existence and multiplicity of solutions for p x curl systems arising in electromagnetism abstract in this paper we study the existence and multiplicity of solutions to a class of p x curl systems arising in electromagnetism the results obtained in this paper extend several contributions concerning the p curl operator and we focus on new existence results which are due to the presence of variable exponent to our best knowledge our results are new even in the semilinear case

view variation of point set and line segment features the variation with respect to view of 2d features defined for projections of 3d point sets and line segments is studied it is established that general case view invariants do not exist for any number of points given true perspective weak perspective or orthographic projection models feature variation under the weak perspective approximation is then addressed though there are no general case weak perspective invariants there are special case invariants of practical importance those cited in the literature are derived from linear dependence relations and the invariance of this type of relation to linear transformation the variation with respect to view is studied for an important set of 2d line segment features the relative orientation size and position of one line segment with respect to another the analysis includes an evaluation criterion for feature utility in terms of view variation this relationship is a function of both the feature and the particular configuration of 3d line segments the use of this information in objection recognition is demonstrated for difficult discrimination tasks

convergence analysis of a finite volume method for maxwell s equations in nonhomogeneous media in this paper we analyze a recently developed finite volume method for the time dependent maxwell s equations in a three dimensional polyhedral domain composed of two dielectric materials with different parameter values for the electric permittivity and the magnetic permeability convergence and error estimates of the numerical scheme are established for general nonuniform tetrahedral triangulations of the physical domain in the case of nonuniform rectangular grids the scheme converges with second order accuracy in the discrete l2 norm despite the low regularity of the true solution over the entire domain in particular the finite volume method is shown to be superconvergent in the discrete h curl norm in addition the explicit dependence of the error estimates on the material parameters is given

a boundedness criterion for generalized calderon zygmund operators in 1965 a p calderon showed the l2 boundedness of the so called first calderon commutator this is one of the first examples of a non convolution operator associated to a kernel which satisfies certain size and smoothness properties comparable to those of the kernel of the hilbert transform these properties together with the l2 boundedness imply the lp boundedness for all p s in 1 oo many operators in analysis such as certain classes of pseudo differential operators and the cauchy integral operator on a curve are associated with kernels having these properties for these operators one of the major questions is if they are bounded on l2 we are going to give necessary and sufficient conditions for such an operator to be bounded on l2 they are essentially that the images of the function 1 under the actions of the operator and its adjoint both lie in bmo in the case of the aforementioned first commutator this can be checked by an integration by parts in the first section we present some basic notions and state the theorem which is proved in sections 2 and 3 in section 4 we show how to recover some classical results in sections 5 and 6 we construct a functional calculus for small perturbations of a and in section 7 we show a connection between the theory of calderon zygmund operators and kato s conjecture it is a pleasure to express our thanks to r r coifman and y meyer for suggesting many elegant simplifications in our proofs and most of the applications we also wish to thank stephen semmes for several pertinent remarks

the sharp weighted bound for general calderon zygmund operators for a general calderon zygmund operator t on r n it is shown that ktfkl2 w c t sup q a q w q w 1 a k fkl2 w for all muckenhoupt weights w 2 a2 this optimal estimate was known as the a2 conjecture a recent result of perez treil volberg reduced the problem to a testing condition on indicator functions which is verified in this paper the proof consists of the following elements i a variant of the nazarov treil volberg method of random dyadic systems with just one random system and completely without bad parts ii a resulting representation of a general calderon zygmund operator as an average of dyadic shifts and iii improvements of the lacey petermichl reguera estimates for these dyadic shifts which allow summing up the series in the obtained representation

