the renormalized electron mass in non relativistic quantum electrodynamics abstract this work addresses the problem of infrared mass renormalization for a non relativistic electron minimally coupled to the quantized electromagnetic field the standard translationally invariant system of an electron in non relativistic qed we assume that the interaction of the electron with the quantized electromagnetic field is subject to an ultraviolet regularization and an infrared regularization parametrized by 0 for the value p 0 of the conserved total momentum of electron and photon field bounds on the renormalized mass are established which are uniform in 0 and the existence of a ground state is proved for p 0 sufficiently small bounds on the renormalized mass are derived for any fixed 0 a key ingredient of our proofs is the operator theoretic renormalization group based on the isospectral smooth feshbach map it provides an explicit finite algorithm for determining the renormalized electron mass at p 0 to any given precision

higher order svd analysis for dynamic texture synthesis videos representing flames water smoke etc are often defined as dynamic textures textures because they are characterized by the redundant repetition of a pattern and dynamic because this repetition is also in time and not only in space dynamic textures have been modeled as linear dynamic systems by unfolding the video frames into column vectors and describing their trajectory as time evolves after the projection of the vectors onto a lower dimensional space by a singular value decomposition svd the trajectory is modeled using system identification techniques synthesis is obtained by driving the system with random noise in this paper we show that the standard svd can be replaced by a higher order svd hosvd originally known as tucker decomposition hosvd decomposes the dynamic texture as a multidimensional signal tensor without unfolding the video frames on column vectors this is a more natural and flexible decomposition since it permits us to perform dimension reduction in the spatial temporal and chromatic domain while standard svd allows for temporal reduction only we show that for a comparable synthesis quality the hosvd approach requires on average five times less parameters than the standard svd approach the analysis part is more expensive but the synthesis has the same cost as existing algorithms our technique is thus well suited to dynamic texture synthesis on devices limited by memory and computational power such as pdas or mobile phones

smoothness and analyticity of perturbation expansions in qed abstract we consider the ground state of an atom in the framework of non relativistic qed we assume that the ultraviolet cutoff is of the order of the rydberg energy and that the atomic hamiltonian has a non degenerate ground state we show that the ground state energy and the ground state are k times continuously differentiable functions of the fine structure constant and respectively the square root of the fine structure constant on some nonempty interval 0 c k

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

template matching of binary targets in grey scale images a nonparametric approach this paper introduces a nonparametric similarity measure based on the kolmogorov smirnov ks statistic to be used in template matching problems where a target of binary characteristics is to be located in a grey scale image ks statistic yields the best expected value for a binary domain similarity measure if the threshold selection to binarize the image had been optimized to take into account the geometric constraints of the template there is however no need to actually binarize the image some good properties of a ks based similarity measure are exposed and compared with the corresponding properties of normalized correlation a practical algorithm to implement a template matching procedure based on the ks statistic is shown and its computing time is compared with normalized correlation a ks based similarity measure proves to be usually much faster computationally that normalized correlation finally some experimental results are shown

edge detection in machine vision using a simple l 1 norm template matching algorithm abstract template matching based on the sum of absolute errors the l 1 norm is an effective means of edge detection in certain controlled imaging environments where the form of the edges to be detected is known the algorithm employs a 1 d edge profile as the template edges are detected by computing the l 1 norm of an error vector obtained by subtracting an edge template from the image data this paper evaluates the performance of the l 1 norm template matching algorithm and draws comparisons to classical correlation matching the l 1 norm template matching algorithm has potential for integrated circuit and printed circuit board inspection and other inspection applications where the lighting and view aspect can be controlled

renormalization group analysis of spectral problems in quantum field theory abstract in this paper we present a self contained and detailed exposition of the new renormalization group technique proposed in 1 2 its main feature is that the renormalization group transformation acts directly on a space of operators rather than on objects such as a propagator the partition function or correlation functions we apply this renormalization transformation to a hamiltonian describing the physics of an atom interacting with the quantized electromagnetic field and we prove that excited atomic states turn into resonances when the coupling between electrons and field is nonvanishing

lambertian reflectance and linear subspaces we prove that the set of all lambertian reflectance functions the mapping from surface normals to intensities obtained with arbitrary distant light sources lies close to a 9d linear subspace this implies that in general the set of images of a convex lambertian object obtained under a wide variety of lighting conditions can be approximated accurately by a low dimensional linear subspace explaining prior empirical results we also provide a simple analytic characterization of this linear space we obtain these results by representing lighting using spherical harmonics and describing the effects of lambertian materials as the analog of a convolution these results allow us to construct algorithms for object recognition based on linear methods as well as algorithms that use convex optimization to enforce nonnegative lighting functions we also show a simple way to enforce nonnegative lighting when the images of an object lie near a 4d linear space we apply these algorithms to perform face recognition by finding the 3d model that best matches a 2d query image

