a review of geometric transformations for nonrigid body registration this paper provides a comprehensive and quantitative review of spatial transformations models for nonrigid image registration it explains the theoretical foundation of the models and classifies them according to this basis this results in two categories physically based models described by partial differential equations of continuum mechanics e g linear elasticity and fluid flow and basis function expansions derived from interpolation and approximation theory e g radial basis functions b splines and wavelets recent work on constraining the transformation so that it preserves the topology or is diffeomorphic is also described the final section reviews some recent evaluation studies the paper concludes by explaining under what conditions a particular transformation model is appropriate

application of the fisher rao metric to ellipse detection the parameter space for the ellipses in a two dimensional image is a five dimensional manifold where each point of the manifold corresponds to an ellipse in the image the parameter space becomes a riemannian manifold under a fisher rao metric which is derived from a gaussian model for the blurring of ellipses in the image two points in the parameter space are close together under the fisher rao metric if the corresponding ellipses are close together in the image the fisher rao metric is accurately approximated by a simpler metric under the assumption that the blurring is small compared with the sizes of the ellipses under consideration it is shown that the parameter space for the ellipses in the image has a finite volume under the approximation to the fisher rao metric as a consequence the parameter space can be replaced for the purpose of ellipse detection by a finite set of points sampled from it an efficient algorithm for sampling the parameter space is described the algorithm uses the fact that the approximating metric is flat and therefore locally euclidean on each three dimensional family of ellipses with a fixed orientation and a fixed eccentricity once the sample points have been obtained ellipses are detected in a given image by checking each sample point in turn to see if the corresponding ellipse is supported by the nearby image pixel values the resulting algorithm for ellipse detection is implemented a multiresolution version of the algorithm is also implemented the experimental results suggest that ellipses can be reliably detected in a given low resolution image and that the number of false detections can be reduced using the multiresolution algorithm

piecewise linear mapping functions for image registration abstract a new approach to determination of mapping functions for registration of digital images is presented given the coordinates of corresponding control points in two images of the same scene first the images are divided into triangular regions by triangulating the control points then a linear mapping function is obtained by registering each pair of corresponding triangular regions in the images the overall mapping function is then obtained by piecing together the linear mapping functions

sharp constants for moser trudinger inequalities on spheres in complex space ℂn the main results of this paper concern sharp constants for the moser trudinger inequalities on spheres in complex space c n we derive moser trudinger inequalities for smooth functions and holomorphic functions with different sharp constants see theorem 1 1 the sharp moser trudinger inequalities under consideration involve the complex tangential gradients for the functions and thus we have shown here such inequalities in the cr setting though there is a close connection in spirit between inequalities proven here on complex spheres and those on the heisenberg group for functions with compact support in any finite domain proven earlier by the same authors 17 derivation of the sharp constants for moser trudinger inequalities on complex spheres are more complicated and difficult to obtain than on the heisenberg group variants of moser onofri type inequalities are also given on complex spheres as applications of our sharp inequalities see theorems 1 2 and 1 3 one of the key ingredients in deriving the main theorems is a sharp representation formula for functions on the complex spheres in terms of complex tangential gradients see theorem 1 4 c 2004 wiley periodicals inc

principal warps thin plate splines and the decomposition of deformations the decomposition of deformations by principal warps is demonstrated the method is extended to deal with curving edges between landmarks this formulation is related to other applications of splines current in computer vision how they might aid in the extraction of features for analysis comparison and diagnosis of biological and medical images in indicated

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

maximum likelihood image matching image matching applications such as tracking and stereo commonly use the sum of squared difference ssd measure to determine the best match however this measure is sensitive to outliers and is not robust to template variations alternative measures have also been proposed that are more robust to these issues we improve upon these using a probabilistic formulation for image matching in terms of maximum likelihood estimation that can be used for both edge template matching and gray level image matching this formulation generalizes previous edge matching methods based on distance transforms we apply the techniques to stereo matching and feature tracking uncertainty estimation techniques allow feature selection to be performed by choosing features that minimize the localization uncertainty

digital analysis of rotated images the problem of estimating the relative rotations of two images taken from the same scene is considered and a numerical method for computing such rotations is presented the main features of the proposed method consist of the possibility of fast in place computations with no preliminary interpolation of the data and a considerable precision for moderate rotation angles the final estimate is performed with a least square criterion but in the present case even such computations can be substantially simplified a detailed analysis shows that for practical applications the influence of discretization errors does not affect in a relevant way the precision of the results that is also confirmed by numerical experiments

linear time euclidean distance transform algorithms two linear time and hence asymptotically optimal algorithms for computing the euclidean distance transform of a two dimensional binary image are presented the algorithms are based on the construction and regular sampling of the voronoi diagram whose sites consist of the unit feature pixels in the image the first algorithm which is of primarily theoretical interest constructs the complete voronoi diagram the second more practical algorithm constructs the voronoi diagram where it intersects the horizontal lines passing through the image pixel centers extensions to higher dimensional images and to other distance functions are also discussed

vocal tract normalization in articulatory space using thin plate spline method inter subject normalization is a key issue of group analysis of articulatory data to obtain a general description of kinematic properties of human speech production multisubject articulatory study however is scarce due to the difficulty of normalization in articulatory domain in order to reduce intersubject variations among articulatory space a simple normalization procedure was proposed using a thin plate spline method the purpose of this normalization processing is to reduce the morphological differences of vocal tracts such as shape and size among different subjects nonlinear factors of the reduction are considered in this normalization procedure the electromagnetic articulographic emma data were used in our experiments which were obtained from the ntt emma database for three subjects data included a physiological articulatory model has been used to serve as the template the landmarks were defined consistently in vocal tract space over the template and all subjects the evaluations showed that the variances over subjects have been reduced 2 1 mm for consonants and 2 3 mm for vowels averaged over all tongue pellets

