quadratic stabilizability of uncertain linear systems existence of a nonlinear stabilizing control does not imply existence of a linear stabilizing control this note is concerned with the problem of stabilizing an uncertain linear system via state feedback control an uncertain system which admits a stabilizing state feedback control and some associated quadratic lyapunov function is said to be quadratically stabilizable in a number of recent papers conditions are given under which quadratic stabilizability via nonlinear control implies quadratic stabilizability via linear control these papers restrict the manner in which the uncertain parameters are permitted to enter structurally into the state equation in order to establish this result this note presents an example which shows that this implication is not true for more general uncertain linear systems to this end we describe an uncertain linear system which is quadratically stabilizable via nonlinear control but not quadratically stabilizable via linear control

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

eigenfaces vs fisherfaces recognition using class specific linear projection we develop a face recognition algorithm which is insensitive to large variation in lighting direction and facial expression taking a pattern classification approach we consider each pixel in an image as a coordinate in a high dimensional space we take advantage of the observation that the images of a particular face under varying illumination but fixed pose lie in a 3d linear subspace of the high dimensional image space if the face is a lambertian surface without shadowing however since faces are not truly lambertian surfaces and do indeed produce self shadowing images will deviate from this linear subspace rather than explicitly modeling this deviation we linearly project the image into a subspace in a manner which discounts those regions of the face with large deviation our projection method is based on fisher s linear discriminant and produces well separated classes in a low dimensional subspace even under severe variation in lighting and facial expressions the eigenface technique another method based on linearly projecting the image space to a low dimensional subspace has similar computational requirements yet extensive experimental results demonstrate that the proposed fisherface method has error rates that are lower than those of the eigenface technique for tests on the harvard and yale face databases

invariant properties of straight homogeneous generalized cylinders and their contours a fundamental group in computer vision is the recovery of three dimensional shape from image data while this problem is in general underconstrained the authors show that it can be simplified in the case where the objects being viewed are generalized cylinders they consider the class of straight homogeneous generalized cylinders shgcs without any further assumption on the viewing direction or the precise shape of these objects they present a rigorous mathematical study of the geometry of shgcs and characterize their gaussian curvature and occluding contours and use these results to prove several new invariant properties of the contours of shgcs these properties are in turn used in two implemented algorithms for recovering shgc descriptions from image contours several examples of segmentation of real images are given other applications are also discussed

3d object modeling and recognition using local affine invariant image descriptors and multi view spatial constraints this article introduces a novel representation for three dimensional 3d objects in terms of local affine invariant descriptors of their images and the spatial relationships between the corresponding surface patches geometric constraints associated with different views of the same patches under affine projection are combined with a normalized representation of their appearance to guide matching and reconstruction allowing the acquisition of true 3d affine and euclidean models from multiple unregistered images as well as their recognition in photographs taken from arbitrary viewpoints the proposed approach does not require a separate segmentation stage and it is applicable to highly cluttered scenes modeling and recognition results are presented

a paraperspective factorization method for shape and motion recovery the factorization method first developed by tomasi and kanade 1992 recovers both the shape of an object and its motion from a sequence of images using many images and tracking many feature points to obtain highly redundant feature position information the method robustly processes the feature trajectory information using singular value decomposition svd taking advantage of the linear algebraic properties of orthographic projection however an orthographic formulation limits the range of motions the method can accommodate paraperspective projection first introduced by ohta et al 1981 is a projection model that closely approximates perspective projection by modeling several effects not modeled under orthographic projection while retaining linear algebraic properties our paraperspective factorization method can be applied to a much wider range of motion scenarios including image sequences containing motion toward the camera and aerial image sequences of terrain taken from a low altitude airplane

growth and integrability in the dynamics of mappings the growth of some numerical characteristics of the mappings under their iterations in the context of the general problem of integrability is discussed in the general case such characteristics as complexity by arnold or the number of the different images for the multiple valued mappings are growing exponentially it is shown that the integrability is closely related with thepolynomial growth the analogies with quantum integrable systems are discussed

