label propagation and higher order constraint based segmentation of fluid associated regions in retinal sd oct images the segmentation of the fluid associated region in the retina plays an important role in the treatment of retinal diseases such as diabetic retinopathy dr and age related macular degeneration amd the existing methods for the detection of the fluid region generally suffer from the limitation of the segmentation accuracy and the expensive time costs to overcome these problems in this paper we propose an interactive segmentation method for the fluid associated region in three dimensional 3 d spectral domain optical coherence tomography sd oct retinal imaging in which only a few seeds in one sd oct slice are needed after which the algorithm finishes the segmentation automatically to improve the segmentation accuracy the higher order constraint is introduced into the conventional markov random field mrf framework to impose the superpixel consistency to maintain temporal coherence of the 3 d sd oct slices the labeling information is propagated slice by slice via a proposed motion estimation based algorithm the proposed higher order based energy function can be efficiently solved by the max flow algorithm on a specified graph with several auxiliary nodes experiments on 28 sd oct cubes demonstrate the competitiveness of the proposed method compared with the state of the art methods

a local algorithm for the computation of image velocity via constructive interference of global fourier components a novel fourier based technique for local motion detection from image sequences is proposed in this method the instantaneous velocities of local image points are inferred directly from the global 3d fourier components of the image sequence this is done by selecting those velocities for which the superposition of the corresponding fourier gratings leads to constructive interference at the image point hence image velocities can be assigned locally even though position is computed from the phases and amplitudes of global fourier components spanning the whole image sequence that have been filtered based on the motion constraint equation reducing certain aperture effects typically arising from windowing in other methods regularization is introduced for sequences having smooth flow fields aperture effects and their effect on optic flow regularization are investigated in this context the algorithm is tested on both synthetic and real image sequences and the results are compared to those of other local methods finally we show that other motion features i e motion direction can be computed using the same algorithmic framework without requiring an intermediate representation of local velocity which is an important characteristic of the proposed method

computing optical flow via variational techniques defined as the apparent motion in a sequence of images the optical flow is very important in the computer vision community where its accurate estimation is necessary for many applications it is o

building blocks for computer vision with stochastic partial differential equations we discuss the basic concepts of computer vision with stochastic partial differential equations spdes in typical approaches based on partial differential equations pdes the end result in the best case is usually one value per pixel the expected value error estimates or even full probability density functions pdfs are usually not available this paper provides a framework allowing one to derive such pdfs rendering computer vision approaches into measurements fulfilling scientific standards due to full error propagation we identify the image data with random fields in order to model images and image sequences which carry uncertainty in their gray values e g due to noise in the acquisition process the noisy behaviors of gray values is modeled as stochastic processes which are approximated with the method of generalized polynomial chaos wiener askey chaos the wiener askey polynomial chaos is combined with a standard spatial approximation based upon piecewise multi linear finite elements we present the basic building blocks needed for computer vision and image processing in this stochastic setting i e we discuss the computation of stochastic moments projections gradient magnitudes edge indicators structure tensors etc finally we show applications of our framework to derive stochastic analogs of well known pdes for de noising and optical flow extraction these models are discretized with the stochastic galerkin method our selection of spde models allows us to draw connections to the classical deterministic models as well as to stochastic image processing not based on pdes several examples guide the reader through the presentation and show the usefulness of the framework

hierarchical estimation and segmentation of dense motion fields in this paper we present a comprehensive energy based framework for the estimation and the segmentation of the apparent motion in image sequences the robust cost functions and the associated hierarchical minimization techniques that we propose mix efficiently non parametric dense representations local interacting parametric representations and global non interacting parametric representations related to a partition into regions experimental comparisons both on synthetic and real images demonstrate the merit of the approach on different types of photometric and kinematic contents ranging from moving rigid objects to moving fluids

