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

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

an initial and boundary value problem for the zakharov kuznestov equation in a bounded domain motivated by the study of boundary control problems for the zakharov kuznetsov equation we study in this article the initial and boundary value problem for the zk short for zakharov kuznetsov equation posed in a limited domain 0 1 x 2 2 d d 1 2 this article is related to saut and temam an initial boundary value problem for the zakharov kuznetsov equation adv differ equ 15 11 12 1001 1031 2010 in which the authors studied the same problem in the band 0 1 x rd d 1 2 but this article is not a straightforward adaptation of saut and temam an initial boundary value problem for the zakharov kuznetsov equation adv differ equ 15 11 12 1001 1031 2010 indeed many new issues arise in particular for the function spaces due to the loss of the fourier transform in the tangential directions orthogonal to 0x in this article after studying a number of suitable function spaces we show the existence and uniqueness of solutions for the linearized equation using the

computing redundant resources for the resource constrained project scheduling problem several efficient lower bounds and time bound adjustment methods for the resource constrained project scheduling problem rcpsp have recently been proposed some of them are based on redundant resources in this paper we define redundant functions which are very useful for computing redundant resources we also describe an algorithm for computing all maximal redundant functions once all these redundant functions have been determined we have to identify those that are useful for bounding surprisingly their number is reasonable even for large resource capacities so a representative subset of them can be tabulated to be used efficiently computational results on classical rcpsp instances confirm their usefulness

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

design of multiparameter steerable functions using cascade basis reduction an efficient method of computing the least squares optimal basis functions to steer any function locally is presented the method combines the lie group theoretic and the singular value decomposition approaches its efficiency is demonstrated with the design of basis functions to steer a gabor function under the four parameter linear transformation group

some comments on fourier analysis uncertainty and modeling investigation of the problem of simultaneously concentrating a function and its fourier transform has led to some interesting special functions that have widespread applications in engineering they provide a means of proving a rigorous version of an engineering folk theorem called the 2wt theorem many generalizations of these ideas seem to possess a similar elegant mathematical structure a brief descriptive review is given of these developments

a harmonic retrieval framework for discontinuous motion estimation motion discontinuities arise when there are occlusions or multiple moving objects in the scene that is imaged conventional regularization techniques use smoothness constraints but are not applicable to motion discontinuities in this paper we show that discontinuous or multiple motion estimation can be viewed as a multicomponent harmonic retrieval problem from this viewpoint a number of established techniques for harmonic retrieval ran be applied to solve the challenging problem of discontinuous or multiple motion compared with existing techniques the resulting algorithm is not iterative which not only implies computational efficiency but also obviates concerns regarding convergence or local minima it also adds flexibility to spatio temporal techniques which have suffered from lack of explicit modeling of discontinuous motion experimental verification of our framework on both synthetic data as well as real image data is provided

an exact algorithm for the resource constrained project scheduling problem based on a new mathematical formulation in this paper we consider the project scheduling problem with resource constraints where the objective is to minimize the project makespan we present a new 0 1 linear programming formulation of the problem that requires an exponential number of variables corresponding to all feasible subsets of activities that can be simultaneously executed without violating resource or precedence constraints different relaxations of the above formulation are used to derive new lower bounds which dominate the value of the longest path on the precedence graph and are tighter than the bound proposed by stinson et al 1978 a tree search algorithm based on the above formulation that uses new lower bounds and dominance criteria is also presented computational results indicate that the exact algorithm can solve hard instances that cannot be solved by the best algorithms reported in the literature

robust optical flow estimation based on a sparse motion trajectory set this paper presents an approach to the problem of estimating a dense optical flow field the approach is based on a multiframe irregularly spaced motion trajectory set where each trajectory describes the motion of a given point as a function of time from this motion trajectory set a dense flow field is estimated using a process of interpolation a set of localized motion models are estimated with each pixel labeled as belonging to one of the motion models a markov random field framework is adopted allowing the incorporation of contextual constraints to encourage region like structures the approach is compared with a number of conventional optical flow estimation algorithms taken over a number of real and synthetic sequences results indicate that the method produces more accurate results for sequences with known ground truth flow also applying the method to real sequences with unknown flow results in lower dfd for all of the sequences tested