a similarity based aspect graph approach to 3d object recognition this paper describes a view based method for recognizing 3d objects from 2d images we employ an aspect graph structure where the aspects are not based on the singularities of visual mapping but are instead formed using a notion of shape similarity between views specifically the viewing sphere is endowed with a metric of dis similarity for each pair of views and the problem of aspect generation is viewed as a segmentation of the viewing sphere into homogeneous regions the viewing sphere is sampled at regular 5 degree intervals and the similarity metric is used in an iterative procedure to combine views into aspects with a prototype representing each aspect this is done in a region growing regime which stands in contrast to the usual edge detection styles to computing the aspect graph the aspect growth is constrained such that two aspects of an object remain distinct under the given similarity metric once the database of 3d objects is organized as a set of aspects and prototypes for these aspects for each object unknown views of database objects are compared with the prototypes and the results are ordered by similarity we use two similarity metrics for shape one based on curve matching and the other based on matching shock graphs which for a database of 64 objects and unknown views of objects from the database give a recall rate of 90 3 74 2 59 7 and 95 2 69 0 57 5 respectively for the top three matchess cumulative recall rate based on the top three matches is 98 and 100 respectively the result of indexing unknown views of objects not in the database also produce intuitive matches we also develop a hierarchical indexing scheme to prune unlikely objects at an early stage to improve the efficiency of indexing resulting in savings of 35 at the top level and of 55 at the next level cumulatively

an operator valued tb theorem we establish conditions similar to the tb theorem of david journe and semmes which guarantee the boundedness of an integral transformation t with l x valued kernel on lxp rn where 1 p and x is a banach space with the unconditionality property of martingale differences umd

towards a unified field theory for classical electrodynamics in this paper we introduce a model which describes the relation of matter and the electromagnetic field from a unitarian standpoint in the spirit of ideas of born and infeld in this model based on a semilinear perturbation of maxwell equations the particles are finite energy solitary waves due to the presence of the nonlinearity in this respect the matter and the electromagnetic field have the same nature finite energy means that particles have finite mass and this makes electrodynamics consistent with the special relativity we analyze the invariants of the motion of the semilinear maxwell equations sme and their static solutions in the magnetostatic case i e when the electric field e 0 and the magnetic field h does not depend on time sme are reduced to the semilinear equation open image in new window where denotes the curloperator f is the gradient of a strictly convex smooth function f r3 r and a r3 r3 is the gauge potential related to the magnetic field h h a due to the presence of the curl operator 1 is a strongly degenerate elliptic equation moreover physical considerations impel f to be flat at zero f 0 0 and this fact leads us to study the problem in a functional setting related to the orlicz space lp lq the existence of a nontrivial finite energy solution of 1 is proved under suitable growth conditions on f the proof is carried out by using a suitable variational framework related to the hodge splitting of the vector field a

structure from motion using line correspondences a theory is presented for the computation of three dimensional motion and structure from dynamic imagery using only line correspondences the traditional approach of corresponding microfeatures interesting points highlights corners high curvature points etc is reviewed and its shortcomings are discussed then a theory is presented that describes a closed form solution to the motion and structure determination problem from line correspondences in three views the theory is compared with previous ones that are based on nonlinear equations and iterative methods

minimal representations of 3d models in terms of image parameters under calibrated and uncalibrated perspective indexing is a well known paradigm for object recognition in indexing each 3d model is represented as the set of values assumed by a given vector of image parameters in correspondence to all the possible images of the 3d model an open problem posed by jacobs 1992 concerned the minimum dimensionality of such sets under perspective this paper proves that under calibrated or uncalibrated perspective the minimum dimensionality of the set representing any 3d modeled point set is two two dimensional representations are found also for 3d curved objects

model based recognition of 3d objects from single images in this work we treat major problems of object recognition which have received relatively little attention lately among them are the loss of depth information in the projection from a 3d object to a single 2d image and the complexity of finding feature correspondences between images we use geometric invariants to reduce the complexity of these problems there are no geometric invariants of a projection from 3d to 2d however given certain modeling assumptions about the 3d object such invariants can be found the modeling assumptions can be either a particular model or a generic assumption about a class of models here we use such assumptions for single view recognition we find algebraic relations between the invariants of a 3d model and those of its 2d image under general projective projection these relations can be described geometrically as invariant models in a 3d invariant space illuminated by invariant light rays and projected onto an invariant version of the given image we apply the method to real images