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

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

partial differential equations for zooming deinterlacing and dejittering in this paper for imaging applications we introduce partial differential equations pdes which allow for correcting displacement errors for dejittering and for deinterlacing respectively in multi channel data these equations are derived via semi groups for non convex energy functionals as a particular example for gray valued data we find the mean curvature equation and the corresponding non convex energy functional as a further application for correction of displacement errors we study image interpolation in particular zooming of digital color images for actual image zooming the solutions of the proposed pdes are projected onto a space of functions satisfying interpolation constraints a comparison of the test results with standard and state of the art interpolation algorithms shows the competitiveness of this approach

bootstrap resampling for image registration uncertainty estimation without ground truth we address the problem of estimating the uncertainty of pixel based image registration algorithms given just the two images to be registered for cases when no ground truth data is available our novel method uses bootstrap resampling it is very general applicable to almost any registration method based on minimizing a pixel based similarity criterion we demonstrate it using the ssd sad correlation and mutual information criteria we show experimentally that the bootstrap method provides better estimates of the registration accuracy than the state of the art cramer rao bound method additionally we evaluate also a fast registration accuracy estimation frae method which is based on quadratic sensitivity analysis ideas and has a negligible computational overhead frae mostly works better than the cramer rao bound method but is outperformed by the bootstrap method

determining optical flow for irregular domains by minimizing quadratic functionals of a certain class snyder 1989 has recently classified all smoothness terms which involve first order derivatives of the flowfield u x t and of the image grey value function g x t the physically plausible smoothness terms belonging to this class are known from the work of horn and schunck 1981 and nagel 1987 in this paper we discuss the possibilities of approximating the solutions to the minimization problems of horn schunk 1981 and nagel 1987 in particular it is shown that these solutions exist are unique and depend continuously on the input data these properties make it possible while taking into consideration arbitrary models of the grey value function to approximate efficiently the weak solutions of the associated boundary value problems in irregularly shaped domains with a sufficiently smooth boundary using finite elements experiments with image sequences from synthetic as well as outdoor scenes show how the orientation dependency of the smoothness term in nagel s approach influences the results

estimating optical flow in segmented images using variable order parametric models with local deformations this paper presents a new model for estimating optical flow based on the motion of planar regions plus local deformations the approach exploits brightness information to organize and constrain the interpretation of the motion by using segmented regions of piecewise smooth brightness to hypothesize planar regions in the scene parametric flow models are estimated in these regions in a two step process which first computes a coarse fit and then estimates the appropriate parametrization of the motion of the region the initial fit is refined using a generalization of the standard area based regression approaches since the assumption of planarity is likely to be violated we allow local deformations from the planar assumption in the same spirit as physically based approaches which model shape using coarse parametric models plus local deformations this parametric plus deformation model exploits the strong constraints of parametric approaches while retaining the adaptive nature of regularization approaches experimental results on a variety of images model produces accurate flow estimates while the incorporation of brightness segmentation boundaries

scaling theorems for zero crossings we characterize some properties of the zero crossings of the laplacian of signals in particular images filtered with linear filters as a function of the scale of the filter extending recent work by witkin 16 we prove that in any dimension the only filter that does not create generic zero crossings as the scale increases is the gaussian this result can be generalized to apply to level crossings of any linear differential operator it applies in particular to ridges and ravines in the image intensity in the case of the second derivative along the gradient there is no filter that avoids creation of zero crossings unless the filtering is performed after the derivative is applied

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

edge direction preserving image zooming a mathematical and numerical analysis we focus in this paper on some reconstruction restoration methods whose aim is to improve the resolution of digital images the main point here is to study the ability of such methods to preserve one dimensional 1d structures indeed such structures are important since they are often carried by the image edges first we focus on linear methods give a general framework to design them and show that the preservation of 1d structures pleads in favor of the cancellation of the periodization of the image spectrum more precisely we show that preserving 1d structures implies the linear methods to be written as a convolution of the sinc interpolation as a consequence we cannot cope linearly with gibbs effects sharpness of the results and the preservation of the 1d structure second we study variational nonlinear methods and in particular the one based on total variation we show that this latter permits us to avoid these shortcomings we also prove the existence and consistency of an approximate solution to this variational problem at last this theoretical study is highlighted by experiments both on synthetic and natural images which show the effects of the described methods on images as well as on their spectrum

robust optic flow computation this paper formulates the optic flow problem as a set of over determined simultaneous linear equations it then introduces and studies two new robust optic flow methods the first technique is based on using the least median of squares lmeds to detect the outliers then the inlier group is solved using the least square technique the second method employs a new robust statistical method named the least median of squares orthogonal distances lmsod to identify the outliers and then uses total least squares to solve the optic flow problem the performance of both methods are studied by experiments on synthetic and real image sequences these methods outperform other published methods both in accuracy and robustness

an axiomatic approach to image interpolation we discuss possible algorithms for interpolating data given in a set of curves and or points in the plane we propose a set of basic assumptions to be satisfied by the interpolation algorithms which lead to a set of models in terms of possibly degenerate elliptic partial differential equations the absolute minimal lipschitz extension model amle is singled out and studied in more detail we show experiments suggesting a possible application the restoration of images with poor dynamic range

optical flow a curve evolution approach a novel approach for the computation of optical flow based on an l sup 1 type minimization is presented it is shown that the approach has inherent advantages since it does not smooth the flow velocity across the edges and hence preserves edge information a numerical approach based on computation of evolving curves is proposed for computing the optical flow field computations are carried out on a number of real image sequences in order to illustrate the theory as well as the numerical approach

