pattern matching with affine moment descriptors this paper proposes a method for matching images based on their higher order moments without knowing the point correspondences it is assumed that the disparity between the images can be explained by an affine transformation the second order statistics is used to transform the image points into canonical form which reduces the affine matching problem for determining an orthonormal transformation matrix between the two point sets next higher order complex moments are used to solve the remaining transformation these affine moment descriptors are expressed in terms of the central moments of the original data it is also shown that the resulting descriptors can be converted into affine moment invariants a general framework for deriving affine moment descriptors as well as moment invariants is described the experiments carried out with simulated data and real images indicate that the proposed method utilizing the second and third order statistics can provide good alignment results from noisy and spurious observations

least squares estimation of transformation parameters between two point patterns in many applications of computer vision the following problem is encountered two point patterns sets of points x sub i and x sub i i 1 2 n are given in m dimensional space and the similarity transformation parameters rotation translation and scaling that give the least mean squared error between these point patterns are needed recently k s arun et al 1987 and b k p horn et al 1987 presented a solution of this problem their solution however sometimes fails to give a correct rotation matrix and gives a reflection instead when the data is severely corrupted the proposed theorem is a strict solution of the problem and it always gives the correct transformation parameters even when the data is corrupted

the revised fundamental theorem of moment invariants a revised fundamental theorem of moment invariants for pattern recognition which corrects the fundamental theorem proposed by m k hu 1962 is presented the correction affects neither similitude scale nor rotation invariants derived using the original theorem but it does affect features invariant to general linear transformations four of the latter invariants were presented originally by hu these are revised to take the correction to the fundamental theorem into account furthermore these four invariants are combined to yield three new invariants which are additionally invariant to changes in the illumination of an image

error bounds for the large time step glimm scheme applied to scalar conservation laws in this paper we derive an l 1 error bound for the large time step i e large courant number version of the glimm scheme when used for the approximation of solutions to a genuinely nonlinear i e convex scalar conservation law for a generic class of piecewise constant data we show that the error is bounded by o delta x 1 2 vert log delta x vert for courant numbers up to 1 the order of the error is the same as that given by hoff and smoller 5 in 1985 for the glimm scheme under the restriction of courant numbers up to 1 2

on the accuracy of fractional step methods for conservation laws in two dimensions in this paper it is shown that on the assumption of the initial data belonging to bv bf r 2 cap l infty bf r 2 the convergence rates in l 1 bf r 2 for both godunov s spatial splitting method and strang s splitting method for scalar conservation laws in two dimensional spaces are of o delta t 1 2 where delta t is the splitting time step the author illustrates by numerical experiments that for some two dimensional riemann problems the rate is of the order o delta t it is also shown by counterexamples that if the initial data belongs to l infty bf r 2 no error estimate of the type o delta t beta for any beta 0 is valid

error bounds for the methods of glimm godunov and leveque the expected error in l 1 r at time t for glimm s scheme when applied to a scalar conservation law is bounded by left h frac 2 sqrt 3 left frac h delta t right 1 2 right left u 0 right bv bf r where h is the mesh size and delta t is the time step we show that the error in godunov s scheme is bounded by the same expression and use this result to analyze a variant of a large time step numerical method of leveque that may be viewed as a combination of godunov s scheme and a method of dafermos

comparing images using the hausdorff distance the hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another efficient algorithms for computing the hausdorff distance between all possible relative positions of a binary image and a model are presented the focus is primarily on the case in which the model is only allowed to translate with respect to the image the techniques are extended to rigid motion the hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived the method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods it is shown that the method extends naturally to the problem of comparing a portion of a model against an image

beam division multiple access transmission for massive mimo communications we study multicarrier multiuser multiple input multiple output mu mimo systems in which the base station employs an asymptotically large number of antennas we analyze a fully correlated channel matrix and provide a beam domain channel model where the channel gains are independent of sub carriers for this model we first derive a closed form upper bound on the achievable ergodic sum rate based on which we develop asymptotically necessary and sufficient conditions for optimal downlink transmission that require only statistical channel state information at the transmitter furthermore we propose a beam division multiple access bdma transmission scheme that simultaneously serves multiple users via different beams by selecting users within non overlapping beams the mu mimo channels can be equivalently decomposed into multiple single user mimo channels this scheme significantly reduces the overhead of channel estimation as well as the processing complexity at transceivers for bdma transmission we work out an optimal pilot design criterion to minimize the mean square error mse and provide optimal pilot sequences by utilizing the zadoff chu sequences simulations demonstrate the near optimal performance of bdma transmission and the advantages of the proposed pilot sequences

