elastically adaptive deformable models we present a technique for the automatic adaptation of a deformable model s elastic parameters within a kalman filter framework for shape estimation applications the novelty of the technique is that the model s elastic parameters are not constant but spatio temporally varying the variation of the elastic parameters depends on the distance of the model from the data and the rate of change of this distance each pass of the algorithm uses physics based modeling techniques to iteratively adjust both the geometric and the elastic degrees of freedom of the model in response to forces that are computed from the discrepancy between the model and the data by augmenting the state equations of an extended kalman filter to incorporate these additional variables we are able to significantly improve the quality of the shape estimation therefore the model s elastic parameters are always initialized to the same value and they are subsequently modified depending on the data and the noise distribution we present results demonstrating the effectiveness of our method for both two dimensional and three dimensional data

twist based acquisition and tracking of animal and human kinematics this paper demonstrates a new visual motion estimation technique that is able to recover high degree of freedom articulated human body configurations in complex video sequences we introduce the use and integration of a mathematical technique the product of exponential maps and twist motions into a differential motion estimation this results in solving simple linear systems and enables us to recover robustly the kinematic degrees of freedom in noise and complex self occluded configurations a new factorization technique lets us also recover the kinematic chain model itself we are able to track several human walk cycles several wallaby hop cycles and two walk cycels of the famous movements of eadweard muybridge s motion studies from the last century to the best of our knowledge this is the first computer vision based system that is able to process such challenging footage

interpretation of image flow a spatio temporal approach a general formulation is described for the interpretation of image flow in the framework of this formulation computational methods have been derived for image flow interpretation for many important cases including simple cases of nonrigid and nonuniform motions it is possible to derive computational methods for other situations not considered explicitly the formulation is general in that it is applicable to any situation provided that the scene geometry the scene transformation and the image flow are all smooth or analytic

a geometric approach to the classification of the equilibrium shapes of self gravitating fluids the classification of the equilibrium shapes that a self gravitating fluid can take in a riemannian manifold is a classical problem in mathematical physics in this paper it is proved that the equilibrium shapes are isoparametric submanifolds some geometric properties of them are also obtained e g classification and existence for some riemannian spaces and relationship with the isoperimetric problem and the group of isometries of the manifold our approach to the problem is geometrical and allows to study the equilibrium shapes on general riemannian spaces

color texture segmentation based on the modal energy of deformable surfaces this paper presents a new approach for the segmentation of color textured images which is based on a novel energy function the proposed energy function which expresses the local smoothness of an image area is derived by exploiting an intermediate step of modal analysis that is utilized in order to describe and analyze the deformations of a 3 d deformable surface model the external forces that attract the 3 d deformable surface model combine the intensity of the image pixels with the spatial information of local image regions the proposed image segmentation algorithm has two steps first a color quantization scheme which is based on the node displacements of the deformable surface model is utilized in order to decrease the number of colors in the image then the proposed energy function is used as a criterion for a region growing algorithm the final segmentation of the image is derived by a region merge approach the proposed method was applied to the berkeley segmentation database the obtained results show good segmentation robustness when compared to other state of the art image segmentation algorithms

estimation of object motion parameters from noisy images an approach is presented for the estimation of object motion parameters based on a sequence of noisy images the problem considered is that of a rigid body undergoing unknown rotational and translational motion the measurement data consists of a sequence of noisy image coordinates of two or more object correspondence points by modeling the object dynamics as a function of time estimates of the model parameters including motion parameters can be extracted from the data using recursive and or batch techniques this permits a desired degree of smoothing to be achieved through the use of an arbitrarily large number of images some assumptions regarding object structure are presently made results are presented for a recursive estimation procedure the case considered here is that of a sequence of one dimensional images of a two dimensional object thus the object moves in one transverse dimension and in depth preserving the fundamental ambiguity of the central projection image model loss of depth information an iterated extended kalman filter is used for the recursive solution noise levels of 5 10 percent of the object image size are used approximate cramer rao lower bounds are derived for the model parameter estimates as a function of object trajectory and noise level this approach may be of use in situations where it is difficult to resolve large numbers of object match points but relatively long sequences of images 10 to 20 or more are available