linear and incremental acquisition of invariant shape models from image sequences we show how to automatically acquire euclidian shape representations of objects from noisy image sequences under weak perspective the proposed method is linear and incremental requiring no more than pseudoinverse a nonlinear but numerically sound preprocessing stage is added to improve the accuracy of the results even further experiments show that attention to noise and computational techniques improves the shape results substantially with respect to previous methods proposed for ideal images

relative affine structure canonical model for 3d from 2d geometry and applications we propose an affine framework for perspective views captured by a single extremely simple equation based on a viewer centered invariant we call relative affine structure via a number of corollaries of our main results we show that our framework unifies previous work including euclidean projective and affine in a natural and simple way and introduces new extremely simple algorithms for the tasks of reconstruction from multiple views recognition by alignment and certain image coding applications

ground state solutions for a periodic schrodinger equation with superlinear nonlinearities abstract in this paper we consider the following schrodinger equation u v x u g x u for x r n u x 0 as x where v is a periodic continuous real function with 0 in a gap of the spectrum a a v and the classical ambrosetti rabinowitz superlinear condition on g is replaced by a general super quadratic condition

noise resistant invariants of curves projective invariants are shape descriptors that are independent of the point of view from which the shape is seen and therefore are of major importance in object recognition they make it possible to match an image of an object to one stored in a database without the need for searching for the correct viewpoint an invariant representation of a general curve is obtained the calculation is local and does not suffer from the occlusion problem of global descriptors to make the method robust differentiation techniques that give much more reliable results than previous ones are developed these differentiation methods are useful in many other applications as well

superlinear schrodinger operators abstract we find nontrivial and ground state solutions for the nonlinear schrodinger equation under conditions weaker than those previously assumed

ground state solutions for some indefinite variational problems abstract we consider the nonlinear stationary schrodinger equation u v x u f x u in r n here f is a superlinear subcritical nonlinearity and we mainly study the case where both v and f are periodic in x and 0 belongs to a spectral gap of v inspired by previous work of li et al 2006 11 and pankov 2005 13 we develop an approach to find ground state solutions i e nontrivial solutions with least possible energy the approach is based on a direct and simple reduction of the indefinite variational problem to a definite one and gives rise to a new minimax characterization of the corresponding critical value our method works for merely continuous nonlinearities f which are allowed to have weaker asymptotic growth than usually assumed for odd f we obtain infinitely many geometrically distinct solutions the approach also yields new existence and multiplicity results for the dirichlet problem for the same type of equations in a bounded domain

geometric invariants and object recognition we discuss the role of the general invariance concept in object recognition and review the classical and recent literature on projective invariance invariants help solve major problems of object recognition for instance different images of the same object often differ from each other because of the different viewpoint from which they were obtained to match the two images common methods thus need to find the correct viewpoint a difficult problem that can involve search in a high dimensional space of all possible points of view and or finding point correspondences geometric invariants are shape descriptors computed from the geometry of the shape that remain unchanged under geometric transformations such as changing the viewpoint thus they can be matched without search deformations of objects are another important class of geometric changes for which invariance is useful

generalization to novel views universal class based andmodel based processing a major problem in object recognition is that a novel image of a given object can be different from all previously seen images images can vary considerably due to changes in viewing conditions such as viewing position and illumination in this paper we distinguish between three types of recognition schemes by the level at which generalization to novel images takes place universal class and model based the first is applicable equally to all objects the second to a class of objects and the third uses known properties of individual objects we derive theoretical limitations on each of the three generalization levels for the universal level previous results have shown that no invariance can be obtained here we show that this limitation holds even when the assumptions made on the objects and the recognition functions are relaxed we also extend the results to changes of illumination direction for the class level previous studies presented specific examples of classes of objects for which functions invariant to viewpoint exist here we distinguish between classes that admit such invariance and classes that do not we demonstrate that there is a tradeoff between the set of objects that can be discriminated by a given recognition function and the set of images from which the recognition function can recognize these objects furthermore we demonstrate that although functions that are invariant to illumination direction do not exist at the universal level when the objects are restricted to belong to a given class an invariant function to illumination direction can be defined a general conclusion of this study is that class based processing that has not been used extensively in the past is often advantageous for dealing with variations due to viewpoint and illuminant changes