infrared renormalization in non relativistic qed and scaling criticality abstract we consider a spin 1 2 electron in the framework of non relativistic quantum electrodynamics qed let h p denote the fiber hamiltonian corresponding to the conserved total momentum p r 3 of the electron and the photon field regularized by a fixed ultraviolet cutoff in the interaction term and an infrared regularization parametrized by 0 1 ultimately our goal is to remove the latter by taking 0 we prove that there exists a constant 0 0 1 independent of 0 such that for all p 1 3 and all values of the finestructure constant 0 0 there exists a ground state eigenvalue of multiplicity two at the bottom of the essential spectrum moreover we prove that the renormalized electron mass satisfies 1 m ren p 1 c uniformly in 0 in units where the bare mass has the value 1 and we prove the existence of the renormalized mass in the limit 0 our analysis uses the isospectral renormalization group method of bach frohlich sigal introduced in v bach j frohlich i m sigal quantum electrodynamics of confined non relativistic particles adv math 137 2 1998 299 395 v bach j frohlich i m sigal renormalization group analysis of spectral problems in quantum field theory adv math 137 1998 205 298 and further developed in v bach t chen j frohlich i m sigal smooth feshbach map and operator theoretic renormalization group methods j funct anal 203 1 2003 44 92 v bach t chen j frohlich i m sigal the renormalized electron mass in non relativistic qed j funct anal 243 2 2007 426 535 the limit 0 determines a scaling critical or endpoint type renormalization group problem in which the interaction is strictly marginal of scale independent size a main result of this paper is the development of a method that provides rigorous control of the renormalization of a strictly marginal quantum field theory characterized by a non trivial scaling limit the key ingredients entering this analysis include a hierarchy of exact algebraic cancelation identities exploiting the spatial and gauge symmetries of the model and a combination of the isospectral renormalization group method with the strong induction principle

smooth feshbach map and operator theoretic renormalization group methods abstract a new variant of the isospectral feshbach map defined on operators in hilbert space is presented it is constructed with the help of a smooth partition of unity instead of projections and is therefore called smooth feshbach map it is an effective tool in spectral and singular perturbation theory as an illustration of its power a novel operator theoretic renormalization group method is described and applied to analyze a general class of hamiltonians on fock space the main advantage of the new renormalization group method over its predecessors is its technical simplicity which it owes to the use of the smooth feshbach map

a physics based analysis of image appearance models linear and multilinear models pca 3dmm aam asm and multilinear tensors of object shape appearance have been very popular in computer vision in this paper we analyze the applicability of these heuristic models from the fundamental physical laws of object motion and image formation we prove that under suitable conditions the image appearance space can be closely approximated to be multilinear with the illumination and texture subspaces being trilinearly combined with the direct sum of the motion and deformation subspaces this result provides a physics based understanding of many of the successes and limitations of the linear and multilinear approaches existing in the computer vision literature and also identifies some of the conditions under which they are valid it provides an analytical representation of the image space in terms of different physical factors that affect the image formation process numerical analysis of the accuracy of the physics based models is performed and tracking results on real data are presented

χ2 test for feature detection abstract in this paper 2 tests are applied to detect local visual features each feature and its noise is modeled by a random vector y with a multivariate normal distribution denoted by y n y y the mean vector y and the variance covariance matrix y characterize the structure of the feature blurring in real images is modeled by gaussian distribution the variance vector in the blur is obtained by simulated annealing and estimated by a linear matrix b then b is used to blur each feature y let z by n 1 where n 1 is a random vector for noise then z n z z n b y b 1 y b n after the transformation f z z z t z 1 z z the random vector z becomes a random variable with 2 distribution therefore the 2 test can measure the similarity between data and the expectation vector of each model

infrared finite algorithms in qed ii the expansion of the groundstate of an atom interacting with the quantized radiation field abstract in this paper we present an explicit and constructive algorithm enabling us to calculate the groundstate and the groundstate energy of a non relativistic atom minimally coupled to the quantized radiation field up to an error of arbitrary finite order in the fine structure constant because of infrared divergences which invalidate a straightforward taylor expansion an iterative construction is employed to remove the infrared cut off in photon momentum space and to produce a convergent algorithm