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

combining total variation regularization with window based time delay estimation in ultrasound elastography a major challenge of free hand palpation ultrasound elastography use is estimating the displacement of rf samples between pre and post compressed rf data the problem of displacement estimation is ill posed since the displacement of one sample by itself cannot be uniquely calculated to resolve this problem two categories of methods have emerged the first category assumes that the displacement of samples within a small window surrounding the reference sample is constant the second class imposes smoothness regularization and optimizes an energy function herein we propose a novel method that combines both approaches and as such is more robust to noise the second contribution of this work is the introduction of the l1 norm as the regularization term in our cost function which is often referred to as the total variation tv regularization compared to previous work that used the l2 norm regularization optimization of the new cost function is more challenging however the advantages of using the l1 norm are twofold first it leads to substantial improvement in the sharpness of displacement estimates second to optimize the cost function with the l1 norm regularization we use an iterative method that further increases the robustness we name our proposed method total variation regularization and window based time delay estimation overwind and show that it is robust to signal decorrelation and generates sharp displacement and strain maps for simulated experimental phantom and in vivo data in particular overwind improves strain contrast to noise ratio cnr by 27 26 144 05 and 49 90 on average in simulation phantom and in vivo data respectively compared to our recent global ultrasound elastography glue method

global 2d digital image correlation for motion estimation in a finite element framework a variational formulation and a regularized pyramidal multi grid implementation in this study the inverse problem of reconstructing the in plane 2d displacements of a monitored surface through a sequence of two dimensional digital images severely ill posed in hadamard s sense is deeply investigated a novel variational formulation is presented for the continuum 2d digital image correlation problem and critical issues such as semi coercivity and solution multiplicity are discussed by functional analysis tools in the framework of a galerkin finite element discretization of the displacement field a robust implementation for 2d digital image correlation is outlined aiming to attenuate the spurious oscillations which corrupt the deformation scenario especially when very fine meshes are adopted recourse is made to a hierarchical family of grids linked by suitable restriction and prolongation operators and defined over an image pyramid multi grid cycles are performed ascending and descending along the pyramid with only one newton iteration per level irrespective of the tolerance satisfaction as if the problem were linear at each level the conventional least square matching functional is herein enriched by a tychonoff regularization provision preserving the solution against an unstable response the algorithm is assessed on the basis of both synthetic and truly experimental image pairs copyright 2013 john wiley sons ltd

dense estimation and object based segmentation of the optical flow with robust techniques we address the issue of recovering and segmenting the apparent velocity field in sequences of images as for motion estimation we minimize an objective function involving two robust terms the first one cautiously captures the optical flow constraint while the second a priori term incorporates a discontinuity preserving smoothness constraint to cope with the nonconvex minimization problem thus defined we design an efficient deterministic multigrid procedure it converges fast toward estimates of good quality while revealing the large discontinuity structures of flow fields we then propose an extension of the model by attaching to it a flexible object based segmentation device based on deformable closed curves different families of curve equipped with different kinds of prior can be easily supported experimental results on synthetic and natural sequences are presented including an analysis of sensitivity to parameter tuning

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

reversible interpolation of vectorial images by an anisotropic diffusion projection pde in this paper a nonlinear model for the interpolation of vector valued images is proposed this model is based on an anisotropic diffusion pde and performs an interpolation that is reversible the interpolation solution is restricted to the subspace of functions that can recover the discrete input image after an appropriate smoothing and sampling the proposed nonlinear diffusion flow lies on this subspace while its strength and anisotropy adapt to the local variations and geometry of image structures the derived method effectively reconstructs the real image structures and yields a satisfactory interpolation result compared to classic and other existing pde based interpolation methods our proposed method seems to increase the accuracy of the result and to reduce the undesirable artifacts such as blurring ringing block effects and edge distortion we present extensive experimental results that demonstrate the potential of the method as applied to graylevel and color images