sharp sobolev inequalities on the sphere and the moser trudinger inequality where de denotes normalized surface measure v is the conformal gradient and q 2n n 2 a modern folklore theorem is that by taking the infinitedimensional limit of this inequality one obtains the gross logarithmic sobolev inequality for gaussian measure which determines nelson s hypercontractive estimates for the hermite semigroup see 8 one observes using conformal invariance that the above inequality is equivalent to the sharp sobolev inequality on rn for which boundedness and extremal functions can be easily calculated using dilation invariance and geometric symmetrization the roots here go back to hardy and littlewood the advantage of casting the problem on the sphere is that the role of the constants is evident and one is led immediately to the conjecture that this inequality should hold whenever possible for example 2 q 0o if n 2 this is in fact true and will be demonstrated in section 2 a clear question at this point is what is the situation in dimension 2 two important arguments 25 26 27 dealt with this issue both motivated by geometric variational problems because q goes to infinity for dimension 2 the appropriate function space is the exponential class responding in part

on the reconstruction aspects of moment descriptors the problem of reconstruction of an image from discrete and noisy data by the method of moments is examined the set of orthogonal moments based on legendre polynomials is employed a general class of signal dependent noise models is taken into account an asymptotic expansion for the global reconstruction error is established this reveals mutual relationships between a number of moments the image smoothness sampling rate and noise model characteristics the problem of an automatic data driven section of an optimal number of moments is studied this is accomplished with the help of cross validation techniques

symmetric phase only matched filtering of fourier mellin transforms for image registration and recognition presents a new method to match a 2d image to a translated rotated and scaled reference image the approach consists of two steps the calculation of a fourier mellin invariant fmi descriptor for each image to be matched and the matching of the fmi descriptors the fmi descriptor is translation invariant and represents rotation and scaling as translations in parameter space the matching of the fmi descriptors is achieved using symmetric phase only matched filtering spomf the performance of the fmi spomf algorithm is the same or similar to that of phase only matched filtering when dealing with image translations the significant advantage of the new technique is its capability to match rotated and scaled images accurately and efficiently the innovation is the application of spomf to the fmi descriptors which guarantees high discriminating power and excellent robustness in the presence of noise this paper describes the principle of the new method and its discrete implementation for either image detection problems or image registration problems practical results are presented for various applications in medical imaging remote sensing fingerprint recognition and multiobject identification

review of shape representation and description techniques more and more images have been generated in digital form around the world there is a growing interest in 1nding images in large collections or from remote databases in order to 1nd an image the image has to be described or represented by certain features shape is an important visual feature of an image searching for images using shape features has attracted much attention there are many shape representation anddescription techniques in the literature in this paper we classify and review these important techniques we examine implementation procedures for each technique and discuss its advantages and disadvantages some recent research results are also included and discussed in this paper finally we identify some promising techniques for image retrieval according to standard principles

fourier analysis and optimal hardy adams inequalities on hyperbolic spaces of any even dimension abstract recently the second and third authors established the sharp hardy adams inequalities of second order derivatives with the best constants on the hyperbolic space b 4 of dimension four 40 adv math 2017 a key method used in dimension four in 40 is that the following hardy operator when n 4 and k 2 b n k u 2 d x i 1 k 2 i 1 2 b n u 2 1 x 2 2 k d x can be decomposed exactly as the product of fractional laplacians however such a decomposition in dimension four is no longer possible in the case n 4 and 2 k n 2 and the situation here is thus considerably more difficult and complicated therefore it remains open as whether a sharp hardy adams inequality still holds on higher dimensional hyperbolic space b n for n 4 the main purpose of this paper is to use a substantially new method of estimating the hardy operator to establish the sharp hardy adams inequalities on hyperbolic spaces b n for all even dimension n and n 4 as applications of such inequalities we will improve substantially the known adams inequalities on hyperbolic space b n in the literature and also strengthen the classical adams inequality and the hardy inequality on euclidean balls in any even dimension the later inequality can be viewed as the borderline case of the sharp hardy sobolev maz ya inequalities for higher order derivatives in high dimensions obtained recently by the second and third authors 41

sharp moser trudinger inequality on the heisenberg group at the critical case and applications let h cn r be the n dimensional heisenberg group q 2n 2 be the homogeneous dimension of h q qq 1 and z 4 t2 14 be the homogeneous norm of z t h then we prove the following sharp moser trudinger inequality on h theorem 1 6 there exists a positive constant q q 2 n 12 q 12 q2 1 n 1 q 1 such that for any pair satisfying 0 q 0 q 1 q there holds sup u 1 1 h1 exp u q q 1 k 0q 2 kk u kq q 1 c q the constant q 1 q is best possible in the sense that the supremum is infinite if q 1 q here is any positive number and u 1 h hu q h u q 1 q our result extends the sharp moser trudinger inequality by cohn and lu 2001 19 on domains of finite measure on h and sharpens the recent result of cohn et al 2012 18 where such an inequality was studied for the subcritical case q 1 q we carry out a completely different and much simpler argument than that in cohn et al 2012 18 to conclude the critical case our method avoids using the rearrangement argument which is not available in an optimal way on the heisenberg group and can be used in more general settings such as riemanian manifolds appropriate metric spaces etc as applications we establish the existence and multiplicity of nontrivial nonnegative solutions to certain nonuniformly subelliptic equations of q laplacian type on the heisenberg group theorems 1 8 1 9 1 10 and 1 11 divh hu q 2 hu v u q 2u f u eh with nonlinear terms f of maximal exponential growth exp u qq 1 as u in particular when e 0 the existence of a nontrivial solution is also given