the tb theorem on non homogeneous spaces 0 introduction main objects and results 3 0 1 main results 4 0 2 an application of t1 heorem electric intensity capacity 7 0 3 how to interpret calderon zygmund operator t 9 0 3 1 bilinear form is defined on lipschitz functions 10 0 3 2 bilinear form is defined for smooth functions 11 0 3 3 apriori boundedness 12 0 4 plan of the paper 15

recognizing articulated objects using a region based invariant transform in this paper we present a new method for representing and recognizing objects based on invariants of the object s regions we apply the method to articulated objects in low resolution noisy range images articulated objects such as a back hoe can have many degrees of freedom in addition to the unknown variables of viewpoint recognizing such an object in an image can involve a search in a high dimensional space that involves all these unknown variables here we use invariance to reduce this search space to a manageable size the low resolution of our range images makes it hard to use common features such as edges to find invariants we have thus developed a new featureless method that does not depend on feature detection instead of local features we deal with whole regions of the object we define a transform that converts the image into an invariant representation on a grid based on invariant descriptors of entire regions centered around the grid points we use these region based invariants for indexing and recognition while the focus here is on articulation the method can be easily applied to other problems such as the occlusion of fixed objects

3d object recognition using invariance abstract the systems and concepts described in this paper document the evolution of the geometric invariance approach to object recognition over the last five years invariance overcomes one of the fundamental difficulties in recognising objects from images that the appearance of an object depends on viewpoint this problem is entirely avoided if the geometric description is unaffected by the imaging transformation such invariant descriptions can be measured from images without any prior knowledge of the position orientation and calibration of the camera these invariant measurements can be used to index a library of object models for recognition and provide a principled basis for the other stages of the recognition process such as feature grouping and hypothesis verification object models can be acquired directly from images allowing efficient construction of model libraries without manual intervention a significant part of the paper is a summary of recent results on the construction of invariants for 3d objects from a single perspective view a proposed recognition architecture is described which enables the integration of multiple general object classes and provides a means for enforcing global scene consistency various criticisms of the invariant approach are articulated and addressed

a global tb theorem for compactness and boundedness of calderon zygmund operators abstract we prove a tb theorem that characterizes all calderon zygmund operators that extend compactly on l p r n 1 p the result whose proof does not require the property of accretivity can be used to prove compactness of the double layer potential operator on a wide class of domains the study also provides conditions for boundedness of singular integral operators by means of non accretive testing functions

ground state solutions for semilinear time harmonic maxwell equations this paper is concerned with the time harmonic semilinear maxwell equation u u f x u in with the boundary condition u 0 on where 3 is a simply connected smooth bounded domain with connected boundary and 3 is the exterior normal here denotes the curl operator in 3 and the boundary condition holds when is surrounded by a perfect conductor by using the generalized nehari manifold method due to szulkin and weth handbook of nonconvex analysis and applications international press somerville 2010 pp 597 632 and some new techniques existence of ground state solutions for above equation is established under some generic conditions on f

identification of a discrete planar symmetric shape from a single noisy view in this paper we propose a method for identifying a discrete planar symmetric shape from an arbitrary viewpoint our algorithm is based on a newly proposed notion of a view s skeleton we show that this concept yields projective invariants which facilitate the identification procedure it is furthermore shown that the proposed method may be extended to the case of noisy data to yield an optimal estimate of a shape in question substantiating examples are provided