stability theorem and truncation error analysis for the glimm scheme and for a front tracking method for flows with strong discontinuities typical nonlinear wave interaction problems involve strong waves moving through a background of weak disturbance previous existence theorems and error analysis for computations are usually restricted to more idealized situations such as small data or single equations we consider here the problem of a single strong discontinuity interacting with a weak background for general hyperbolic systems of conservation laws we obtain the stability consistency theorems and upper bounds of the truncation errors for the glimm scheme and for a front tracking method the major error in the glimm scheme is the error generated by the strong discontinuity this error is reduced when a front tracking method is applied to follow the location of the strong discontinuity this demonstrates an advantage of front tracking methods in one space dimension

cross weighted moments and affine invariants for image registration and matching a framework for deriving a class of new global affine invariants for both object matching and positioning based on a novel concept of cross weighted moments with fractional weights is presented the fractional weight factor allows for a more flexible range to balance between the capability to discriminate between objects that differ only in small shape details and the sensitivity of small shape details to the presence of the noise moreover it makes it possible to arrive at low order zero order affine invariants that are more robust than those derived from higher order regular moments the affine transformation parameters are recovered from the zero and the first order cross weighted moments without requiring any feature point correspondence information the equations used to find the affine transformation parameters are linear algebraic the sensitivity of the cross weighted moment invariants to noise missing data and perspective effects is shown on real images

affine invariant recognition of gray scale characters using global affine transformation correlation describes a technique of gray scale character recognition that offers both noise tolerance and affine invariance the key ideas are twofold first is the use of normalized cross correlation as a matching measure to realize noise tolerance second is the application of global affine transformation gat to the input image so as to achieve affine invariant correlation with the target image in particular optimal gat is efficiently determined by the successive iteration method using topographic features of gray scale images as matching constraints we demonstrate the high matching ability of the proposed gat correlation method using gray scale images of numerals subjected to random gaussian noise and a wide range of affine transformation moreover extensive recognition experiments show that the achieved recognition rate of 94 3 percent against rotation within 30 degrees scale change within 30 percent and translation within 20 percent of the character width along with random gaussian noise is sufficiently high compared to the 42 8 percent offered by simple correlation

error bounds for a deterministic version of the glimm scheme consider the hyperbolic system of conservation laws u t f u x 0 let u be the unique viscosity solution with initial condition u 0 x bar u x and let ue be an approximate solution constructed by the glimm scheme corresponding to the mesh sizes delta x delta t o delta x with a suitable choice of the sampling sequence we prove the estimate big u ve t cdot u t cdot big bf l 1 strut l 1 o 1 cdot sqrt delta x big ln delta x big

on the sublinear behavior of massive multi user mimo sum rates for deterministic channel models this paper studies the behavior of the sum rate of outdoor multi user multiple input multiple output systems where a uniform linear array is utilized at the base station bs as the number of bs antennas and the number of users increase two schemes are studied for the downlink the zero forcing and the maximum ratio transmission mrt to begin with the channel matrix is described deterministically using direct scattering theory its matrix elements are the fourier coefficients of functions that have a physical significance being connected to the geometry of the environment for the case when the energy is not arriving at the bs from every spatial direction we prove for the zf scheme that the achievable sum rate behavior is sublinear in the number of antennas at the bs for the mrt scheme we prove that there is a link between the sum rate and the distribution of the users in the city to numerically evaluate the sum rate for a given city schematically described by its streets and its buildings we introduce a model for the fourier coefficients of the aforementioned functions which mixes geometrical and statistical ingredients we randomly distribute high buildings that will act as strong scatterers and look at the influence of their number on the sum rate with the zf scheme we perform the calculations for the case where the number of bs antennas m t is equal to the number of users m r and for the case where m t is larger than m r we observe that the sum rate first increases linearly with the number of bs antennas and becomes sublinear after m t reaches a certain value the threshold depends on the number of high buildings with the mrt scheme the calculations confirm the theoretical predictions and the sum rate is greater if the users are spread over all of the city