high accuracy sub pixel motion estimation from noisy images in fourier domain in this paper we propose a new method for estimating sub pixel motion via exploiting the principle of phase correlation in the fourier domain the method is based on linear weighting of the height of the main peak on the one hand and the difference between its two neighboring side peaks on the other using both synthetic and real data we show that the proposed method outperforms many established approaches and achieves improved accuracy even in the presence of noisy samples

extremal functions for moser s inequality let q be a bounded smooth domain in ri and u x a c1 function with compact support in q moser s inequality states that there is a constant co depending only on the dimension n such that 1 wn1 n j ee n u dx co where iqi is the lebesgue measure of q and wn 1 the surface area of the unit ball in rn we prove in this paper that there are extremal functions for this inequality in other words we show that the sup j nw u dx u e wj 11vuh1n 1 is attained earlier results include carleson chang 1986 q is a ball in any dimension and flucher 1992 q is any domain in 2 dimensions

artificial neural network method for solution of boundary value problems with exact satisfaction of arbitrary boundary conditions a method for solving boundary value problems bvps is introduced using artificial neural networks anns for irregular domain boundaries with mixed dirichlet neumann boundary conditions bcs the approximate ann solution automatically satisfies bcs at all stages of training including before training commences this method is simpler than other ann methods for solving bvps due to its unconstrained nature and because automatic satisfaction of dirichlet bcs provides a good starting approximate solution for significant portions of the domain automatic satisfaction of bcs is accomplished by the introduction of an innovative length factor several examples of bvp solution are presented for both linear and nonlinear differential equations in two and three dimensions error norms in the approximate solution on the order of 10 4 to 10 5 are reported for all example problems

nonlinear schrodinger equations and sharp interpolation estimates a sharp sufficient condition for global existence is obtained for the nonlinear schrodinger equation begin array 20 c nls 2i phi t delta phi left phi right 2 sigma phi 0 x in mathbb r n t in mathbb r end array in the case 2 n this condition is in terms of an exact stationary solution nonlinear ground state of nls it is derived by solving a variational problem to obtain the best constant for classical interpolation estimates of nirenberg and gagliardo

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

two dimensional object alignment based on the robust oriented hausdorff similarity measure this paper proposes an oriented hausdorff similarity ohs measure for robust object alignment the ohs measure is introduced by replacing the distance concept of conventional hausdoff distance hd algorithms by the similarity concept of the hough transform ht the proposed algorithm can be considered as the modified directed ht using the distance transform dt the orientation information at each pixel is also used to remove incorrect correspondences

image analysis by tchebichef moments this paper introduces a new set of orthogonal moment functions based on the discrete tchebichef polynomials the tchebichef moments can be effectively used as pattern features in the analysis of two dimensional images the implementation of the moments proposed in this paper does not involve any numerical approximation since the basis set is orthogonal in the discrete domain of the image coordinate space this property makes tchebichef moments superior to the conventional orthogonal moments such as legendre moments and zernike moments in terms of preserving the analytical properties needed to ensure information redundancy in a moment set the paper also details the various computational aspects of tchebichef moments and demonstrates their feature representation capability using the method of image reconstruction

adams inequality with the exact growth condition in ℝ4 adams inequality is an extension of the trudinger moser inequality to the case when the sobolev space considered has more than one derivative the goal of this paper is to give the optimal growth rate of the exponential type function in adams inequality when the problem is considered in the whole space 4 2014 wiley periodicals inc

hammer hierarchical attribute matching mechanism for elastic registration a new approach is presented for elastic registration of medical images and is applied to magnetic resonance images of the brain experimental results demonstrate very high accuracy in superposition of images from different subjects there are two major novelties in the proposed algorithm first it uses an attribute vector i e a set of geometric moment invariants gmis that are defined on each voxel in an image and are calculated from the tissue maps to reflect the underlying anatomy at different scales the attribute vector if rich enough can distinguish between different parts of an image which helps establish anatomical correspondences in the deformation procedure it also helps reduce local minima by reducing ambiguity in potential matches this is a fundamental deviation of our method referred to as the hierarchical attribute matching mechanism for elastic registration hammer from other volumetric deformation methods which are typically based on maximizing image similarity second in order to avoid being trapped by local minima i e suboptimal poor matches hammer uses a successive approximation of the energy function being optimized by lower dimensional smooth energy functions which are constructed to have significantly fewer local minima this is achieved by hierarchically selecting the driving features that have distinct attribute vectors thus drastically reducing ambiguity in finding correspondence a number of experiments demonstrate that the proposed algorithm results in accurate superposition of image data from individuals with significant anatomical differences

graph matching with a dual step em algorithm this paper describes a new approach to matching geometric structure in 2d point sets the novel feature is to unify the tasks of estimating transformation geometry and identifying point correspondence matches unification is realized by constructing a mixture model over the bipartite graph representing the correspondence match and by affecting optimization using the em algorithm according to our em framework the probabilities of structural correspondence gate contributions to the expected likelihood function used to estimate maximum likelihood transformation parameters these gating probabilities measure the consistency of the matched neighborhoods in the graphs the recovery of transformational geometry and hard correspondence matches are interleaved and are realized by applying coupled update operations to the expected log likelihood function we evaluate the technique on two real world problems