constraints on deformable models recovering 3d shape and nongrid motion abstract inferring the 3d structures of nonrigidly moving objects from images is a difficult yet basic problem in computational vision our approach makes use of dynamic elastically deformable object models that offer the geometric flexibility to satisfy a diversity of real world visual constraints we specialize these models to include intrinsic forces inducing a preference for axisymmetry image based constraints are applied as extrinsic forces that mold the symmetry seeking model into shapes consistent with image data we describe an extrinsic force that applies constraints derived from profiles of monocularly viewed objects we generalize this constraint force to incorporate profile information from multiple views and use it to exploit binocular image data for time varying images the force becomes dynamic and the model is able to infer not only depth but nonrigid motion as well we demonstrate the recovery of 3d shape and nonrigid motion from natural imagery

closed form solutions for physically based shape modeling and recognition the authors present a closed form physically based solution for recovering a three dimensional 3 d solid model from collections of 3 d surface measurements given a sufficient number of independent measurements the solution is overconstrained and unique except for rotational symmetries the proposed approach is based on the finite element method fem and parametric solid modeling using implicit functions this approach provides both the convenience of parametric modeling and the expressiveness of the physically based mesh formulation and in addition can provide great accuracy at physical simulation a physically based object recognition method that allows simple closed form comparisons of recovered 3 d solid models is presented the performance of these methods is evaluated using both synthetic range data with various signal to noise ratios and using laser rangefinder data

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

optical flow constraints on deformable models with applications to face tracking optical flow provides a constraint on the motion of a deformable model we derive and solve a dynamic system incorporating flow as a hard constraint producing a model based least squares optical flow solution our solution also ensures the constraint remains satisfied when combined with edge information which helps combat tracking error accumulation constraint enforcement can be relaxed using a kalman filter which permits controlled constraint violations based on the noise present in the optical flow information and enables optical flow and edge information to be combined more robustly and efficiently we apply this framework to the estimation of face shape and motion using a 3d deformable face model this model uses a small number of parameters to describe a rich variety of face shapes and facial expressions we present experiments in extracting the shape and motion of a face from image sequences which validate the accuracy of the method they also demonstrate that our treatment of optical flow as a hard constraint as well as our use of a kalman filter to reconcile these constraints with the uncertainty in the optical flow are vital for improving the performance of our system

a symmetry result for the torsion equation in an unbounded domain in 2d abstract we investigate an overdetermined problem for the torsion equation u 1 with two kinds of free boundary conditions in an unbounded domain and present a symmetry result in the case of 2d the proof is based on the maximum principle in the proof we use the sliding method and some convex arguments

could the processed seismic wavelet be simpler than we think j p lindsey 1988 in a clearly written short piece opens an old question which concerns the analytic properties of seismic wavelets this well conceived study concludes that most of the roots of a seismic wavelet as expressed by its z transform representation lie on or are very near the unit circle the present discussion does not seek to characterize the form of all seismic wavelets but only many if not most of those which have been processed with deconvolutions or inversion type operators to have reduced length broadened bandwidth and some desirable phase property for such wavelets despite the diversity by which they are obtained remarkably simple operations having very few parameters can be extremely effective as a case in point constant phase rotations appear to carry such wavelets to zero phase symmetric form to a very good approximation i start with empirical attributes which appear to characterize most processed seismic wavelets such wavelets tend to be of 40 100 ms duration with a

a symmetry result for the torsion equation in an unbounded domain in 3d abstract we investigate an overdetermined problem for the torsion equation u 1 in an unbounded domain in r 3 under some additional conditions we show that the solution is a one dimensional quadratic function and that the boundary of the domain is a pair of parallel planes the proof is based on the maximum principle