a representation for shape based on peaks and ridges in the difference of low pass transform this paper defines a multiple resolution representation for the two dimensional gray scale shapes in an image this representation is constructed by detecting peaks and ridges in the difference of lowpass dolp transform descriptions of shapes which are encoded in this representation may be matched efficiently despite changes in size orientation or position motivations for a multiple resolution representation are presented first followed by the definition of the dolp transform techniques are then presented for encoding a symbolic structural description of forms from the dolp transform this process involves detecting local peaks and ridges in each bandpass image and in the entire three dimensional space defined by the dolp transform linking adjacent peaks in different bandpass images gives a multiple resolution tree which describes shape peaks which are local maxima in this tree provide landmarks for aligning manipulating and matching shapes detecting and linking the ridges in each dolp bandpass image provides a graph which links peaks within a shape in a bandpass image and describes the positions of the boundaries of the shape at multiple resolutions detecting and linking the ridges in the dolp three space describes elongated forms and links the largest peaks in the tree the principles for determining the correspondence between symbols in pairs of such descriptions are then described such correspondence matching is shown to be simplified by using the correspondence at lower resolutions to constrain the possible correspondence at higher resolutions

image feature localization by multiple hypothesis testing of gabor features several novel and particularly successful object and object category detection and recognition methods based on image features local descriptions of object appearance have recently been proposed the methods are based on a localization of image features and a spatial constellation search over the localized features the accuracy and reliability of the methods depend on the success of both tasks image feature localization and spatial constellation model search in this paper we present an improved algorithm for image feature localization the method is based on complex valued multiresolution gabor features and their ranking using multiple hypothesis testing the algorithm provides very accurate local image features over arbitrary scale and rotation we discuss in detail issues such as selection of filter parameters confidence measure and the magnitude versus complex representation and show on a large test sample how these influence the performance the versatility and accuracy of the method is demonstrated on two profoundly different challenging problems faces and license plates

bounds on eigenvalues of matrix products with an application to the algebraic riccati equation lower and upper summation bounds for the eigenvalues of the product xy are presented under various restrictions on matrices x y in r sup n n an application to the algebraic riccati equation yields a trace lower bound it is observed that these bounds are tighter than those in the literature

dynamics of bimeromorphic maps of surfaces we classify bimeromorphic self maps f x inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i of compact kahler surfaces x in terms of their actions f h 1 1 x inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i on cohomology we observe that the growth rate of f n is invariant under bimeromorphic conjugacy and that by conjugating one can always arrange that f n f n we show that the sequence f n can be bounded grow linearly grow quadratically or grow exponentially in the first three cases we show that after conjugating f is an automorphism virtually isotopic to the identity f preserves a rational fibration or f preserves an elliptic fibration respectively in the last case we show that there is a unique up to scaling expanding eigenvector for f that is nef and that f is bimeromorphically conjugate to an automorphism if and only if 2 0 we go on in this case to construct a dynamically natural positive current representing and we study the growth rate of periodic orbits of f we conclude by illustrating our results with a particular family of examples

a matrix inequality associated with bounds on solutions of algebraic riccati and lyapunov equations a new proof is presented for the inequality tr xy leq parallel x parallel 2 cdot tr y this argument is valid under the condition that y be real symmetric nonnegative definite x may be any square matrix

robust stabilization of linear systems with norm bounded time varying uncertainty abstract in this paper robust stabilization of a class of linear systems with norm bounded time varying uncertainties is considered it is shown that for this class of uncertain systems quadratic stabilizability via linear control is equivalent to the existence of a positive definite symmetric matrix solution to a parameter dependent riccati equation also a construction for the stabilizing feedback law is given in terms of the solution to the riccati equation