a method for enforcing integrability in shape from shading algorithms an approach for enforcing integrability a particular implementation of the approach an example of its application to extending an existing shape from shading algorithm and experimental results showing the improvement that results from enforcing integrability are presented a possibly nonintegrable estimate of surface slopes is represented by a finite set of basis functions and integrability is enforced by calculating the orthogonal projection onto a vector subspace spanning the set of integrable slopes the integrability projection constraint was applied to extending an iterative shape from shading algorithm of m j brooks and b k p horn 1985 experimental results show that the extended algorithm converges faster and with less error than the original version good surface reconstructions were obtained with and without known boundary conditions and for fairly complicated surfaces

application of the conditional population mixture model to image segmentation the problem of image segmentation is considered in the context of a mixture of probability distributions the segments fall into classes a probability distribution is associated with each class of segment parametric families of distributions are considered a set of parameter values being associated with each class with each observation is associated an unobservable label indicating from which class the observation arose segmentation algorithms are obtained by applying a method of iterated maximum likelihood to the resulting likelihood function a numerical example is given choice of the number of classes using akaike s information criterion aic for model identification is illustrated

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

quantum electrodynamics of confined nonrelativistic particles abstract we consider a system of finitely many nonrelativistic quantum mechanical electrons bound to static nuclei the electrons are minimally coupled to the quantized electromagnetic field but we impose an ultraviolet cutoff on the electromagnetic vector potential appearing in covariant derivatives and the interactions between the radiation field and electrons localized very far from the nuclei are turned off for a class of hamiltonians we prove exponential localization of bound states establish the existence of a ground state and derive sufficient conditions for its uniqueness furthermore we show that excited bound states of the unperturbed system become unstable and turn into resonances when the electrons are coupled to the radiation field to this end we develop a novel renormalization transformation which acts directly on the space of hamiltonians

dynamic shape and appearance models we propose a model of the joint variation of shape and appearance of portions of an image sequence the model is conditionally linear and can be thought of as an extension of active appearance models to exploit the temporal correlation of adjacent image frames inference of the model parameters can be performed efficiently using established numerical optimization techniques borrowed from finite element analysis and system identification techniques

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

maximum likelihood thresholding based on population mixture models maximum likelihood thresholding methods are presented on the basis of population mixture models it turns out that the standard thresholding proposed by otsu which is based on a discriminant criterion and also minimizes the mean square errors between the original image and the resultant binary image is equivalent to the maximization of the likelihood of the conditional distribution in the population mixture model under the assumption of normal distributions with a common variance it is also shown that kittler and illingworth s thresholding which minimizes a criterion related to the average classification error rate assuming normal distribution with different variances is equivalent to the maximization of the likelihood of the joint distribution in the population mixture model a multi thresholding algorithm based on dynamic programming is also presented

ground states in non relativistic quantum electrodynamics the excited states of a charged particle interacting with the quantized electromagnetic field and an external potential all decay but such a particle should have a true ground state one that minimizes the energy and satisfies the schrodinger equation we prove quite generally that this state exists for all values of the fine structure constant and the ultraviolet cutoff we also show the same thing for a many particle system under physically natural conditions

matching shape sequences in video with applications in human movement analysis we present an approach for comparing two sequences of deforming shapes using both parametric models and nonparametric methods in our approach kendall s definition of shape is used for feature extraction since the shape feature rests on a non euclidean manifold we propose parametric models like the autoregressive model and autoregressive moving average model on the tangent space and demonstrate the ability of these models to capture the nature of shape deformations using experiments on gait based human recognition the nonparametric model is based on dynamic time warping we suggest a modification of the dynamic time warping algorithm to include the nature of the non euclidean space in which the shape deformations take place we also show the efficacy of this algorithm by its application to gait based human recognition we exploit the shape deformations of a person s silhouette as a discriminating feature and provide recognition results using the nonparametric model our analysis leads to some interesting observations on the role of shape and kinematics in automated gait based person authentication

convergent expansions in non relativistic qed analyticity of the ground state we consider the ground state of an atom in the framework of non relativistic qed we show that the ground state as well as the ground state energy are analytic functions of the coupling constant which couples to the vector potential under the assumption that the atomic hamiltonian has a non degenerate ground state moreover we show that the corresponding expansion coefficients are precisely the coefficients of the associated raleigh schrodinger series as a corollary we obtain that in a scaling limit where the ultraviolet cutoff is of the order of the rydberg energy the ground state and the ground state energy have convergent power series expansions in the fine structure constant with dependent coefficients which are finite for 0

multilinear graph embedding representation and regularization for images given a set of images finding a compact and discriminative representation is still a big challenge especially when multiple latent factors are hidden in the way of data generation to represent multifactor images although multilinear models are widely used to parameterize the data most methods are based on high order singular value decomposition hosvd which preserves global statistics but interprets local variations inadequately to this end we propose a novel method called multilinear graph embedding mge as well as its kernelization mkge to leverage the manifold learning techniques into multilinear models our method theoretically links the linear nonlinear and multilinear dimensionality reduction we also show that the supervised mge encodes informative image priors for image regularization provided that an image is represented as a high order tensor from our experiments on face and gait recognition the superior performance demonstrates that mge better represents multifactor images than classic methods including hosvd and its variants in addition the significant improvement in image or tensor completion validates the potential of mge for image regularization