a new approach to sharp moser trudinger and adams type inequalities a rearrangement free argument abstract the main purpose of this paper is two fold on the one hand we will develop a new approach to establish sharp singular moser trudinger and adams type inequalities in unbounded domains of euclidean spaces without using the standard symmetrization on the other hand we will prove the sharp singular adams type inequality on high order sobolev spaces w m n m r n of arbitrary integer order m theorem 1 1 which improves the results of ruf and sani 2013 48 where sharp adams inequalities were established for even m and those of the authors lam and lu 2012 28 29 for odd m but with different and more restricted norms we first establish the sharp local singular adams inequality on domains in r n of finite measure theorem 1 4 we take a perspective that any function in the high order sobolev spaces w m n m r n can be represented as a bessel potential thus we can fully use the tools from harmonic analysis and the kernel properties of the polyharmonic operators i m 2 once we have established this sharp local adams inequality then we can adapt the rearrangement free method we will develop in this paper to derive a global sharp adams inequality from a local one our argument substantially simplifies those in ruf and sani 2013 48 and lam and lu 2012 28 29 and avoids the use of rather deep and complicated comparison principle of solutions to polyharmonic operators used in ruf and sani 2013 48 lam and lu 2012 28 29 moreover our theorem holds on sobolev spaces w n r n of any positive fractional order n theorems 1 6 and 1 7 as consequences we can also establish sharp adams inequalities with less restrictions on the sobolev norms see theorems 1 2 1 3 and 1 5 our approach is surprisingly simple and general and can be easily applied to scenarios such as riemannian and sub riemannian manifolds where symmetrization argument does not work see e g on the heisenberg group lam and lu 2012 30

a general method for geometric feature matching and model extraction popular algorithms for feature matching and model extraction fall into two broad categories generate and test and hough transform variations however both methods suffer from problems in practical implementations generate and test methods are sensitive to noise in the data they often fail when the generated model fit is poor due to error in the data used to generate the model position hough transform variations are less sensitive to noise but implementations for complex problems suffer from large time and space requirements and from the detection of false positives this paper describes a general method for solving problems where a model is extracted from or fit to data that draws benefits from both generate and test methods and those based on the hough transform yielding a method superior to both an important component of the method is the subdivision of the problem into many subproblems this allows efficient generate and test techniques to be used including the use of randomization to limit the number of subproblems that must be examined each subproblem is solved using pose space analysis techniques similar to the hough transform which lowers the sensitivity of the method to noise this strategy is easy to implement and results in practical algorithms that are efficient and robust we describe case studies of the application of this method to object recognition geometric primitive extraction robust regression and motion segmentation

a comparative study of transformation functions for nonrigid image registration transformation functions play a major role in nonrigid image registration in this paper the characteristics of thin plate spline tps multiquadric mq piecewise linear pl and weighted mean wm transformations are explored and their performances in nonrigid image registration are compared tps and mq are found to be most suitable when the set of control point correspondences is not large fewer than a thousand and variation in spacing between the control points is not large when spacing between the control points varies greatly pl is found to produce a more accurate registration than tps and mq when a very large set of control points is given and the control points contain positional inaccuracies wm is preferred over tps mq and pl because it uses an averaging process that smoothes the noise and does not require the solution of a very large system of equations use of transformation functions in the detection of incorrect correspondences is also discussed

stability conditions of delay differential systems sufficient conditions of asymptotic stability independent of delay of both the retarded and neutral types of delay differential systems are obtained the main results are based on the sufficient conditions under which the roots of the determinant of a given l l complex matrix polynomial lie either in the open left half plane or inside the unit circle therefore the explicit computation of the determinant polynomial is not required

sharp exponential integrability for critical riesz potentials and fractional laplacians on rn abstract we derive sharp adams inequalities for the riesz and more general riesz like potentials on the whole of r n as a consequence we obtain sharp moser trudinger inequalities for the critical sobolev spaces w n r n 0 n these inequalities involve fractional laplacians higher order gradients general homogeneous elliptic operators with constant coefficients and general trace type borel measures

approximate input sensitive algorithms for point pattern matching we study input sensitive algorithms for point pattern matching under various transformations and the hausdorff metric as a distance function given point sets p and q in the plane the problem of point pattern matching is to determine whether p is similar to some portion of q where p may undergo transformations from a group g of allowed transformations all algorithms are based on methods for extracting small subsets from q that can be matched to a small subset of p the runtime is proportional to the number k of these subsets let d be the number of points in p that are needed to define a transformation in g the key observation is that for some set b p of cardinality larger than d the number of subsets of q of this cardinality that match b is practically small as the problem becomes more constrained we present methods to extract efficiently all these subsets in q we provide algorithms for homothetic rigid and similarity transformations in the plane and give a general method that works for any dimension and for any group of transformations the runtime of our algorithms depends roughly linearly on the number of subsets k in addition to an nlogn factor thus our approximate matching algorithms run roughly in time o nlogn kmlogn where m and n are the number of points in p and q respectively the constants hidden in the big o vary depending on the group of transformations g

line based recognition using a multidimensional hausdorff distance a line feature based approach for model based recognition using a four dimensional hausdorff distance is proposed this approach reduces the problem of finding the rotation scaling and translation transformations between a model and an image to the problem of finding a single translation minimizing the hausdorff distance between two sets of points in a four dimensional space the implementation of the proposed algorithm can be naturally extended to higher dimensional spaces to efficiently find correspondences between n dimensional patterns the method performance and sensitivity to segmentation problems are quantitatively characterized using an experimental protocol with simulated data it is shown that the algorithm performs well is robust to occlusion and outliers and that it degrades nicely as the segmentation problems increase experiments with real images are also presented