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

3d object localisation from multi view image detections in this work we present a novel approach to recover objects 3d position and occupancy in a generic scene using only 2d object detections from multiple view images the method reformulates the problem as the estimation of a quadric ellipsoid in 3d given a set of 2d ellipses fitted to the object detection bounding boxes in multiple views we show that a closed form solution exists in the dual space using a minimum of three views while a solution with two views is possible through the use of non linear optimisation and object constraints on the size of the object shape in order to make the solution robust toward inaccurate bounding boxes a likely occurrence in object detection methods we introduce a data preconditioning technique and a non linear refinement of the closed form solution based on implicit subspace constraints results on synthetic tests and on different real datasets involving challenging scenarios demonstrate the applicability and potential of our method in several realistic scenarios

discrete versions of some classical integrable systems and factorization of matrix polynomials discrete versions of several classical integrable systems are investigated such as a discrete analogue of the higher dimensional force free spinning top euler arnold equations the heisenberg chain with classical spins and a new discrete system on the stiefel manifold the integrability is shown with the help of a lax pair representation which is found via a factorization of certain matrix polynomials the complete description of the dynamics is given in terms of abelian functions the flow becomes linear on a prym variety corresponding to a spectral curve the approach is also applied to the billiard problem in the interior of ann dimensional ellipsoid

some relations between dimension and lyapounov exponents we consider differentiable maps and compact invariant sets we introduce dimensional quantities related to the ergodic invariant measures and prove some simple relations

on the trace bound of a matrix product this paper generalizes the main result given by fang et al ibid vol 39 p 2489 90 1994 to provide tighter bounds on the trace of the product of two real matrices

training less color object recognition for autonomous robotics abstract this paper looks at the challenge of object recognition from the perspective of achieving the final goals of practical real world autonomous robot vision applications that of identifying a target of interest in the robot s field of view and properly localizing its position in preparation for the higher level goal of tracking and navigation a unified framework is introduced that combines a multidimensional feature histogram approach with a multiscale pyramid approach for training less color object recognition and localization with direct application to autonomous robotic agents this framework addresses the high computational cost associated with multidimensional processing by deriving the multidimensional laplacian feature histogram pyramid a novel approach to a unified multidimensional multiscale histogram representation furthermore a taylor series formulation is employed to combine the multiscale levels of the multidimensional laplacian feature histogram pyramid into one efficient multidimensional multiscale laplacian taylor feature histogram for rapid object recognition and localization the paper describes the criteria for target detection and localization by autonomous robots and how this newly developed framework fits these needs comparative results demonstrate the robustness of this recognition framework to noise and localization of target objects in cluttered scenes

a probabilistic framework for 3d visual object representation we present an object representation framework that encodes probabilistic spatial relations between 3d features and organizes these features in a hierarchy features at the bottom of the hierarchy are bound to local 3d descriptors higher level features recursively encode probabilistic spatial configurations of more elementary features the hierarchy is implemented in a markov network detection is carried out by a belief propagation algorithm which infers the pose of high level features from local evidence and reinforces local evidence from globally consistent knowledge effectively producing a likelihood for the pose of the object in the detection scene we also present a simple learning algorithm that autonomously builds hierarchies from local object descriptors we explain how to use our framework to estimate the pose of a known object in an unknown scene experiments demonstrate the robustness of hierarchies to input noise viewpoint changes and occlusions

a trace bound for a general square matrix product estimates of bounds on the solutions of lyapunov and riccati equations are important for analysis and synthesis of linear systems in this paper we propose new trace bounds for the product of two general matrices the key point for removing the restriction of symmetry is to replace eigenvalues partly by singular values in the equation of bounds the results obtained are valid for both symmetric and nonsymmetric cases and give tighter bounds in certain cases