classes of weights related to schrodinger operators abstract in this work we obtain boundedness on weighted lebesgue spaces on r d of the semi group maximal function riesz transforms fractional integrals and g function associated to the schrodinger operator v where v satisfies a reverse holder inequality with exponent greater than d 2 we consider new classes of weights that locally behave as muckenhoupt s weights and actually include them the notion of locality is defined by means of the critical radius function of the potential v given in shen 1995 8

dual computation of projective shape and camera positions from multiple images given multiple image data from a set of points in 3d there are two fundamental questions that can be addressed what is the structure of the set of points in 3d what are the positions of the cameras relative to the points in this paper we show that for projective views and with structure and position defined projectively these problems are dual because they can be solved using constraint equations where space points and camera positions occur in a reciprocal way more specifically by using canonical projective reference frames for all points in space and images the imaging of point sets in space by multiple cameras can be captured by constraint relations involving three different kinds of parameters only coordinates of 1 space points 2 camera positions 3 image points the duality implies that the problem of computing camera positions fromp points in q views can be solved with the same algorithm as the problem of directly reconstructing q 4 points in p 4 views this unifies different approaches to projective reconstruction methods based on external calibration and direct methods exploiting constraints that exist between shape and image invariants

local invariants for recognition geometric invariants are shape descriptors that remain unchanged under geometric transformations such as projection or changing the viewpoint a new method of obtaining local projective and affine invariants is developed and implemented for real images being local the invariants are much less sensitive to occlusion than global invariants the invariants computation is based on a canonical method this consists of defining a canonical coordinate system by the intrinsic properties of the shape independently of the given coordinate system since this canonical system is independent of the original one it is invariant and all quantities defined in it are invariant the method was applied without the use of a curve parameter this was achieved by fitting an implicit polynomial to an arbitrary curve in a vicinity of each curve point several configurations are treated a general curve without any correspondence and curves with known correspondences of one or two feature points or lines experimental results for different 2d objects in 3d space are presented

algebraic functions for recognition in the general case a trilinear relationship between three perspective views is shown to exist the trilinearity result is shown to be of much practical use in visual recognition by alignment yielding a direct reprojection method that cuts through the computations of camera transformation scene structure and epipolar geometry moreover the direct method is linear and sets a new lower theoretical bound on the minimal number of points that are required for a linear solution for the task of reprojection the proof of the central result may be of further interest as it demonstrates certain regularities across homographics of the plane and introduces new view invariants experiments on simulated and real image data were conducted including a comparative analysis with epipolar intersection and the linear combination methods with results indicating a greater degree of robustness in practice and a higher level of performance in reprojection tasks

recognition by linear combinations of models an approach to visual object recognition in which a 3d object is represented by the linear combination of 2d images of the object is proposed it is shown that for objects with sharp edges as well as with smooth bounding contours the set of possible images of a given object is embedded in a linear space spanned by a small number of views for objects with sharp edges the linear combination representation is exact for objects with smooth boundaries it is an approximation that often holds over a wide range of viewing angles rigid transformations with or without scaling can be distinguished from more general linear transformations of the object by testing certain constraints placed on the coefficients of the linear combinations three alternative methods of determining the transformation that matches a model to a given image are proposed

motion of points and lines in the uncalibrated case in the present paper we address the problem of computing structure and motion given a set point and or line correspondences in a monocular image sequence when the camera is not calibrated

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

matching 3 d line segments with applications to multiple object motion estimation a two stage algorithm for matching line segments using three dimensional data is presented in the first stage a tree search based on the orientation of the line segments is applied to establish potential matches the sign ambiguity of line segments is fixed by a simple congruency constraint in the second stage a hough clustering technique based on the position of line segments is applied to verify potential matches any paired line segments of a match that cannot be brought to overlap by the translation determined by the clustering are removed from the match unlike previous methods this algorithm combats noise more effectively and ensures the global consistency of a match while the original motivation for the algorithm is multiple object motion estimation from stereo image sequences the algorithm can also be applied to other domains such as object recognition and object model construction from multiple views