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

existence and nonexistence of extremal functions for sharp trudinger moser inequalities abstract our main purpose in this paper is to establish the existence and nonexistence of extremal functions also known as maximizers and symmetry of extremals for several trudinger moser type inequalities on the entire space r n including both the critical and subcritical trudinger moser inequalities see theorems 1 1 1 2 1 3 1 4 1 5 most of earlier works on existence of maximizers in the literature rely on the complicated blow up analysis of pdes for the associated euler lagrange equations of the corresponding moser functionals the new approaches developed in this paper are using the identities and relationship between the supremums of the subcritical trudinger moser inequalities and the critical ones established by the same authors in 25 combining with the continuity of the supremum function that is observed for the first time in the literature these allow us to establish the existence and nonexistence of the maximizers for the trudinger moser inequalities in different ranges of the parameters including those inequalities with the exact growth this method is considerably simpler and also allows us to study the symmetry problem of the extremal functions and prove that the extremal functions for the subcritical singular truddinger moser inequalities are symmetric moreover we will be able to calculate the exact values of the supremums of the trudinger moser type in certain cases these appear to be the first results in this direction

description and discrimination of planar shapes using shape matrices a shape descriptor has been developed which can describe a shape independent of its translation rotation and scaling the description is in the form of a matrix and it is obtained by a polar quantization of a shape the quantization process takes into consideration not only a shape s outer geometry but its inner geometry as well the descriptor is information preserving and if the quantization parameters are selected properly it is possible to reconstruct an original shape from its description in this technique shape discrimination is possible by a simple exclusive or operation on shape descriptions

shape classification using invariant features and contextual information in the bag of words model in this paper we describe a classification framework for binary shapes that have scale rotation and strong viewpoint variations to this end we develop several novel techniques first we employ the spectral magnitude of log polar transform as a local feature in the bag of words model second we incorporate contextual information in the bag of words model using a novel method to extract bi grams from the spatial co occurrence matrix third a novel metric termed weighted gain ratio is proposed to select a suitable codebook size in the bag of words model the proposed metric is generic and hence it can be used for any clustering quality evaluation task fourth a joint learning framework is proposed to learn features in a data driven manner and thus avoid manual fine tuning of the model parameters we test our shape classification system on the animal shapes dataset and significantly outperform state of the art methods in the literature highlightsa shape classifier tolerant to scale rotation and viewpoint changes is proposed the inclusion of the histogram of bi grams improves the bag of words model codebook selection and feature learning improve the classification accuracy we report best results on the animal shapes dataset using the proposed method

a sharp inequality of j moser for higher order derivatives in fact go nwl 1 where wnis the area of the surface of the unit n ball also he notes that if 3 exceeds go then 1 can no longer hold with some co independent of the u satisfying 2 the fact that this result holds for some 3 0 independent of u has been observed now by several authors with a variety of proofs see 24 20 23 22 10 4 1 2 13 14 for example the earliest of these arguments expands the exponential function in a power series then observing that the norm in the imbedding

attributed relational graph matching based on the nested assignment structure in this paper we propose a new arg matching scheme based on the nested assignment structure to assess the similarity between two attributed relational graphs args args are represented by nodes and edges containing unary attributes and binary relations between nodes respectively the nested assignment structure consists of inner and outer steps in the inner step to form a distance matrix combinatorial differences between every pair of nodes in two args are computed by using an assignment algorithm then in the outer step a correspondence between nodes in the two args is established by using an assignment algorithm based on the distance matrix the proposed arg matching scheme consists of three procedures as follows first in the initializing procedure the nested assignment structure is performed to generate an initial correspondence between nodes in two args next the correspondence is refined by iteratively performing the updating procedure which also utilizes the nested assignment structure until the correspondence does not change finally the verifying procedure can be performed in case that some nodes to be matched in the two args are missing from experimental results the proposed arg matching scheme shows superior matching performance and localizes target objects robustly and correctly even in severely noisy and occluded scenes

template matching in rotated images a rotationally invariant template matching using normalized invariant moments is described it is shown that if normalized invariant moments in circular windows are used then template matching in rotated images becomes similar to template matching in translated images a speedup technique based on the idea of two stage template matching is also described in this technique the zeroth order moment is used in the first stage to determine the likely match positions and the second and third order moments are used in the second stage to determine the best match position among the likely ones

design and recovery of 2 d and 3 d shapes using rational gaussian curves and surfaces a new representation for parametric curves and surfaces is introduced here it is in rational form and uses rational gaussian bases this representation allows design of 2 d and 3 d shapes and makes recovery of shapes from noisy image data possible the standard deviations of gaussians in a curve or surface control the smoothness of a recovered shape the control points of a surface in this representation are not required to form a regular grid and a scattered set of control points is sufficient to reconstruct a surface examples of shape design shape recovery and image segmentation using the proposed representation are given