influence of environment richness on the increase of mimo capacity with number of antennas we study the capacity of mimo systems with uniform linear arrays in complex media as the number of antennas increases the distance between adjacent antennas is kept constant the transfer matrix describing the channel is expressed in terms of the antennas and the physical characteristics of the environment using direct scattering theory we prove that the capacity increases logarithmically when the number of antennas in the system belongs to a large interval of intermediate values we then take the case where the number of antennas is large and we study the effects on the capacity of adding a new scatterer using a city model with buildings of different sizes randomly distributed in space we show numerically that initially the capacity increases at a nearly linear rate as the number of antennas increases after a certain threshold the capacity growth becomes logarithmic we show that the number of antennas where this transition occurs increases as the number of buildings increases

numerical approximation of the euler maxwell model in the quasineutral limit we derive and analyze an asymptotic preserving scheme for the euler maxwell system in the quasi neutral limit we prove that the linear stability condition on the time step is independent of the scaled debye length l when l 0 numerical validation performed on riemann initial data and for a model plasma opening switch device show that the ap scheme is convergent to the euler maxwell solution when dx l 0 where dx is the spatial discretization but when l dx 0 the ap scheme is consistent with the quasi neutral euler maxwell system the scheme is also perfectly consistent with the gauss equation the possibility of using large time and space steps leads to several orders of magnitude reductions in computer time and storage

higher dimensional affine registration and vision applications affine registration has a long and venerable history in computer vision literature and in particular extensive work has been done for affine registration in r2 and r3 this paper studies affine registration in rm with m typically ranging from 4 to 12 to justify breaking of this dimension barrier the first part of the paper describes three novel matching problems that can be formulated and solved as affine point set registration problems in dimensions greater than three stereo correspondence under motion image set matching and covariant point set matching problems that are not only interesting in their own right but also have potential for important vision applications unfortunately most of the existing affine registration algorithms do not generalize easily to higher dimensions due to their inefficiency therefore the second part of this paper develops a novel algorithm for estimating the affine transform between two point sets in rm specifically the algorithm follows the common approach of iteratively solving the correspondences and transform the initial correspondences are determined using the novel notion of local spectral features features constructed from local distance matrices unlike many correspondence based methods the proposed algorithm is capable of registering point sets of different size and the use of local features provides some degree of robustness against noise and outliers the proposed algorithm is validated on a variety of synthetic point sets in different dimensions with varying degrees of deformation and noise and the paper also shows experimentally that several instances of the aforementioned three matching problems can indeed be solved satisfactorily using the proposed affine registration algorithm

an error estimate for finite volume methods for multidimensional conservation laws in this paper an l ll error estimate for a class of finite volume methods for the approximation of scalar multidimensional conservation laws is obtained these methods can be formally high order accurate and are defined on general triangulations the error is proven to be of order ft 4 where h represents the size of the mesh via an extension of kuznetsov approximation theory for which no estimate of the total variation and of the modulus of con tinuity in time are needed the result is new even for the finite volume method constructed from monotone numerical flux functions

reliable and efficient pattern matching using an affine invariant metric we present a new pattern similarity measure that behaves well under affine transformations our similarity measure is useful for pattern matching since it is defined on patterns with multiple components satisfies the metric properties is invariant under affine transformations and is robust with respect to perturbation and occlusion we give an algorithm based on hierarchical subdivision of transformation space which minimises our measure under the group of affine transformations given two patterns in addition we present results obtained using an implementation of this algorithm

fast algorithm for point pattern matching invariant to translations rotations and scale changes abstract based on 2 d cluster approach a fast algorithm for point pattern matching is proposed to effectively solve the problems of optimal matches between two point pattern under geometrical transformation and correctly identify the missing or spurious points of patterns theorems and algorithms are developed to determine the matching pairs support of each point pair and its transformation parameters scaling s and rotation on a two parameter space s experiments are conducted both on real and synthetic data the experimental results show that the proposed matching algorithm can handle translation rotation and scaling differences under noisy or distorted condition the computational time is just about 0 5 s for 50 to 50 point matching on sun 4 workstation