a branch and bound algorithm for the resource constrained project scheduling problem a branch and bound algorithm is presented for the resource constrained project scheduling problem rcpsp given are n activities which have to be processed without preemptions during the processing period of an activity constant amounts of renewable resources are needed where the available capacity of each resource type is limited furthermore finish start precedence relations between the activities are given the objective is to determine a schedule with minimal makespan the branching scheme starts from a graph representing a set of conjunctions the classical finish start precedence constraints and disjunctions induced by the resource constraints then it either introduces disjunctive constraints between pairs of activities or places these activities in parallel concepts of immediate selection are developed in connection with this branching scheme immediate selection allows to add conjunctions as well as further disjunctions and parallelity relations computational results based on the test data of kolisch et al kolisch r sprecher a drexl a 1995 management science 41 1693 1703 and kolisch and sprecher kolisch r sprecher a 1997 psplib a project scheduling problem library ejor 96 pp 205 216 are reported

physics based flow estimation of fluids abstract we present a physics based method to compute the optical flow of a fluid in most situations gray level changes in an image do not provide sufficient information to completely ascertain optical flow necessitating the use of a supplementary constraint for this the smoothness constraint is often employed this constraint is however general and does not express well a priori knowledge of a specific object we therefore propose a method in which physical equations describing the object are used as supplementary constraints in this way more accurate flow estimation can be achieved the physical model employed is a combination of the continuity equation and navier stokes equations after describing how we integrate these equations into fluid flow estimation we demonstrate the effectiveness of the proposed method by presenting experimental results of its application to simulated and real karman flows

slow feature analysis unsupervised learning of invariances invariant features of temporally varying signals are useful for analysis and classification slow feature analysis sfa is a new method for learning invariant or slowly varying features from a vectorial input signal it is based on a nonlinear expansion of the input signal and application of principal component analysis to this expanded signal and its time derivative it is guaranteed to find the optimal solution within a family of functions directly and can learn to extract a large number of decorrelated features which are ordered by their degree of invariance sfa can be applied hierarchically to process high dimensional input signals and extract complex features sfa is applied first to complex cell tuning properties based on simple cell output including disparity and motion then more complicated input output functions are learned by repeated application of sfa finally a hierarchical network of sfa modules is presented as a simple model of the visual system the same unstructured network can learn translation size rotation contrast or to a lesser degree illumination invariance for one dimensional objects depending on only the training stimulus surprisingly only a few training objects suffice to achieve good generalization to new objects the generated representation is suitable for object recognition performance degrades if the network is trained to learn multiple invariances simultaneously

a note on the 2d generalized zakharov kuznetsov equation local global and scattering results abstract we consider the generalized two dimensional zakharov kuznetsov equation u t x u x u k 1 0 where k 3 is an integer number for k 8 we prove local well posedness in the l 2 based sobolev spaces h s r 2 where s is greater than the critical scaling index s k 1 2 k for k 3 we also establish a sharp criteria to obtain global h 1 r 2 solutions a nonlinear scattering result in h 1 r 2 is also established assuming the initial data is small and belongs to a suitable lebesgue space

the feasibility of motion and structure from noisy time varying image velocity information this research addresses the problem of noise sensitivity inherent in motion and structure algorithms the motion and structure paradigm is a two step process first we measure image velocities and perhaps their spatial and temporal derivatives are obtained from time varying image intensity data and second we use these data to compute the motion of a moving monocular observer in a stationary environment under perspective projection relative to a single 3 d planar surface the first contribution of this article is an algorithm that uses time varying image velocity information to compute the observer s translation and rotation and the normalized surface gradient of the 3 d planar surface the use of time varying image velocity information is an important tool in obtaining a more robust motion and structure calculation the second contribution of this article is an extensive error analysis of the motion and structure problem any motion and structure algorithm that uses image velocity information as its input should exhibit error sensitivity behavior compatible with the results reported here we perform an average and worst case error analysis for four types of image velocity information full and normal image velocities and full and normal sets of image velocity and its derivatives these derivatives are simply the coefficients of a truncated taylor series expansion about some point in space and time the main issues we address here are just how sensitive is a motion and structure computation in the presence of noisy input or alternately how accurate must our image velocity information be how much and what type of input data is needed and under what circumstances is motion and structure feasible that is when can we be sure that a motion and structure computation will produce usable results we base our answers on a numerical error analysis we conduct for a large number of motions