noisy logo recognition using line segment hausdorff distance logo recognition is of great interest in the document and shape analysis domain in order to develop a recognition method that is robust to employ under adverse conditions such as different scale orientation broken curves added noise and occlusion a modified line segment hausdorff distance is proposed in this paper the new approach has the advantage to incorporate structural and spatial information to compute dissimilarity between two sets of line segments rather than two sets of points the proposed technique has been applied on line segments generated from logos with encouraging results clear cut distinction between the correct and incorrect matches has been observed this suggests a strong potential for logo and shape recognition system

on critical cases of sobolev s inequalities abstract we present a new form of the trudinger type inequality which shows an explicit dependence moreover we give an alternative proof of the brezis gallouet wainger inequality

sharp subcritical moser trudinger inequalities on heisenberg groups and subelliptic pdes the aim of this paper is to prove a sharp subcritical moser trudinger inequality on the whole heisenberg group let h cn rh cn r be the n n dimensional heisenberg group q 2n 2q 2n 2 be the homogeneous dimension of hh q qq 1 and z 4 t2 14 be the homogeneous norm of z t h z t h then we establish the following inequality on hh theorem 1 1 there exists a positive constant q q 2 n 12 q 12 q2 1 n 1 q 1 such that for any pair satisfying 0 q0 q 0 q 1 q there exists a constant 0 c c 0 c c such that the following inequality holds sup hu lq h 11 u lq h q h1 exp u q q 1 k 0q 2 kk u kq q 1 c the above result is the best possible in the sense when q 1 q the integral is still finite for any u w1 q h u w1 q h but the supremum is infinite in contrast to the analogous inequality in euclidean spaces proved in adachi and tanaka 1999 6 using symmetrization our argument is completely different and avoids the symmetrization method which is not available on the heisenberg group in an optimal way moreover our restriction on the norm hu lq h 1 hu lq h 1 of the function uu is much weaker than hu lq h u lq h 1 which was assumed in lam and lu 2012 16 as a consequence our inequality fails at q 1 q in contrast to the one in 16 as an application of this inequality we will prove that the following nonlinear subelliptic equation of qq laplacian type without perturbation equation 0 1 qu v u q 2u f u in h has a nontrivial weak solution where the nonlinear term ff has the critical exponential growth e u qq 1 as u u but does not satisfy the ambrosetti rabinowitz condition

an efficient fuzzy algorithm for aligning shapes under affine transformations abstract a fuzzy algorithm for aligning object shapes under affine transformations is proposed in this paper the algorithm with the name of fuzzy alignment algorithm faa extends marques algorithm to affine transformations it can efficiently estimate the point correspondence and the relevant affine transformational parameters between the feature points of the object shape and the reference shape in this algorithm the fuzzy point correspondence degrees are used to describe an uncertainty point assignment then both the parameters of the affine transformation and the fuzzy correspondence degrees are iteratively calculated by minimizing a constrained fuzzy objective function to prevent faa from sinking into local minimum when the shapes are greatly deformed an initialization method based on affine invariants is designed comparing to the eigenvector method the effectiveness and robustness of the proposed algorithm is investigated with a sensitivity study based on randomly generated points at last good performance of faa is illustrated with several experiments on aligning digits and object shapes

moment preserving pattern matching abstract an accurate template matching algorithm of low computational complexity that facilitates low cost hardware design and vlsi implementation is highly desired by many image processing applications this paper describes a template matching method called moment preserving pattern matching mppm which reduces the computational complexity of template matching significantly and provides several advantages in hardware implementation the methodology is based on the concepts of pairing function and moment preserving quantization the experimental results show that it is computationally fast and accurate in locating the template if noise corruption is not too severe for obtaining a template matching algorithm of high accuracy and robustness against noise and low computational cost mppm is applied to a two stage matching scheme a statistical model for estimating the correlation threshold is also given

piecewise cubic mapping functions for image registration in a recent paper 1 a registration technique was proposed that registered two images by triangulating the images and mapping corresponding triangular regions in the images using a linear function this paper extends the previous technique to include piecewise nonlinear functions as mapping functions a nonlinear mapping function in addition to providing continuous mapping provides smooth transition from one local function to another the obtained mapping function which is a piecewise combination of local mapping functions is therefore continuous and smooth all over a technique based on the clough tocher subtriangulation 2 is described which determines piecewise cubic mapping functions for image registration

classification of solutions to the higher order liouville s equation on mathbb r 2m we classify the solutions to the equation mu 2m 1 e2mu on mathbb r 2m giving rise to a metric g e 2u g mathbb r 2m with finite total q curvature in terms of analytic and geometric properties the analytic conditions involve the growth rate of u and the asymptotic behaviour of u at infinity as a consequence we give a geometric characterization in terms of the scalar curvature of the metric e 2u g mathbb r 2m at infinity and we observe that the pull back of this metric to s2m via the stereographic projection can be extended to a smooth riemannian metric if and only if it is round

stability of interval matrix polynomial in continuous and discrete cases abstract sufficient conditions of asymptotic stability of interval matrix polynomial of both continuous and discrete cases are given these conditions are presented in terms of the positive definiteness of either an ln ln or l l hermitian and interval matrix therefore the computation of the determinant interval polynomial is avoided

3 d to 2 d pose determination with regions this paper presents a novel approach to parts based object recognition in the presence of occlusion we focus on the problem of determining the pose of a 3 d object from a single 2 d image when convex parts of the object have been matched to corresponding regions in the image we consider three types of occlusions self occlusion occlusions whose locus is identified in the image and completely arbitrary occlusions we show that in the first two cases this is a convex optimization problem derive efficient algorithms and characterize their performance for the last case we prove that the problem of finding valid poses is computationally hard but provide an efficient approximate algorithm this work generalizes our previous work on region based object recognition which focused on the case of planar models