displacement estimates through adaptive affinities a technique that is functionally equivalent to the oriented smoothing concept and reduces numerical complexity and computational costs by eliminating the smoothness requirement from the iteration process is introduced local affine transformations are applied to propagate uniquely computed flow vectors into homogeneous regions and along edges in a single step the window within which the local affine transformation is performed can adapt to the local structure of the intensity pattern in accordance with the oriented smoothness concept as formulated by h nagel 1987

kronecker markov prior for dynamic 3d reconstruction recovering dynamic 3d structures from 2d image observations is highly under constrained because of projection and missing data motivating the use of strong priors to constrain shape deformation in this paper we empirically show that the spatiotemporal covariance of natural deformations is dominated by a kronecker pattern we demonstrate that this pattern arises as the limit of a spatiotemporal autoregressive process and derive a kronecker markov random field as a prior distribution over dynamic structures this distribution unifies shape and trajectory models of prior art and has the individual models as its marginals the key assumption of the kronecker mrf is that the spatiotemporal covariance is separable into the product of a temporal and a shape covariance and can therefore be modeled using the matrix normal distribution analysis on motion capture data validates that this distribution is an accurate approximation with significantly fewer free parameters using the trace norm we present a convex method to estimate missing data from a single sequence when the marginal shape distribution is unknown the kronecker markov distribution fit to a single sequence outperforms state of the art methods at inferring missing 3d data and additionally provides covariance estimates of the uncertainty

symmetry seeking models and 3d object reconstruction we propose models of 3d shape which may be viewed as deformable bodies composed of simulated elastic material in contrast to traditional purely geometric models of shape deformable models are active their shapes change in response to externally applied forces we develop a deformable model for 3d shape which has a preference for axial symmetry symmetry is represented even though the model does not belong to a parametric shape family such as generalized cylinders rather a symmetry seeking property is designed into internal forces that constrain the deformations of the model we develop a framework for 3d object reconstruction based on symmetry seeking models instances of these models are formed from monocular image data through the action of external forces derived from the data the forces proposed in this paper deform the model in space so that the shape of its projection into the image plane is consistent with the 2d silhouette of an object of interest the effectiveness of our approach is demonstrated using natural images

curvature based algorithms for nonrigid motion and correspondence estimation we present a novel technique for utilizing the gaussian curvature information in 3d nonrigid motion estimation in the absence of known correspondence differential geometric constraints derived in the paper allow one to estimate parameters of the local affine motion model given the values of gaussian curvature before and after motion these constraints can be further combined with the previously known constraints based on the unit normals before and after motion our experiments demonstrate that the resulting hybrid algorithm is more accurate than each of its constituents and more accurate than the classical icp algorithm we also present a technique for curvilinear orthogonalization of quadratic monge patches that is essential in our derivation and useful in other applications

3 d shape recovery using distributed aspect matching an approach to the recovery of 3 d volumetric primitives from a single 2 d image is presented the approach first takes a set of 3 d volumetric modeling primitives and generates a hierarchical aspect representation based on the projected surfaces of the primitives conditional probabilities capture the ambiguity of mappings between levels of the hierarchy from a region segmentation of the input image the authors present a formulation of the recovery problem based on the grouping of the regions into aspects no domain independent heuristics are used only the probabilities inherent in the aspect hierarchy are exploited once the aspects are recovered the aspect hierarchy is used to infer a set of volumetric primitives and their connectivity as a front end to an object recognition system the approach provides the indexing power of complex 3 d object centered primitives while exploiting the convenience of 2 d viewer centered aspect matching aspects are used to represent a finite vocabulary of 3 d parts from which objects can be constructed

tracking of tubular molecules for scientific applications in this paper we present a system for detection and tracking of tubular molecules in images the automatic detection and characterization of the shape location and motion of these molecules can enable new laboratory protocols in several scientific disciplines the uniqueness of the proposed system is twofold at the macro level the novelty of the system lies in the integration of object localization and tracking using geometric properties at the micro level in the use of high and low level constraints to model the detection and tracking subsystem the underlying philosophy for object detection is to extract perceptually significant features from the pixel level image and then use these high level cues to refine the precise boundaries in the case of tubular molecules the perceptually significant features are antiparallel line segments or equivalently their axis of symmetries the axis of symmetry infers a coarse description of the object in terms of a bounding polygon the polygon then provides the necessary boundary condition for the refinement process which is based on dynamic programming for tracking the object in a time sequence of images the refined contour is then projected onto each consecutive frame