hierarchical construction of orientation and velocity selective filters as a step towards the early measurement of visual primitives the authors outline design criteria for the extraction of orientation and velocity information and present a variety of tools useful in the construction of simple linear filters a hierarchical parallel processing scheme is used in which nodes compute a weighted sum of inputs from within a small spatio temporal neighborhood the resulting scheme is easily analyzed and provides mechanisms sensitive to narrow ranges of both image velocity and orientation the hierarchical approach in combination with separability in the first levels yields an efficient implementation

estimation of motion from sequential images using integral constraints abstract a novel method for estimating nonuniform motion from sequential images is presented which is based on integral brightness constancy constraints the equations which transform arbitrary integrals between sequential images are expressed as a function of the displacement field and intensity changes the apparent displacement field is then computed by iterative projections onto the solution space of each linearized transformation equation some properties of this technique are demonstrated on a synthetic image pair realistic motion estimation is also demonstrated using sequential tagged cine magnetic resonance images

estimation of motions in color image sequences using hypercomplex fourier transforms although the motion estimation problem has been extensively studied most of the proposed estimation approaches deal mainly with monochrome videos the most usual way to apply them also in color image sequences is to process each color channel separately a different more sophisticated approach is to process the color channels in a ldquoholisticrdquo manner using quaternions as proposed by ell and sangwine in this paper we extend standard spatiotemporal fourier based approaches to handle color image sequences using the hypercomplex fourier transform we show that translational motions are manifested as energy concentration along planes in the hypercomplex 3d fourier domain and we describe a methodology to estimate the motions based on this property furthermore we compare the three channels separately approach with our approach and we show that the computational effort can be reduced by a factor of 1 3 using the hypercomplex fourier transform also we propose a simple accompanying method to extract the moving objects in the hypercomplex fourier domain our experimental results on synthetic and natural images verify our arguments throughout the paper

a linear programming and constraint propagation based lower bound for the rcpsp abstract a new destructive lower bound for the resource constrained project scheduling problem rcpsp is presented given are n activities which have to be processed without preemptions during the processing period of an activity constant amounts of renewable resources are needed where the available capacity of each resource type is limited furthermore finish start precedence relations between the activities are given the objective is to determine a schedule with minimal makespan the lower bound calculations are based on two methods for proving infeasibility of a given threshold value t for the makespan the first uses constraint propagation techniques while the second is based on a linear programming formulation a column generation procedure is presented for the linear programming formulation and computational results are reported for an algorithm combining both concepts

lower bounds for resource constrained project scheduling problems abstract a destructive lower bound for the multi mode resource constrained project scheduling problem with minimal and maximal time lags is presented given are n activities which may be processed in different modes without preemptions during processing certain amounts of renewable and non renewable resources are needed where the available capacity of each resource type is limited furthermore minimal and maximal time lags between the activities are given the objective is to determine a schedule with minimal makespan the lower bound calculations are based on two methods for proving infeasibility of a given threshold value t for the makespan the first uses constraint propagation techniques while the second is based on a linear programming formulation which is solved by a column generation procedure computational results are reported for several test instances of the multi mode problem with and without time lags and the single mode version with time lags

optical flow using spatiotemporal filters a model is presented consonant with current views regarding the neurophysiology and psychophysics of motion perception that combines the outputs of a set of spatiotemporal motion energy filters to estimate image velocity a parallel implementation computes a distributed representation of image velocity a measure of image flow uncertainty is formulated preliminary results indicate that this uncertainty measure may be used to recognize ambiguity due to the aperture problem the model appears to deal with the aperture problem as well as the human visual system since it extracts the correct velocity for some patterns that have large differences in contrast at different spatial orientations