the infinite number of generalized dimensions of fractals and strange attractors abstract we show that fractals in general and strange attractors in particular are characterized by an infinite number of generalized dimensions dq q 0 to this aim we develop a rescaling transformation group which yields analytic expressions for all the quantities dq we prove that lim q 0 dq fractal dimension d limq 1dq information dimension and dq 2 correlation exponent v dq with other integer q s correspond to exponents associated with ternary quaternary and higher correlation functions we prove that generally dq dq for any q q for homogeneous fractals dq dq a particularly interesting dimension is dq for two examples feigenbaum attractor generalized baker s transformation we calculate the generalized dimensions and find that d is a non trivial number all the other generalized dimensions are bounded between the fractal dimension and d

rationality for isolated expansive sets abstract an expansive isolated set of a diffeomorphism with nondegenerate periodic points has a rational zeta function

on the complexity of some birational transformations using three different approaches we analyse the complexity of various birational maps constructed from simple operations inversions on square matrices of arbitrary size the first approach comprises the study of the images of lines and relies mainly on univariate polynomial algebra the second approach is a singularity analysis and the third method is more numerical using integer arithmetics these three methods have their own domain of application but they give corroborating results and lead us to a conjecture on the algebraic entropy of a class of maps constructed from matrix inversions

new matrix bounds and iterative algorithms for the discrete coupled algebraic riccati equation abstractthe discrete coupled algebraic riccati equation dcare has wide applications in control theory and linear system in general for the dcare one discusses every term of the coupled term respectively in this paper we consider the coupled term as a whole which is different from the recent results when applying eigenvalue inequalities to discuss the coupled term our method has less error in terms of the properties of special matrices and eigenvalue inequalities we propose several upper and lower matrix bounds for the solution of dcare further we discuss the iterative algorithms for the solution of the dcare in the fixed point iterative algorithms the scope of lipschitz factor is wider than the recent results finally we offer corresponding numerical examples to illustrate the effectiveness of the derived results

real arnold complexity versus real topological entropy for a one parameter dependent two dimensional birational transformation we consider a family of birational transformations of two variables depending on one parameter for which simple rational expressions with integer coefficients for the exact expression of the dynamical zeta function have been conjectured moreover an equality between the asymptotic of the arnold complexity and the exponential of the topological entropy has been conjectured this identification takes place for the birational mapping seen as a mapping bearing on two complex variables acting in a complex projective space we revisit this identification between these two quite universal complexities by considering now the mapping as a mapping bearing on two real variables the definitions of the two previous topological complexities arnold complexity and topological entropy are modified according to this real variables point of view most of the universality is lost however the results presented here are again in agreement with an identification between the asymptotic of the real arnold complexity and the exponential of the real topological entropy a detailed analysis of the real arnold complexity as a function of the parameter of this family of birational transformations of two variables is given

dimensions and entropies of strange attractors from a fluctuating dynamics approach abstract it is shown that the fluctuations in the divergence of near by trajectories on strictly deterministic strange attractors can be modelled by stochastic concepts in particular we propose kramers moyal type equations for correlation functions between points on the attractor the drift terms are the lyapunov exponents the diffusion terms depend on the above fluctuations from this we obtain bounds on generalized dimensions and entropies numerical results show that in nearly all studied cases henon map zaslavskii map mackey glass eq the attractors are fractal measures in the sense of farmer information dimension hausdorff dimension metric entropy topological entropy

new estimates of upper bounds for the solutions of the continuous algebraic riccati equation and the redundant control inputs problems abstract in this paper according to the properties of the given matrix of the continuous algebraic riccati equation care a new positive semi definite matrix is constructed and then basing on some significant properties of the matrix eigenvalue and eigenvalue inequality using inequality techniques and formula transformation and the new positive semi definite matrix a class of new upper bounds of the care is obtained consequently in redundant control inputs system by the derived bounds inequality techniques and the important property of the matrix eigenvalue and singular value we present some new sufficient conditions to guarantee the decrease of controller gain when increasing the control input which are more adaptable than previous results finally we show the effectiveness of the results by numerical examples