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

on the independence of rotation moment invariants abstract the problem of the independence and completeness of rotation moment invariants is addressed in this paper first a general method for constructing invariants of arbitrary orders by means of complex moments is described as a major contribution of the paper it is shown that for any set of invariants there exists a relatively small basis by means of which all other invariants can be generated the method how to construct such a basis and how to prove its independence and completeness is presented some practical impacts of the new results are mentioned at the end of the paper

on a class of polynomial triangular macro elements in this paper we present a new class of polynomial triangular macro elements of arbitrary degree which are an extension of the classical clough tocher cubic scheme their most important property is that the degree plays the role of a tension parameter since these macro elements tend to the plane interpolating the vertices data graphical examples showing their use in scattered data interpolation are reported

sharp adams type inequalities in sobolev spaces wm nm rn for arbitrary integer m the main purpose of our paper is to prove sharp adams type inequalities in unbounded domains of rn for the sobolev space wm nm rn for any positive integer m less than n our results complement those of ruf and sani in press 35 where such inequalities have been established for even integer m we extend the main techniques of ruf and sani in press 35 which are the combinations of the comparison principle of talenti 1976 36 and trombetti and vazquez 1985 38 for polyharmonic operators and a symmetrization argument together with constructions of radial auxiliary functions to the case when m is odd moreover we offer a completely different but much simpler approach to prove the comparison principle using the power of bessel potentials and the riesz rearrangement see remarks 3 2 and 3 3 this approach is of independent interest and works for any differential operators with appropriate radial kernels as corollaries of our main theorems we will derive the adams type inequalities in the case when n 2m for all positive integer m by using different sobolev norms

fast computation of krawtchouk moments the paper describes the calculation of the krawtchouk moments kms from an image which is a computationally demanding task we present two original methods that use the outputs of cascaded digital filters in deriving kms the first approach uses the digital filter outputs to form geometric moments gms and the kms are obtained via gms the second method uses a direct relationship to obtain kms from the digital filter outputs this is possible thanks to the formulation of krawtchouk polynomials in terms of binomial functions which are equivalent to the digital filter outputs in this study the performance of the proposed techniques is compared with other existing methods of kms calculation the experimental study shows that the first and the second proposed techniques perform 57 and 87 faster than the recurrence method for a real image of a size 128 128 pixels which performs a significant improvement

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

line segment hausdorff distance on face matching abstract a novel concept of line segment hausdorff distance is proposed in this paper researchers apply hausdorff distance to measure the similarity of two point sets it is extended here to match two sets of line segments the new approach has the advantage to incorporate structural and spatial information to compute the similarity the added information can conceptually provide more and better distinctive capability for recognition this would strengthen and enhance the matching process of similar objects such as faces the proposed technique has been applied online segments generated from the edge maps of faces with encouraging result that supports the concept experimentally the results also implicate that line segments could provide sufficient information for face recognition this might imply a new way for face coding and recognition

stability of a matrix polynomial in continuous systems two sufficient conditions under which the roots of the determinant of a given m times m matrix polynomial of n th order lie in the open left half plane have been obtained the first condition is given in terms of the positive definiteness of an mn times mn symmetric matrix while the second condition is given in terms of the positive definiteness of an m times m matrix that is a function of s re s leq 0 these conditions are represented in terms of rational functions of the coefficient matrices of the given matrix polynomial therefore the explicit computation of the determinant polynomial is not required

the position orientation masking approach to parametric search for template matching a new search method over x y spl theta called position orientation masking is introduced it is applied to vertices that are allowed to be separated into different bands of acuteness position orientation masking yields exactly one spl theta value for each x y that it considers to be the location of a possible occurrence of an object detailed matching of edge segments is performed at only these candidate x y spl theta to determine if objects actually do occur there template matching is accelerated dramatically since the candidates comprise only a small fraction of all x y spl theta position orientation masking eliminates the need for exhaustive search when deriving the candidate x y spl theta search is guided by correlations between template vertices and distance transforms of image vertices when a poor correlation is encountered at a particular position and orientation nearby positions at that orientation and nearby orientations at that position are masked out position and orientation traversal are by quadrant and binary decomposition

adams inequalities for bi laplacian and extremal functions in dimension four let be a smooth oriented bounded domain be the sobolev space and be the first eigenvalue of the bi laplacian operator 2 then for any a 0a o we have and the above supremum is infinity when a o this strengthens adams inequality in dimension 4 d adams a sharp inequality of j moser for high order derivatives ann of math 128 1988 365 398 where he proved the above inequality holds for a 0 moreover we prove that for sufficiently small a an extremal function for the above inequality exists as a special case of our results we thus show that there exists with such that this establishes the existence of an extremal function of the original adams inequality in dimension 4

stability of a matrix polynomial in discrete systems two sufficient conditions that the determinant of a nonsingular real m times m matrix polynomial of n th order has all its roots inside the unit circle have been obtained these conditions are represented in terms of rational functions of the coefficient matrices therefore these conditions do not require the computation of the determinant polynomial the first condition is given in terms of the positive definiteness of an mn times mn symmetric matrix while the second condition is expressed by the positive definiteness of an m times m hermitian matrix which is a function of z z leq 1 the first condition implies the second and hence is more restrictive than the second