local and global well posedness for the 2d generalized zakharov kuznetsov equation this paper addresses well posedness issues for the initial value problem ivp as sociated with the generalized zakharov kuznetsov equation namely ut xu u k ux 0 x y 2 r 2 t 0 u x y 0 u0 x y for 2 k 7 the ivp above is shown to be locally well posed for data in h s r 2 s 3 4 for k 8 local well posedness is shown to hold for data in h s r 2 s sk where sk 1 3 2k 4 furthermore for k 3 if u0 2 h 1 r 2 and satisfies ku0kh1 1 then the solution is shown to be global in h 1 r 2 for k 2 if u0 2 h s r 2 s 53 63 and satisfies ku0kl2 p 3k kl2 where is the corresponding ground state solution then the solution is shown to be global in h s r 2

regularization of optical flow with m band wavelet transform abstract the optical flow is an important tool for problems arising in the analysis of image sequences flow fields generated by various existing solving techniques are often noisy and partially incorrect especially near occlusions or motion boundaries therefore the additional information on the scene gained from a sequence of images is usually worse in this paper discrete wavelet transform has been adopted in order to enhance the reliability of optical flow estimation a generalization of the well known dyadic orthonormal wavelets to the case of the dilation scale factor m 2 with n vanishing moments has been used and it has proved to be a useful regularizing tool the advantages in the computations have been shown by experimental results performed on real image sequences

the zakharov kuznetsov equation in weighted sobolev spaces abstract in this work we consider the initial value problem ivp associated to the two dimensional zakharov kuznetsov equation u t x 3 u x y 2 u u x u 0 x y r 2 t r u x y 0 u 0 x y we study the well posedness of the ivp in the weighted sobolev spaces h s r 2 l 2 1 x 2 y 2 r d x d y with s r r

psychophysical and computational studies towards a theory of human stereopsis psychophysical studies are described which pose a strong challenge to models of human stereopsis based on the processing of disparity information within independent spatial frequency tuned binocular channels these studies support instead the proposal that the processes of human binocular combination integrally relate the extraction of disparity information with the construction of raw primal sketch assertions this proposal implies global binocular combination rules using principles of figural continuity and cross channel correspondence to disambiguate local matches found independently within spatial frequency channels exploratory small scale computational experiments with stereo algorithms based on these rules are described and found to be successful in dealing with a variety of stereo inputs the constraints presented by objects which are exploited by these algorithms are discussed

regular solutions of the 2d zakharov kuznetsov equation on a half strip abstract we formulate on a half strip an initial boundary value problem for the zakharov kuznetsov equation existence and uniqueness of a regular solution as well as the exponential decay rate of small solutions as t are proven

a branch price and cut algorithm for multi mode resource leveling abstract we propose a new mixed integer programming formulation and solution algorithm for a multi mode resource constrained project scheduling problem with availability constraints calendars and the objective to minimize the resource availability cost our model exploits the problem structure and has an exponential number of variables which necessitates a column generation approach the linear programming relaxation is strengthened by adding valid inequalities that need to be carefully separated in order to show the desired effect integer optimal solutions are obtained by an exact state of the art branch price and cut algorithm classical time indexed mixed integer programming formulations for similar problems quite often fail already on instances with only 30 jobs depending on the network complexity and the total freedom of arranging jobs a reason is the typically very weak linear programming relaxation our model can be interpreted as a non trivial dantzig wolfe reformulation of a time indexed formulation in particular for larger instances our reformulation gives significantly tighter dual bounds enabling us to optimally solve instances with 50 multi mode jobs this outperforms the classical formulation by far

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

initial boundary value problems in a rectangle for two dimensional zakharov kuznetsov equation abstract initial boundary value problems in a bounded rectangle with different types of boundary conditions for two dimensional zakharov kuznetsov equation are considered results on global well posedness in the classes of weak and regular solution are established as applications of the developed technique results on boundary controllability and long time decay of weak solutions are also obtained

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

an initial boundary value problem in a strip for two dimensional zakharov kuznetsov burgers equation abstract an initial boundary value problem in a strip with homogeneous dirichlet boundary conditions for two dimensional zakharov kuznetsov burgers equation is considered results on global well posedness and large time decay of solutions in the spaces h s for s 0 2 are established

