets imm bioid xm2vts lfw and fgnet talking face results show that the proposed approach significantly increases the fitting performance

hyperplane approximation for template matching hager and belhumeur 1998 proposed a general framework for object tracking in video images it consists of low order parametric models for the image motion of a target region these models are used to predict movement and to track the target the difference in intensity between the pixels belonging to the current region and the pixels of the selected target learned during an offline stage allows a straightforward prediction of the region position in the current image the main aim of the article is to propose an important improvement within this framework making the convergence faster with the same amount of online computation

density and uniqueness in percolation two results on site percolation on thed dimensional lattice d 1 arbitrary are presented in the first theorem we show that for stationary underlying probability measures each infinite cluster has a well defined density with probability one the second theorem states that if in addition the probability measure satisfies the finite energy condition of newman and schulman then there can be at most one infinite cluster with probability one the simple arguments extend to a broad class of finite dimensional models including bond percolation and regular lattices

crossing probabilities for voronoi percolation we prove that the standard russo seymour welsh theory is valid for voronoi percolation this implies that at criticality the crossing probabilities for rectangles are bounded by constants depending only on their aspect ratio this result has many consequences such as the polynomial decay of the one arm event at criticality

minimal spanning forests minimal spanning forests on infinite graphs are weak limits of minimal spanning trees from finite subgraphs these limits can be taken with free or wired boundary conditions and are denoted fmsf free minimal spanning forest and wmsf wired minimal spanning forest respectively the wmsf is also the union of the trees that arise from invasion percolation started at all vertices we show that on any cayley graph where critical percolation has no infinite clusters all the component trees in the wmsf have one end a s in z d this was proved by alexander ann probab 23 1995 87 104 but a different method is needed for the nonamenable case we also prove that the wmsf components are thin in a different sense namely on any graph each component tree in the wmsf has p c 1 a s where p c denotes the critical probability for having an infinite cluster in bernoulli percolation on the other hand the fmsf is shown to be thick on any connected graph the union of the fmsf and independent bernoulli percolation with arbitrarily small parameter is a s connected in conjunction with a recent result of gaboriau this implies that in any cayley graph the expected degree of the fmsf is at least the expected degree of the fsf the weak limit of uniform spanning trees we also show that the number of infinite clusters for bernoulli p u percolation is at most the number of components of the fmsf where p u denotes the critical probability for having a unique infinite cluster finally an example is given to show that the minimal spanning tree measure does not have negative associations

average steady nonuniform flow in stratified formations abstract a mathematical model of average nonuniform flow in heterogeneous stratified media is developed the averaged darcy s law is obtained by deriving the analytical expression of the effective conductivity tensor for media with small heterogeneities the fundamental solution of the average flow equation mean green function corresponding to the flow toward a single point source of deterministic discharge is derived the mean head distribution is calculated for a fully penetrating well for a finite length well in an infinite domain and for a dipole well the concept of equivalent conductivity is defined for use in identifying the formation conductivity properties the procedure for identifying the mean conductivity log conductivity variance and vertical integral scale is suggested for the case of dipole flow 1 introduction natural aquifers reveal a wide spatial variability of their properties which affects their flow and transport parameters the effect of formation structure on the process characteristics has been recognized for a long time and numerous approaches that account for the formation heterogeneities have been sug gested the objective of these approaches is to develop theo ries applicable to both identifying aquifer parameters and fore casting flow and transport processes early theories modeled formation heterogeneity by regard ing hydraulic conductivities in the horizontal and vertical

choosing a spanning tree for the integer lattice uniformly consider the nearest neighbor graph for the integer lattice zd in d dimensions for a large finite piece of it consider choosing a spanning tree for that piece uniformly among all possible subgraphs that are spanning trees as the piece gets larger this approaches a limiting measure on the set of spanning graphs for zd this is shown to be a tree if and only if d 4 in this case the tree has only one topological end that is there are no doubly infinite paths when d 2 5 the spanning forest has infinitely many components almost surely with each component having one or two topological ends

generalizing inverse compositional and esm image alignment inverse compositional ic image alignment baker and matthews in int j comput vis 56 3 221 255 2004 uses the symmetry between the roles of the fixed and moving images for faster processing however it requires implementation of compositional optimizer update steps the ic approach can be viewed as an efficient way of computing the similarity measure derivative relative to the fixed image warp parameters since the mapping between the fixed and moving warp parameters is continuous and differentiable this derivative can be converted into the moving warp space using the chain rule this avoids the need for compositional update steps our generalization also allows the efficient second order method esm malis in proceedings of the 2004 ieee international conference on robotics and automation icra04 pp 1843 1848 2004 benhimane and malis in ieee rsj international conference on intelligent robots and systems 2004 malis and benhimane in robot auton syst 52 1 39 52 2005 to be applied to general parameterizations of the transformation experiments using multiple similarity measures and optimizers show that our generalized ic method equals or exceeds the performance of the original ic approach the generalized esm approach is more reliable than the classic approach as it increases the capture radius of the optimization