recovery of nonrigid motion and structure the authors introduce a physically correct model of elastic nonrigid motion this model is based on the finite element method but decouples the degrees of freedom by breaking down object motion into rigid and nonrigid vibration or deformation modes the result is an accurate representation for both rigid and nonrigid motion that has greatly reduced dimensionality capturing the intuition that nonrigid motion is normally coherent and not chaotic because of the small number of parameters involved this representation is used to obtain accurate overstrained estimates of both rigid and nonrigid global motion it is also shown that these estimates can be integrated over time by use of an extended kalman filter resulting in stable and accurate estimates of both three dimensional shape and three dimensional velocity the formulation is then extended to include constrained nonrigid motion examples of tracking single nonrigid objects and multiple constrained objects are presented

shape and nonrigid motion estimation through physics based synthesis a physics based framework for 3 d shape and nonrigid motion estimation for real time computer vision systems is presented the framework features dynamic models that incorporate the mechanical principles of rigid and nonrigid bodies into conventional geometric primitives through the efficient numerical simulation of lagrange equations of motion the models can synthesize physically correct behaviors in response to applied forces and imposed constraints applying continuous kalman filtering theory a recursive shape and motion estimator that employs the lagrange equations as a system model is developed the system model continually synthesizes nonrigid motion in response to generalized forces that arise from the inconsistency between the incoming observations and the estimated model state the observation forces also account formally for instantaneous uncertainties and incomplete information a riccati procedure updates a covariance matrix that transforms the forces in accordance with the system dynamics and prior observation history experiments involving model fitting and tracking of articulated and flexible objects from noisy 3 d data are described

three dimensional reconstruction of points and lines with unknown correspondence across images three dimensional reconstruction from a set of images is an important and difficult problem in computer vision in this paper we address the problem of determining image feature correspondences while simultaneously reconstructing the corresponding 3d features given the camera poses of disparate monocular views first two new affinity measures are presented that capture the degree to which candidate features from different images consistently represent the projection of the same 3d point or 3d line an affinity measure for point features in two different views is defined with respect to their distance from a hypothetical projected 3d pseudo intersection point similarly an affinity measure for 2d image line segments across three views is defined with respect to a 3d pseudo intersection line these affinity measures provide a foundation for determining unknown correspondences using weighted bipartite graphs representing candidate point and line matches across different images as a result of this graph representation a standard graph theoretic algorithm can provide an optimal simultaneous matching and triangulation of points across two views and lines across three views experimental results on synthetic and real data demonstrate the effectiveness of the approach

time varying wavelet estimation and deconvolution by kurtosis maximization phase mismatches sometimes occur between final processedsectionsandzero phasesyntheticsbasedonwelllogs despite best efforts for controlled phase acquisition and processing the latter are often based on deterministic corrections derived from field measurements and physical laws a statisticalanalysisofthedatacanrevealwhetheratime varying nonzero phase is present this assumes that the data should be white with respect to all statistical orders after proper deterministic corrections have been applied kurtosis maximizationbyconstantphaserotationisastatisticalmethod that can reveal the phase of a seismic wavelet it is robust enough to detect time varying phase changes phase only corrections can then be applied by means of a time varying phase rotation alternatively amplitude and phase deconvolution can be achieved using time varying wiener filtering time varyingwaveletextractionanddeconvolutioncanalso be used as a data driven alternative to amplitude only inverse qdeconvolution

matching 3 d anatomical surfaces with non rigid deformations using octree splines presents a new method for determining the minimal nonrigid deformation between two 3d surfaces such as those which describe anatomical structures in 3d medical images although the authors match surfaces they represent the deformation as a volumetric transformation their method performs a least squares minimization of the distance between the two surfaces of interest to quickly and accurately compute distances between points on the two surfaces the authors use a precomputed distance map represented using an octree spline whose resolution increases near the surface to quickly and robustly compute the deformation the authors use a second octree spline to model the deformation function the coarsest level of the deformation encodes the global e g affine transformation between the two surfaces while finer levels encode smooth local displacements which bring the two surfaces into closer registration the authors present experimental results on both synthetic and real 3d surfaces