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

linear programming based algorithms for preemptive and non preemptive rcpsp abstract in this paper the rcpsp resource constrained project scheduling problem is solved using a linear programming model each activity may or may not be preemptive each variable is associated to a subset of independent activities antichains the properties of the model are first investigated in particular conditions are given that allow a solution of the linear program to be a feasible schedule from these properties an algorithm based on neighbourhood search is derived one neighbour solution is obtained through one simplex pivoting if this pivoting preserves feasibility methods to get out of local minima are provided the solving methods are tested on the psplib instances in a preemptive setting and prove efficient they are used when preemption is forbidden with less success and this difference is discussed

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

learning intermediate level representations of form and motion from natural movies we present a model of intermediate level visual representation that is based on learning invariances from movies of the natural environment the model is composed of two stages of processing an early feature representation layer and a second layer in which invariances are explicitly represented invariances are learned as the result of factoring apart the temporally stable and dynamic components embedded in the early feature representation the structure contained in these components is made explicit in the activities of second layer units that capture invariances in both form and motion when trained on natural movies the first layer produces a factorization or separation of image content into a temporally persistent part representing local edge structure and a dynamic part representing local motion structure consistent with known response properties in early visual cortex area v1 this factorization linearizes statistical dependencies among the first layer units making them learnable by the second layer the second layer units are split into two populations according to the factorization in the first layer the form selective units receive their input from the temporally persistent part local edge structure and after training result in a diverse set of higher order shape features consisting of extended contours multiscale edges textures and texture boundaries the motion selective units receive their input from the dynamic part local motion structure and after training result in a representation of image translation over different spatial scales and directions in addition to more complex deformations these representations provide a rich description of dynamic natural images and testable hypotheses regarding intermediate level representation in visual cortex

an efficient temporal distortion measure of videos based on spacetime texture abstract objective video quality assessment vqa plays an important role in controlling video quality most of the existing vqa methods measure motion related temporal distortion based on optical flow methods which are not consistently reliable in modeling general visual dynamics this paper presents a full reference temporal distortion measure based on spacetime texture a uniform and distributive descriptor of a broad set of spacetime structures our method measures the distortion of spacetime texture in video with a motion tuning strategy which effectively captures temporal distortion along the motion trajectories then it estimates self information based visual saliency for spatial pooling by reusing the motion descriptors we evaluated our method on two public vqa databases with a wide variety of distortion types in which the videos were viewed on a large screen or mobile devices the results show that our method correlates highly with the subjective quality and has high computational efficiency

determining optical flow optical flow cannot be computed locally since only one independent measurement is available from the image sequence at a point while the flow velocity has two components a second constraint is needed a method for finding the optical flow pattern is presented which assumes that the apparent velocity of the brightness pattern varies smoothly almost everywhere in the image an iterative implementation is shown which successfully computes the optical flow for a number of synthetic image sequences the algorithm is robust in that it can handle image sequences that are quantized rather coarsely in space and time it is also insensitive to quantization of brightness levels and additive noise examples are included where the assumption of smoothness is violated at singular points or along lines in the image

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

coherent multiscale image processing using quaternion wavelets coherent multiscale image processing using quaternion wavelets by wai lam chan this thesis develops a quaternion wavelet transform qwt as a new multiscale analysis tool for geometric image features the qwt is a near shift invariant tight frame representation whose coefficients sport a magnitude and three phases two phases encode local image shifts while the third contains textural information the qwt can be computed using a dual tree filter bank with linear computational complexity we develop the qwt by applying an alternative theory of 2 d hilbert transforms and analytic signals to the 1 d complex wavelet transform to demonstrate the properties of the qwt s coherent magnitude phase representation we develop a efficient and accurate algorithm for estimating the local geometrical structure of images and a multiscale algorithm for estimating the disparity between a pair of images the latter algorithm has potentials for various applications in image registration and flow estimation it uses an interesting multiscale phase unwrapping procedure and features linear complexity and sub pixel accuracy