robust clustering with applications in computer vision a clustering algorithm based on the minimum volume ellipsoid mve robust estimator is proposed the mve estimator identifies the least volume region containing h percent of the data points the clustering algorithm iteratively partitions the space into clusters without prior information about their number at each iteration the mve estimator is applied several times with values of h decreasing from 0 5 a cluster is hypothesized for each ellipsoid the shapes of these clusters are compared with shapes corresponding to a known unimodal distribution by the kolmogorov smirnov test the best fitting cluster is then removed from the space and a new iteration starts constrained random sampling keeps the computation low the clustering algorithm was successfully applied to several computer vision problems formulated in the feature space paradigm multithresholding of gray level images analysis of the hough space and range image segmentation

estimating the kinematics and structure of a rigid object from a sequence of monocular images the problem considered involves the use of a sequence of noisy monocular images of a three dimensional moving object to estimate both its structure and kinematics the object is assumed to be rigid and its motion is assumed to be smooth a set of object match points is assumed to be available consisting of fixed features on the object the image plane coordinates of which have been extracted from successive images in the sequence structure is defined as the 3 d positions of these object feature points relative to each other rotational motion occurs about the origin of an object centered coordinate system while translational motion is that of the origin of this coordinate system in this work which is a continuation of the research done by the authors and reported previously ibid vol pami 8 p 90 9 jan 1986 results of an experiment with real imagery are presented involving estimation of 28 unknown translational rotational and structural parameters based on 12 images with seven feature points

renormalization analysis for degenerate ground states abstract we consider a hamilton operator which describes a finite dimensional quantum mechanical system with degenerate eigenvalues coupled to a field of relativistic bosons we show that the ground state projection and the ground state energy are analytic functions of the coupling constant in a cone with apex at the origin provided a mild infrared assumption holds to show the result operator theoretic renormalization is used and extended to degenerate situations

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

on photometric issues in 3d visual recognition from asingle 2d image we describe the problem of recognition under changing illumination conditions and changing viewing positions from a computational and human vision perspective on the computational side we focus on the mathematical problems of creating an equivalence class for images of the same 3d object undergoing certain groups of transformations mostly those due to changing illumination and briefly discuss those due to changing viewing positions the computational treatment culminates in proposing a simple scheme for recognizing via alignment an image of a familiar object taken from a novel viewing position and a novel illumination condition on the human vision aspect the paper is motivated by empirical evidence inspired by mooney images of faces that suggest a relatively high level of visual processing is involved in compensating for photometric sources of variability and furthermore that certain limitations on the admissible representations of image information may exist the psychophysical observations and the computational results that follow agree in several important respects such as the same apparent limitations on image representations

shape and motion from image streams under orthography a factorization method inferring scene geometry and camera motion from a stream of images is possible in principle but is an ill conditioned problem when the objects are distant with respect to their size we have developed a factorization method that can overcome this difficulty by recovering shape and motion under orthography without computing depth as an intermediate step an image stream can be represented by the 2fxp measurement matrix of the image coordinates of p points tracked through f frames we show that under orthographic projection this matrix is of rank 3 based on this observation the factorization method uses the singular value decomposition technique to factor the measurement matrix into two matrices which represent object shape and camera rotation respectively two of the three translation components are computed in a preprocessing stage the method can also handle and obtain a full solution from a partially filled in measurement matrix that may result from occlusions or tracking failures the method gives accurate results and does not introduce smoothing in either shape or motion we demonstrate this with a series of experiments on laboratory and outdoor image streams with and without occlusions

template matching based on a grayscale hit or miss transform this paper introduces a class of rank order based template matching criteria that are multiplier free and independent of the dc variations of the image the core component of these criteria is a grayscale morphological hit or miss transform ghmt experimental results show that the ghmt features sharp and robust indications in the presence of gaussian noise the idea of the ghmt is used to develop more general forms of matching criteria that are robust to both gaussian and impulsive noises

analyticity of the self energy in total momentum of an atom coupled to the quantized radiation field abstract we study a neutral atom with a non vanishing electric dipole moment coupled to the quantized electromagnetic field for a sufficiently small dipole moment and small momentum p the one particle self energy of an atom is proven to be a real analytic function of its momentum the main ingredient of our proof is a suitable form of the feshbach schur spectral renormalization group