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

wavelet estimation revisited this article deals with the ubiquitous problem of wavelet estimation in essence the problem consists of estimating at best two unknowns from one equation in the seismic case as it is well known the model of the recorded seismic trace xt is generally formulated as a convolution xt wt rt where wt is the seismic source signature or wavelet and rt is the reflectivity series which is comprised of all primary and multiple reflections since in general we can assume that rt is white or nearly so the amplitude signature of wt may be estimated with some degree of confidence it is of course the phase of wt that presents the difficulty it turns out perhaps somewhat counterintuitively that except for rather special circumstances the phase of a signal uniquely determines the signal to within a scale factor the amplitude spectrum plays no part whatsoever we explore this further below no wonder then that the phase is the all important factor

dynamic programming for detecting tracking and matching deformable contours the problem of segmenting an image into separate regions and tracking them over time is one of the most significant problems in vision terzopoulos et al 1987 proposed an approach to detect the contour regions of complex shapes assuming a user selected initial contour not very far from the desired solution we propose to further explore the information provided by the user s selected points and apply an optimal method to detect contours which allows a segmentation of the image the method is based on dynamic programming dp and applies to a wide variety of shapes it is exact and not iterative we also consider a multiscale approach capable of speeding up the algorithm by a factor of 20 although at the expense of losing the guaranteed optimality characteristic the problem of tracking and matching these contours is addressed for tracking the final contour obtained at one frame is sampled and used as initial points for the next frame then the same dp process is applied for matching a novel strategy is proposed where the solution is a smooth displacement field in which unmatched regions are allowed while cross vectors are not the algorithm is again based on dp and the optimal solution is guaranteed we have demonstrated the algorithms on natural objects in a large spectrum of applications including interactive segmentation and automatic tracking of the regions of interest in medical images

automatic phase correction of common midpoint stacked data the residual wavelet on a processed seismic section is often not zero phase despite all efforts to make it so in this paper we adopt the convolutional model for the processed seismogram assume that the residual phase shift can be approximated by a frequency independent constant and use the varimax norm to generate an algorithm to estimate the residual phase directly application of our algorithm to reflectivities from well logs suggests that it should work in the majority of cases so long as the reflectivity is non gaussian an application of our algorithm to stacked data enhances the interpretability of the seismic section and leads to an improved match between the recovered relative acoustic impedance and a measured velocity log

learning to track the visual motion of contours abstract a development of a method for tracking visual contours is described given an untrained tracker a training motion of an object can be observed over some extended time and stored as an image sequence the image sequence is used to learn parameters in a stochastic differential equation model these are used in turn to build a tracker whose predictor imitates the motion in the training set tests show that the resulting trackers can be markedly tuned to desired curve shapes and classes of motions

a note on an overdetermined system involving mean curvature abstract let be a bounded simply connected domain in r n with connected boundary of class c 2 we show that if there exist n functions satisfying some overdetermined system with boundary conditions involving mean curvature of then is a ball the proof is based on the maximum principle and serrin s theorem

point tracked quantitative analysis of left ventricular surface motion from 3 d image sequences proposes and validates the hypothesis that one can use differential shape properties of the myocardial surfaces to recover dense field motion from standard three dimensional 3 d image sequences mri and ct quantitative measures of left ventricular regional function can be further inferred from the point correspondence maps the noninvasive algorithm derived results are validated on two levels first the motion trajectories are compared to those of implanted imaging opaque markers of a canine model in two imaging modalities where subpixel accuracy is achieved second the validity of using motion parameters path length and thickness changes for detecting myocardial injury area is tested by comparing algorithms derived results to postmortem analysis ttc staining of myocardial tissue where the achieved pearson product moment correlation value is 0 968