recursive estimation of 3d motion and surface structure from local affine flow parameters a recursive structure from motion algorithm based on optical flow measurements taken from an image sequence is described it provides estimates of surface normal in addition to 3d motion and depth the measurements are affine motion parameters which approximate the local flow fields associated with near planar surface patches in the scene these are integrated over time to give estimates of the 3d parameters using an extended kalman filter this also estimates the camera focal length and so the 3d estimates are metric the use of parametric measurements means that the algorithm is computationally less demanding than previous optical flow approaches and the recursive filter builds in a degree of noise robustness results of experiments on synthetic and real image sequences demonstrate that the algorithm performs well

force estimation and prediction from time varying density images we present methods for estimating forces which drive motion observed in density image sequences using these forces we also present methods for predicting velocity and density evolution to do this we formulate and apply a minimum energy flow mef method which is capable of estimating both incompressible and compressible flows from time varying density images both the mef and force estimation techniques are applied to experimentally obtained density images spanning spatial scales from micrometers to several kilometers using density image sequences describing cell splitting for example we show that cell division is driven by gradients in apparent pressure within a cell using density image sequences of fish shoals we also quantify 1 intershoal dynamics such as coalescence of fish groups over tens of kilometers 2 fish mass flow between different parts of a large shoal and 3 the stresses acting on large fish shoals

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

computing optical flow with physical models of brightness variation although most optical flow techniques presume brightness constancy it is well known that this constraint is often violated producing poor estimates of image motion this paper describes a generalized formulation of optical flow estimation based on models of brightness variations that are caused by time dependent physical processes these include changing surface orientation with respect to a directional illuminant motion of the illuminant and physical models of heat transport in infrared images with these models we simultaneously estimate the 2d image motion and the relevant physical parameters of the brightness change model the estimation problem is formulated using total least squares with confidence bounds on the parameters experiments in four domains with both synthetic and natural inputs show how this formulation produces superior estimates of the 2d image motion

well posedness for the two dimensional generalized zakharov kuznetsov equation in anisotropic weighted sobolev spaces abstract we consider the well posedness of the initial value problem associated to the k generalized zakharov kuznetsov equation in fractional weighted sobolev spaces h s r 2 l 2 x 2 r 1 y 2 r 2 d x d y s r 1 r 2 r our method of proof is based on the contraction mapping principle and it mainly relies on the well posedness results recently obtained for this equation in the sobolev spaces h s r 2 and a new pointwise commutator type formula involving the group induced by the linear part of the equation and the fractional anisotropic weights to be considered

decay of regular solutions for the critical 2d zakharov kuznetsov equation posed on rectangles an initial boundary value problem for the critical generalized 2d zakharov kuznetsov equation posed on rectangles is considered the existence uniqueness and exponential decay rate of global regular solutions for small initial data are established

multiple constraints to compute optical flow the computation of the optical flow field from an image sequence requires the definition of constraints on the temporal change of image features in this paper we consider the implications of using multiple constraints in the computational schema in the first step it is shown that differential constraints correspond to an implicit feature tracking therefore the best results either in terms of measurement accuracy and speed in the computation are obtained by selecting and applying the constraints which are best tuned to the particular image feature under consideration considering also multiple image points not only allows us to obtain a locally better estimate of the velocity field but also to detect erroneous measurements due to discontinuities in the velocity field moreover by hypothesizing a constant acceleration motion model also the derivatives of the optical flow are computed several experiments are presented from real image sequences

an effective branch and price algorithm for the preemptive resource constrained project scheduling problem based on minimal interval order enumeration in this paper we address the preemptive resource constrained project scheduling problem prcpsp prcpsp requires a partially ordered set of activities to be scheduled using limited renewable resources such that any activity can be interrupted and later resumed without penalty the objective is to minimize the project duration this paper proposes an effective branch and price algorithm for solving prcpsp based upon minimal interval order enumeration involving column generation as well as constraint propagation experiments conducted on various types of instances have given very satisfactory results our algorithm is able to solve to optimality the entire set of j30 bl and pack instances while satisfying the preemptive requirement furthermore this algorithm provides improved best known lower bounds for some of the j60 j90 and j120 instances in the non preemptive case rcpsp

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

exponential decay of the h1 norm for the 2d zakharov kuznetsov equation on a half strip abstract we formulate on a half strip an initial boundary value problem for the 2d zakharov kuznetsov equation the existence of a unique weak solution was proven as well as exponential decay of the h 1 norm for small initial data