efficient algorithms for robust feature matching abstract one of the basic building blocks in any point based registration scheme involves matching feature points that are extracted from a sensed image to their counterparts in a reference image this leads to the fundamental problem of point matching given two sets of points find the affine transformation that transforms one point set so that its distance from the other point set is minimized because of measurement errors and the presence of outlying data points it is important that the distance measure between the two point sets be robust to these effects we measure distances using the partial hausdorff distance point matching can be a computationally intensive task and a number of theoretical and applied approaches have been proposed for solving this problem in this paper we present two algorithmic approaches to the point matching problem in an attempt to reduce its computational complexity while still providing a guarantee of the quality of the final match our first method is an approximation algorithm which is loosely based on a branch and bound approach due to huttenlocher and rucklidge technical report 1321 dept of computer science cornell university ithaca 1992 proc ieee conf on computer vision and pattern recognition new york 1993 pp 705 706 we show that by varying the approximation error bounds it is possible to achieve a tradeoff between the quality of the match and the running time of the algorithm our second method involves a monte carlo method for accelerating the search process used in the first algorithm this algorithm operates within the framework of a branch and bound procedure but employs point to point alignments to accelerate the search we show that this combination retains many of the strengths of branch and bound search but provides significantly faster search times by exploiting alignments with high probability this method succeeds in finding an approximately optimal match we demonstrate the algorithms performances on both synthetically generated data points and actual satellite images

error bounds for glimm difference approximations for scalar conservation laws on deduit des bornes d erreur pour l approximation aux differences de glimm pour la solution d une loi de conservation scalaire non lineaire

iterative point matching for registration of free form curves and surfaces a heuristic method has been developed for registering two sets of 3 d curves obtained by using an edge based stereo system or two dense 3 d maps obtained by using a correlation based stereo system geometric matching in general is a difficult unsolved problem in computer vision fortunately in many practical applications some a priori knowledge exists which considerably simplifies the problem in visual navigation for example the motion between successive positions is usually approximately known from this initial estimate our algorithm computes observer motion with very good precision which is required for environment modeling e g building a digital elevation map objects are represented by a set of 3 d points which are considered as the samples of a surface no constraint is imposed on the form of the objects the proposed algorithm is based on iteratively matching points in one set to the closest points in the other a statistical method based on the distance distribution is used to deal with outliers occlusion appearance and disappearance which allows us to do subset subset matching a least squares technique is used to estimate 3 d motion from the point correspondences which reduces the average distance between points in the two sets both synthetic and real data have been used to test the algorithm and the results show that it is efficient and robust and yields an accurate motion estimate

determining pose of 3d objects with curved surfaces a method is presented for computing the pose of rigid 3d objects with arbitrary curved surfaces given an input image and a candidate object model and aspect the method will verify whether or not the object is present and if so report pose parameters the curvature method of bash and ullman is used to model points on the object rim while stereo matching is used for internal edge points the model allows an object edge map to be predicted from pose parameters pose is computed via an iterative search for the best pose parameters heuristics are used so that matching can succeed in the presence of occlusion and artifact and without resetting to use of corresponding salient feature points bench tests and simulations show that the method almost always converges to ground truth pose parameters for a variety of objects and for a broad set of starting parameters in the same aspect

an affine invariant curve matching method for photo identification of marine mammals individual identification of marine mammals is of interest to marine biologists this paper aims at the recognition of the edges associated with marine mammals whose pictures are taken under affine transformations the introduced affine curve matching method uses the area of mismatch between a query and a database curve this area is obtained by optimally aligning the curves based on the minimum affine distance involving their distinguishing points the method is applied to databases of sea lions gray whales and dolphins and its performance is compared with two other affine curve matching methods the results show that the introduced curve matching approach outperforms the other approaches and thus further reduces the search time for identifying an individual the developed method is of general purpose as it can be used for other affine curve matching applications

convex hull properties and algorithms abstract convex hull ch is widely used in computer graphic image processing cad cam and pattern recognition we investigate ch properties and derive new properties 1 ch vertices coordinates monotonically increase or decrease 2 the edge slopes monotonically decrease using these properties we proposed two algorithms i e ch algorithm for planar point set and ch algorithm for two available chs the main ideas of the proposed algorithms are as follows a planar point set is divided into several subsets by the extreme points and vertices in these subsets are then separately calculated during the computation the ch properties are used to eliminate concave points this can reduce the computational cost and then improves the speed our first algorithm can extract ch with o n log n time which is the lower bound of planar ch extraction and the second algorithm can obtain ch with o m n time at the worst case

recognizing solid objects by alignment with an image in this paper we consider the problem of recognizing solid objects from a single two dimensional image of a three dimensional scene we develop a new method for computing a transformation from a three dimensional model coordinate frame to the two dimensional image coordinate frame using three pairs of model and image points we show that this transformation always exists for three noncollinear points and is unique up to a reflective ambiguity the solution method is closed form and only involves second order equations we have implemented a recognition system that uses this transformation method to determine possible alignments of a model with an image each of these hypothesized matches is verified by comparing the entire edge contours of the aligned object with the image edges using the entire edge contours for verification rather than a few local feature points reduces the chance of finding false matches the system has been tested on partly occluded objects in highly cluttered scenes