uniform spanning forests we study uniform spanning forest measures on infinite graphs which are weak limits of uniform spanning tree measures from finite subgraphs these limits can be taken with free fsf or wired wsf boundary conditions pemantle proved that the free and wired spanning forests coincide in z d and that they give a single tree iff d 4 in the present work we extend pemantle s alternative to general graphs and exhibit further connections of uniform spanning forests to random walks potential theory invariant percolation and amenability the uniform spanning forest model is related to random cluster models in statistical physics but because of the preceding connections its analysis can be carried further among our results are the following the fsf and wsf in a graph g coincide iff all harmonic dirichlet functions on g are constant the tail fields of the wsf and the fsf are trivial on any graph on any cayley graph that is not a finite extension of z all component trees of the wsf have one end this is new in z d for d 5 on any tree as well as on any graph with spectral radius less than 1 a s all components of the wsf are recurrent the basic topology of the free and the wired uniform spanning forest measures on lattices in hyperbolic space h d is analyzed a cayley graph is amenable iff for all e 0 the union of the wsf and bernoulli percolation with parameter e is connected harmonic measure from infinity is shown to exist on any recurrent proper planar graph with finite codegrees we also present numerous open problems and conjectures

a vector potential and exact flux through surfaces using lagrange and stokes stream functions a vector potential is obtained for two dimensional flow fields using the lagrange stream function and for axisymmetric flow fields using the stokes stream function the flux through surfaces bounded by straight line segments with arbitrary orientation is obtained using the line integral of the tangential component of the vector potential along the boundary of the surface integration of the lagrange stream function results for surfaces in two dimensional flow a cauchy integral of the stokes stream function follows for axisymmetric flow the process of assembling vector potentials and developing closed form expressions to provide exact flux through surfaces is illustrated for a partially penetrating well with uniform flow in a horizontal aquifer a virtual flux is generated through vortex sheets where the lagrange stream function is discontinuous and through singular vortex lines where the stokes stream function is non zero on the axis of symmetry this virtual flux must be accounted for to obtain exact flux the unifying framework presented here to assemble vector potentials obtained using lagrange and stokes stream functions and to compute flux is applicable to three dimensional divergence free steady flow fields that can be decomposed into two dimensional and axisymmetric components

mutual information for lucas kanade tracking milk an inverse compositional formulation mutual information ml is popular for registration via function optimization this work proposes an inverse compositional formulation of ml for levenberg marquardt optimization this yields a constant hessian which may be precomputed speed improvements of 15 percent were obtained with convergence accuracies similar those of the standard formulation

eigentracking robust matching and tracking of articulated objects using a view based representation this paper describes an approach for tracking rigid and articulated objects using a view based representation the approach builds on and extends work on eigenspace representations robust estimation techniques and parameterized optical flow estimation first we note that the least squares image reconstruction of standard eigenspace techniques has a number of problems and we reformulate the reconstruction problem as one of robust estimation second we define a subspace constancy assumption that allows us to exploit techniques for parameterized optical flow estimation to simultaneously solve for the view of an object and the affine transformation between the eigenspace and the image to account for large affine transformations between the eigenspace and the image we define a multi scale eigenspace representation and a coarse to fine matching strategy finally we use these techniques to track objects over long image sequences in which the objects simultaneously undergo both affine image motions and changes of view in particular we use this eigentracking technique to track and recognize the gestures of a moving hand

drawdown and capture zone topology for nonvertical wells 1 an analytic framework is developed to model the three dimensional steady flow generated by wells placed at general nonvertical orientations within a horizontal aquifer this framework uses closed form solutions for a distribution of point sinks and point doublets along the centerline of the well and semi infinite panel elements each with piecewise linearly varying strengths this extends previously published implementations and enables a boundary condition of uniform head along the cylindrical face of the well to be accurately matched the resulting model is used to examine the drawdown and capture zone topology for wells spanning orientations ranging from vertical to horizontal scaling relationships are developed for wells perpendicular to flow that are invariant with respect to drawdown and to the strength of elements the capture zone geometry for such wells is variant with respect to a dimensionless pumping rate going through transition from two dimensional flow in a plane perpendicular to the well to two dimensional flow in a horizontal plane