maximizers for gagliardo nirenberg inequalities and related non local problems in this paper we study the existence of maximizers for two families of interpolation inequalities namely a generalized gagliardo nirenberg inequality and a new inequality involving the riesz energy two basic tools in our argument are a generalization of lieb s translation lemma and a riesz energy version of the brezis lieb lemma

existence and nonexistence of maximizers for variational problems associated with trudinger moser type inequalities in mathbb r n we discuss the existence of a maximizer for a maximizing problem associated with the trudinger moser type inequality in mathbb r n n geq 2 different from the bounded domain case we obtain both of the existence and the nonexistence results the proof requires a careful estimate of the maximizing level with the aid of normalized vanishing sequences

nonlinear shape registration without correspondences in this paper we propose a novel framework to estimate the parameters of a diffeomorphism that aligns a known shape and its distorted observation classical registration methods first establish correspondences between the shapes and then compute the transformation parameters from these landmarks herein we trace back the problem to the solution of a system of nonlinear equations which directly gives the parameters of the aligning transformation the proposed method provides a generic framework to recover any diffeomorphic deformation without established correspondences it is easy to implement not sensitive to the strength of the deformation and robust against segmentation errors the method has been applied to several commonly used transformation models the performance of the proposed framework has been demonstrated on large synthetic data sets as well as in the context of various applications

sharp adams type inequalities in ℝⁿ adams inequality for bounded domains r4 states that the supremum of e 32 u dx over all functions u w 2 2 0 with u 2 1 is bounded by a constant depending on only this bound becomes infinite for unbounded domains and in particular for r4 we prove that if u 2 is replaced by a suitable norm namely u u u 2 then the supremum of e 32 u 1 dx over all functions u w 2 2 0 with u 1 is bounded by a constant independent of the domain furthermore we generalize this result to any w m n m 0 with rn and m an even integer less than n

the parameter r2 in multiquadric interpolation the multiquadric mq method is an effective bivariate interpolant to three dimensional data xi yi zi where the xi yi are arbitrarily located in the plane the accuracy of the mq method is dependent on a user defined parameter r2 and most practitioners select r2 based upon the number of data points and the locations of the xi yi in the plane we observe that the optimal value of r2 is a strong function of the zi and that it is essentially independent of both the number and the locationsof the xi yi points contrary to some opinions we observe that the mq method can effectively interpolate to track data that is data sampled densely along tracks in the plane together with several other observations we present an algorithm that generally yields an effective value for r2

stability of discrete time matrix polynomials this paper derives conditions for the stability of discrete time systems that can be modeled by a vector difference equation where the variables are m spl times 1 vectors and the coefficients are m spl times m matrices stability of the system is related to the locations of the roots of the determinant of a real m spl times m matrix polynomial of nth order in this case sufficient conditions for the system to be stable are derived the conditions are imposed on the spl infin norm of two matrices constructed from the coefficient matrices and do not require the computation of the determinant polynomial the conditions are the extensions of one of the jury sufficient conditions for a scalar polynomial an example is used to illustrate the application of the sufficient conditions

existence and nonexistence of extremals for critical adams inequalities in r4 and trudinger moser inequalities in r2 abstract though much progress has been made with respect to the existence of extremals of the critical first order trudinger moser inequalities in w 1 n r n and higher order adams inequalities on finite domain r n whether there exists an extremal function for the critical higher order adams inequalities on the entire space r n still remains open the current paper represents the first attempt in this direction by considering the critical second order adams inequality in the entire space r 4 the classical blow up procedure cannot apply to solving the existence of critical adams type inequality because of the absence of the polya szego type inequality in this paper we develop some new ideas and approaches based on a sharp fourier rearrangement principle see 31 sharp constants of the higher order gagliardo nirenberg inequalities and optimal poly harmonic truncations to study the existence and nonexistence of the maximizers for the adams inequalities in r 4 of the form s sup u h 2 1 r 4 exp 32 2 u 2 1 u 2 d x where 32 2 we establish the existence of the threshold where 32 2 2 b 2 2 and b 2 1 24 2 such that s is attained if 32 2 and is not attained if 32 2 this phenomenon has not been observed before even in the case of first order trudinger moser inequality therefore we also establish the existence and non existence of an extremal function for the trudinger moser inequality on r 2 furthermore the symmetry of the extremal functions can also be deduced through the fourier rearrangement principle

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

sharp hardy adams inequalities for bi laplacian on hyperbolic space of dimension four abstract we establish sharp hardy adams inequalities on hyperbolic space b 4 of dimension four namely we will show that for any 0 there exists a constant c 0 such that b 4 e 32 2 u 2 1 32 2 u 2 d v 16 b 4 e 32 2 u 2 1 32 2 u 2 1 x 2 4 d x c for any u c 0 b 4 with b 4 h 9 4 h u u d v 1 as applications we obtain a sharpened adams inequality on hyperbolic space b 4 and an inequality which improves the classical adams inequality and the hardy inequality simultaneously the later inequality is in the spirit of the hardy trudinger moser inequality on a disk in dimension two given by wang and ye in 46 and on any convex planar domain by lu and yang in 33 the fourier analysis techniques on hyperbolic and symmetric spaces play an important role in our work

a two stage cross correlation approach to template matching two stage template matching with sum of absolute differences as the similarity measure has been developed by vanderburg and rosenfeld 1 2 this correspondence shows the development of two stage template matching with cross correlation as the similarity measure the threshold value of the first stage is derived analytically and its validity is verified experimentally considerable speed up over the one stage process can be obtained by introducing only a small false dismissal probability