robust processing of optical flow of fluids this paper proposes a new approach coupling physical models and image estimation techniques for modelling the movement of fluids the fluid flow is characterized by turbulent movement and dynamically changing patterns which poses challenges to existing optical flow estimation methods the proposed methodology which relies on navier stokes equations is used for processing fluid optical flow by using a succession of stages such as advection diffusion and mass conservation a robust diffusion step jointly considering the local data geometry and its statistics is embedded in the proposed framework the diffusion kernel is gaussian with the covariance matrix defined by the local second derivatives such an anisotropic kernel is able to implicitly detect changes in the vector field orientation and to diffuse accordingly a new approach is developed for detecting fluid flow structures such as vortices the proposed methodology is applied on artificially generated vector fields as well as on various image sequences

myocardial motion estimation from medical images using the monogenic signal we present a method for the analysis of heart motion from medical images the algorithm exploits monogenic signal theory recently introduced as an n dimensional generalization of the analytic signal the displacement is computed locally by assuming the conservation of the monogenic phase over time a local affine displacement model is considered to account for typical heart motions as contraction expansion and shear a coarse to fine b spline scheme allows a robust and effective computation of the model s parameters and a pyramidal refinement scheme helps to handle large motions robustness against noise is increased by replacing the standard point wise computation of the monogenic orientation with a robust least squares orientation estimate given its general formulation the algorithm is well suited for images from different modalities in particular for those cases where time variant changes of local intensity invalidate the standard brightness constancy assumption this paper evaluates the method s feasibility on two emblematic cases cardiac tagged magnetic resonance and cardiac ultrasound in order to quantify the performance of the proposed method we made use of realistic synthetic sequences from both modalities for which the benchmark motion is known a comparison is presented with state of the art methods for cardiac motion analysis on the data considered these conventional approaches are outperformed by the proposed algorithm a recent global optical flow estimation algorithm based on the monogenic curvature tensor is also considered in the comparison with respect to the latter the proposed framework provides along with higher accuracy superior robustness to noise and a considerably shorter computation time

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

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

variational optical flow computation in real time this paper investigates the usefulness of bidirectional multigrid methods for variational optical flow computations although these numerical schemes are among the fastest methods for solving equation systems they are rarely applied in the field of computer vision we demonstrate how to employ those numerical methods for the treatment of variational optical flow formulations and show that the efficiency of this approach even allows for real time performance on standard pcs as a representative for variational optic flow methods we consider the recently introduced combined local global method it can be considered as a noise robust generalization of the horn and schunck technique we present a decoupled as well as a coupled version of the classical gau spl szlig seidel solver and we develop several multigrid implementations based on a discretization coarse grid approximation in contrast with standard bidirectional multigrid algorithms we take advantage of intergrid transfer operators that allow for nondyadic grid hierarchies as a consequence no restrictions concerning the image size or the number of traversed levels have to be imposed in the experimental section we juxtapose the developed multigrid schemes and demonstrate their superior performance when compared to unidirectional multigrid methods and nonhierachical solvers for the well known 316 spl times 252 yosemite sequence we succeeded in computing the complete set of dense flow fields in three quarters of a second on a 3 06 ghz pentium4 pc this corresponds to a frame rate of 18 flow fields per second which outperforms the widely used gau spl szlig seidel method by almost three orders of magnitude

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

dense correspondences across scenes and scales we seek a practical method for establishing dense correspondences between two images with similar content but possibly different 3d scenes one of the challenges in designing such a system is the local scale differences of objects appearing in the two images previous methods often considered only few image pixels matching only pixels for which stable scales may be reliably estimated recently others have considered dense correspondences but with substantial costs associated with generating storing and matching scale invariant descriptors our work is motivated by the observation that pixels in the image have contexts the pixels around them which may be exploited in order to reliably estimate local scales we make the following contributions i we show that scales estimated in sparse interest points may be propagated to neighboring pixels where this information cannot be reliably determined doing so allows scale invariant descriptors to be extracted anywhere in the image ii we explore three means for propagating this information using the scales at detected interest points using the underlying image information to guide scale propagation in each image separately and using both images together finally iii we provide extensive qualitative and quantitative results demonstrating that scale propagation allows for accurate dense correspondences to be obtained even between very different images with little computational costs beyond those required by existing methods