a vector potential for a partly penetrating well and flux in an approximate method of images a vector potential is formulated for three dimensional steady groundwater flow within a framework that is consistent with the lagrange stream function for twodimensional flow analytical expressions are developed for vector potentials of a point sink and a line sink of both finite and infinite length a previously unpublished vector potential for a partly penetrating well in a horizontal confined aquifer is obtained using the method of images where an infinite series of image line sinks is approximated using a finite number of images and two semi infinite elements singularities and discontinuities within these vector potentials are interpreted as producing a virtual discharge connecting vortex lines into continuous loops over infinity the vector potential is used to accurately and efficiently compute the net flux through surfaces containing singularities in the specific discharge this net flux quantifies errors in the elevation of streamlines associated with a finite number of images and provides a measure to ensure a relatively seamless link between local three dimensional flow and farfield two dimensional flow

estimation of nonlinear errors in variables models for computer vision applications in an errors in variables eiv model all the measurements are corrupted by noise the class of eiv models with constraints separable into the product of two nonlinear functions one solely in the variables and one solely in the parameters is general enough to represent most computer vision problems we show that the estimation of such nonlinear eiv models can be reduced to iteratively estimating a linear model having point dependent i e heteroscedastic noise process particular cases of the proposed heteroscedastic errors in variables heiv estimator are related to other techniques described in the vision literature the sampson method renormalization and the fundamental numerical scheme in a wide variety of tasks the heiv estimator exhibits the same or superior performance as these techniques and has a weaker dependence on the quality of the initial solution than the levenberg marquardt method the standard approach toward estimating nonlinear models

bidirectional composition on lie groups for gradient based image alignment in this paper a new formulation based on bidirectional composition on lie groups bcl for parametric gradient based image alignment is presented contrary to the conventional approaches the bcl method takes advantage of the gradients of both template and current image without combining them a priori based on this bidirectional formulation two methods are proposed and their relationship with state of the art gradient based approaches is fully discussed the first one i e the bcl method relies on the compositional framework to provide the minimization of the compensated error with respect to an augmented parameter vector the second one the projected bcl pbcl corresponds to a close approximation of the bcl approach a comparative study is carried out dealing with computational complexity convergence rate and frequence of convergence numerical experiments using a conventional benchmark show the performance improvement especially for asymmetric levels of noise which is also discussed from a theoretical point of view

lucas kanade 20 years on a unifying framework since the lucas kanade algorithm was proposed in 1981 image alignment has become one of the most widely used techniques in computer vision applications range from optical flow and tracking to layered motion mosaic construction and face coding numerous algorithms have been proposed and a wide variety of extensions have been made to the original formulation we present an overview of image alignment describing most of the algorithms and their extensions in a consistent framework we concentrate on the inverse compositional algorithm an efficient algorithm that we recently proposed we examine which of the extensions to lucas kanade can be used with the inverse compositional algorithm without any significant loss of efficiency and which cannot in this paper part 1 in a series of papers we cover the quantity approximated the warp update rule and the gradient descent approximation in future papers we will cover the choice of the error function how to allow linear appearance variation and how to impose priors on the parameters

groupwise geometric and photometric direct image registration image registration consists in estimating geometric and photometric transformations that align two images as best as possible the direct approach consists in minimizing the discrepancy in the intensity or color of the pixels the inverse compositional algorithm has been recently proposed by baker et al for the direct estimation of groupwise geometric transformations it is efficient in that it performs several computationally expensive calculations at a pre computation phase photometric transformations act on the value of the pixels they account for effects such as lighting change jointly estimating geometric and photometric transformations is thus important for many tasks such as image mosaicing we propose an algorithm to jointly estimate groupwise geometric and photometric transformations while preserving the efficient pre computation based design of the original inverse compositional algorithm it is called the dual inverse compositional algorithm it uses different approximations than the simultaneous inverse compositional algorithm and handles groupwise geometric and global photometric transformations its name stems from the fact that it uses an inverse compositional update rule for both the geometric and the photometric transformations we demonstrate the proposed algorithm and compare it to previous ones on simulated and real data this shows clear improvements in computational efficiency and in terms of convergence

emergent planarity in two dimensional ising models with finite range interactions the known pfaffian structure of the boundary spin correlations and more generally order disorder correlation functions is given a new explanation through simple topological considerations within the model s random current representation this perspective is then employed in the proof that the pfaffian structure of boundary correlations emerges asymptotically at criticality in ising models on mathbb z 2 with finite range interactions the analysis is enabled by new results on the stochastic geometry of the corresponding random currents the proven statement establishes an aspect of universality seen here in the emergence of fermionic structures in two dimensions beyond the solvable cases