image registration and object recognition using affine invariants and convex hulls this paper is concerned with the problem of feature point registration and scene recognition from images under weak perspective transformations which are well approximated by affine transformations and under possible occlusion and or appearance of new objects it presents a set of local absolute affine invariants derived from the convex hull of scattered feature points e g fiducial or marking points corner points inflection points etc extracted from the image the affine invariants are constructed from the areas of the triangles formed by connecting three vertices among a set of four consecutive vertices quadruplets of the convex hull and hence do make direct use of the area invariance property associated with the affine transformation because they are locally constructed they are very well suited to handle the occlusion and or appearance of new objects these invariants are used to establish the correspondences between the convex hull vertices of a test image with a reference image in order to undo the affine transformation between them a point matching approach for recognition follows this the time complexity for registering l feature points on the test image with n feature points of the reference image is of order o n spl times l the method has been tested on real indoor and outdoor images and performs well

efficiently locating objects using the hausdorff distance the hausdorff distance is a measure defined between two point sets here representing a model and an image the hausdorff distance is reliable even when the image contains multiple objects noise spurious features and occlusions in the past it has been used to search images for instances of a model that has been translated or translated and scaled by finding transformations that bring a large number of model features close to image features and vice versa in this paper we apply it to the task of locating an affine transformation of a model in an image this corresponds to determining the pose of a planar object that has undergone weak perspective projection we develop a rasterised approach to the search and a number of techniques that allow us to locate quickly all transformations of the model that satisfy two quality criteria we can also efficiently locate only the best transformation we discuss an implementation of this approach and present some examples of its use

affine invariant comparison of point sets using convex hulls and hausdorff distances many object recognition or identification applications involve comparing features associated with point sets this paper presents an affine invariant point set matching technique which measures the similarity between two point sets by embedding them into an affine invariant feature space the developed technique assumes no a priori knowledge of reference points as is the case in many identification problems reference points of a point set are obtained based on its convex hull an enhanced version of the modified hausdorff distance is also introduced and used in the feature space for comparing two point sets it should be noted that the technique does not attempt to obtain correspondences between the point sets the introduced technique is applied to two real databases and its performance is found favorable as compared to three other affine invariant matching techniques

sublinear capacity scaling laws for sparse mimo channels recent attention on performance analysis of single user multiple input multiple output mimo systems has been on understanding the impact of the spatial correlation model on ergodic capacity in most of these works it is assumed that the statistical degrees of freedom dof in the channel can be captured by decomposing it along a suitable eigenbasis and that the transmitter has perfect knowledge of the statistical dof with an increased interest in large antenna systems in state of the art technologies these implicit channel modeling assumptions in the literature have to be revisited in particular multiantenna measurements have showed that large antenna systems are sparse where only a few dof are dominant enough to contribute towards capacity thus in this work it is assumed that the transmitter can only afford to learn the dominant statistical dof in the channel the focus is on understanding ergodic capacity scaling laws in sparse channels unlike classical results where linear capacity scaling is implicit sparsity of mimo channels coupled with a knowledge of only the dominant dof is shown to result in a new paradigm of sublinear capacity scaling that is consistent with experimental results and physical arguments it is also shown that uniform power signaling over all the antenna dimensions is wasteful and could result in a significant penalty over optimally adapting the antenna spacings in response to the sparsity level of the channel and transmit snr

application of affine invariant fourier descriptors to recognition of 3 d objects the method of fourier descriptors is extended to produce a set of normalized coefficients which are invariant under any affine transformation translation rotation scaling and shearing the method is based on a parameterized boundary description which is transformed to the fourier domain and normalized there to eliminate dependencies on the affine transformation and on the starting point invariance to affine transforms allows considerable robustness when applied to images of objects which rotate in all three dimensions as is demonstrated by processing silhouettes of aircraft maneuvering in three space

efficient registration of stereo images by matching graph descriptions of edge segments we present a new approach to the stereo matching problem images are individually described by aneighborhood graph of line segments coming from a polygonal approximation of the contours the matching process is defined as the exploration of the largest components of adisparity graph built from the descriptions of the two images and is performed by an efficient prediction and propagation technique this approach was tested on a variety of man made environments and it appears to be fast and robust enough for mobile robot navigation and three dimensional part positioning applications