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

robust optical flow computation based on least median of squares regression an optical flow estimation technique is presented which is based on the least median of squares lmeds robust regression algorithm enabling more accurate flow estimates to be computed in the vicinity of motion discontinuities the flow is computed in a blockwise fashion using an affine model through the use of overlapping blocks coupled with a block shifting strategy redundancy is introduced into the computation of the flow this eliminates blocking effects common in most other techniques based on blockwise processing and also allows flow to be accurately computed in regions containing three distinct motions a multiresolution version of the technique is also presented again based on lmeds regression which enables image sequences containing large motions to be effectively handled an extensive set of quantitative comparisons with a wide range of previously published methods are carried out using synthetic realistic computer generated images of natural scenes with known flow and natural images both angular and absolute flow errors are calculated for those sequences with known optical flow displaced frame difference error used extensively in video compression is used for those natural scenes with unknown flow in all of the sequences tested a comparison with those methods that result in a dense flow field greater than 80 spatial coverage show that the lmeds technique produces the least error irrespective of the error measure used

dimension of the loop erased random walk in three dimensions we measure the fractal dimension of loop erased random walk lerw in three dimensions and estimate that it is 1 624 00 0 000 05 lerw is closely related to the uniform spanning tree and the abelian sandpile model we simulated lerw on both the cubic and face centered cubic lattices the corrections to scaling are slightly smaller for the face centered cubic lattice

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

a maximum a posteriori estimation framework for robust high dynamic range video synthesis high dynamic range hdr image synthesis from multiple low dynamic range exposures continues to be actively researched the extension to hdr video synthesis is a topic of significant current interest due to potential cost benefits for hdr video a stiff practical challenge presents itself in the form of accurate correspondence estimation of objects between video frames in particular loss of data resulting from poor exposures and varying intensity makes conventional optical flow methods highly inaccurate we avoid exact correspondence estimation by proposing a statistical approach via maximum a posterior estimation and under appropriate statistical assumptions and choice of priors and models we reduce it to an optimization problem of solving for the foreground and background of the target frame we obtain the background through rank minimization and estimate the foreground via a novel multiscale adaptive kernel regression technique which implicitly captures local structure and temporal motion by solving an unconstrained optimization problem extensive experimental results on both real and synthetic data sets demonstrate that our algorithm is more capable of delivering high quality hdr videos than current state of the art methods under both subjective and objective assessments furthermore a thorough complexity analysis reveals that our algorithm achieves better complexity performance tradeoff than conventional methods

multivariate numerical differentiation we present an innovative method for multivariate numerical differentiation i e the estimation of partial derivatives of multidimensional noisy signals starting from a local model of the signal consisting of a truncated taylor expansion we express through adequate differential algebraic manipulations the desired partial derivative as a function of iterated integrals of the noisy signal iterated integrals provide noise filtering the presented method leads to a family of estimators for each partial derivative of any order we present a detailed study of some structural properties given in terms of recurrence relations between elements of a same family these properties are next used to study the performance of the estimators we show that some differential algebraic manipulations corresponding to a particular family of estimators lead implicitly to an orthogonal projection of the desired derivative in a jacobi polynomial basis functions yielding an interpretation in terms of the popular least squares this interpretation allows one to 1 explain the presence of a spatial delay inherent to the estimators and 2 derive an explicit formula for the delay we also show how one can devise by a proper combination of different elementary estimators of a given order derivative an estimator giving a delay of any prescribed value the simulation results show that delay free estimators are sensitive to noise robustness with respect to noise can be highly increased by utilizing voluntary delayed estimators a numerical implementation scheme is given in the form of finite impulse response digital filters the effectiveness of our derivative estimators is attested by several numerical simulations

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

domain decomposition for variational optical flow computation we present an approach to parallel variational optical flow computation by using an arbitrary partition of the image plane and iteratively solving related local variational problems associated with each subdomain the approach is particularly suited for implementations on pc clusters because interprocess communication is minimized by restricting the exchange of data to a lower dimensional interface our mathematical formulation supports various generalizations to linear nonlinear convex variational approaches three dimensional image sequences spatiotemporal regularization and unstructured geometries and triangulations results concerning the effects of interface preconditioning as well as runtime and communication volume measurements on a pc cluster are presented our approach provides a major step toward real time two dimensional image processing using off the shelf pc hardware and facilitates the efficient application of variational approaches to large scale image processing problems

multimodal estimation of discontinuous optical flow using markov random fields the estimation of dense velocity fields from image sequences is basically an ill posed problem primarily because the data only partially constrain the solution it is rendered especially difficult by the presence of motion boundaries and occlusion regions which are not taken into account by standard regularization approaches in this paper the authors present a multimodal approach to the problem of motion estimation in which the computation of visual motion is based on several complementary constraints it is shown that multiple constraints can provide more accurate flow estimation in a wide range of circumstances the theoretical framework relies on bayesian estimation associated with global statistical models namely markov random fields the constraints introduced here aim to address the following issues optical flow estimation while preserving motion boundaries processing of occlusion regions fusion between gradient and feature based motion constraint equations deterministic relaxation algorithms are used to merge information and to provide a solution to the maximum a posteriori estimation of the unknown dense motion field the algorithm is well suited to a multiresolution implementation which brings an appreciable speed up as well as a significant improvement of estimation when large displacements are present in the scene experiments on synthetic and real world image sequences are reported

ambrosio tortorelli segmentation of stochastic images model extensions theoretical investigations and numerical methods we discuss an extension of the ambrosio tortorelli approximation of the mumford shah functional for the segmentation of images with uncertain gray values resulting from measurement errors and noise our approach yields a reliable precision estimate for the segmentation result and it allows us to quantify the robustness of edges in noisy images and under gray value uncertainty we develop an ansatz space for such images by identifying gray values with random variables the use of these stochastic images in the minimization of energies of ambrosio tortorelli type leads to stochastic partial differential equations for a stochastic smoothed version of the original image and a stochastic phase field for the edge set for the discretization of these equations we utilize the generalized polynomial chaos expansion and the generalized spectral decomposition gsd method in contrast to the simple classical sampling technique this approach allows for an efficient determination of the stochastic properties of the output image and edge set by computations on an optimally small set of random variables also we use an adaptive grid approach for the spatial dimensions to further improve the performance and we extend an edge linking method for the classical ambrosio tortorelli model for use with our stochastic model the performance of the method is demonstrated on artificial data and a data set from a digital camera as well as real medical ultrasound data a comparison of the intrusive gsd discretization with a stochastic collocation and a monte carlo sampling is shown

anisotropic interpolation of sparse generalized image samples practical image acquisition systems are often modeled as a continuous domain prefilter followed by an ideal sampler where generalized samples are obtained after convolution with the impulse response of the device in this paper our goal is to interpolate images from a given subset of such samples we express our solution in the continuous domain considering consistent resampling as a data fidelity constraint to make the problem well posed and ensure edge preserving solutions we develop an efficient anisotropic regularization approach that is based on an improved version of the edge enhancing anisotropic diffusion equation following variational principles our reconstruction algorithm minimizes successive quadratic cost functionals to ensure fast convergence we solve the corresponding sequence of linear problems by using multigrid iterations that are specifically tailored to their sparse structure we conduct illustrative experiments and discuss the potential of our approach both in terms of algorithmic design and reconstruction quality in particular we present results that use as little as 2 of the image samples

sparse occlusion detection with optical flow we tackle the problem of detecting occluded regions in a video stream under assumptions of lambertian reflection and static illumination the task can be posed as a variational optimization problem and its solution approximated using convex minimization we describe efficient numerical schemes that reach the global optimum of the relaxed cost functional for any number of independently moving objects and any number of occlusion layers we test the proposed algorithm on benchmark datasets expanded to enable evaluation of occlusion detection performance in addition to optical flow

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

mathematical models for local nontexture inpaintings dedicated to stanley osher on the occasion of his 60th birthday abstract inspired by the recent work of bertalmio et al on digital inpaintings siggraph 2000 we develop general mathematical models for local inpaintings of nontexture images on smooth regions inpaintings are connected to the harmonic and biharmonic extensions and inpainting orders are analyzed for inpaintings involving the recovery of edges we study a variational model that is closely connected to the classical total variation tv denoising model of rudin osher and fatemi phys d 60 1992 pp 259 268 other models are also discussed based on the mumford shah regularity comm pure appl math xlii 1989 pp 577 685 and curvature driven diffusions cdd of chan and shen j visual comm image rep 12 2001 the broad applications of the inpainting models are demonstrated through restoring scratched old photos disocclusion in vision analysis text removal digital zooming and edge based image coding