real arnold complexity versus real topological entropy for birational transformations we consider a family of birational measure preserving transformations of two variables depending on one parameter for which simple rational expressions with integer coefficients for the exact expression of the dynamical zeta function have been conjectured together with an equality between the multiplicative rate of growth of the arnold complexity and the exponential of the topological entropy this identification takes place for the birational mapping seen as a mapping bearing on two complex variables acting in a complex projective space we revisit this identification between these two quite universal complexities by considering now the mapping as a mapping bearing on two real variables the definitions of the two previous topological complexities arnold complexity and topological entropy are modified according to this real variables point of view most of the universality is lost however the results presented here are again in agreement with an identification between the multiplicative rate of growth of some real arnold complexity and the exponential of some real topological entropy a detailed analysis of this real arnold complexity as a function of the parameter of this family of birational transformations of two variables is given one can also slightly modify the definition of the dynamical zeta function introducing a real dynamical zeta function associated with the counting of the real cycles only similarly one can also introduce some real arnold complexity generating functions we show that several of these two real generating functions seem to have the same singularities furthermore we actually conjecture several simple rational expressions for them yielding again algebraic values for the exponential of the real topological entropy in particular when the parameter of our family of birational transformations becomes large we obtain two interesting compatible nontrivial rational expressions these rational results for real mappings cannot be understood in terms of any obvious markov s partition or symbolic dynamics hyperbolic systems interpretation the birational transformation is far from being hyperbolic it is measure preserving it would be useful to know whether this relation between the arnold complexity and the topological entropy as well as the rationality of the degree generating functions and dynamical zeta functions are a consequence of the measure preserving property of the mapping

the dimension of chaotic attractors dimension is perhaps the most basic property of an attractor in this paper we discuss a variety of different definitions of dimension compute their values for a typical example and review previous work on the dimension of chaotic attractors the relevant definitions of dimension are of two general types those that depend only on metric properties and those that depend on the frequency with which a typical trajectory visits different regions of the attractor both our example and the previous work that we review support the conclusion that all of the frequency dependent dimensions take on the same value which we call the dimension of the natural measure and all of the metric dimensions take on a common value which we call the fractal dimension furthermore the dimension of the natural measure is typically equal to the lyapunov dimension which is defined in terms of lyapunov numbers and thus is usually far easier to calculate than any other definition because it is computable and more physically relevant we feel that the dimension of the natural measure is more important than the fractal dimension

a comparison of affine region detectors the paper gives a snapshot of the state of the art in affine covariant region detectors and compares their performance on a set of test images under varying imaging conditions six types of detectors are included detectors based on affine normalization around harris mikolajczyk and schmid 2002 schaffalitzky and zisserman 2002 and hessian points mikolajczyk and schmid 2002 a detector of maximally stable extremal regions proposed by matas et al 2002 an edge based region detector tuytelaars and van gool 1999 and a detector based on intensity extrema tuytelaars and van gool 2000 and a detector of salient regions proposed by kadir zisserman and brady 2004 the performance is measured against changes in viewpoint scale illumination defocus and image compression the objective of this paper is also to establish a reference test set of images and performance software so that future detectors can be evaluated in the same framework

a structured condition number for self adjoint polynomial matrix equations with applications in linear control abstract based on the classic definition of condition number a structured condition number is proposed for a class of self adjoint polynomial matrix equations the explicit formula of the structured condition number is derived with applying newly defined linear operators the structured condition number can be applied to some important polynomial matrix equations including the continuous time algebraic riccati equation care the discrete time algebraic lyapunov equation dale etc compared with the state of the art condition numbers for care and dale the newly proposed structured condition number can measure the sensitivity of the solution better which is validated by numerical examples

matching widely separated views based on affine invariant regions invariant regions are self adaptive image patches that automatically deform with changing viewpoint as to keep on covering identical physical parts of a scene such regions can be extracted directly from a single image they are then described by a set of invariant features which makes it relatively easy to match them between views even under wide baseline conditions in this contribution two methods to extract invariant regions are presented the first one starts from corners and uses the nearby edges while the second one is purely intensity based as a matter of fact the goal is to build an opportunistic system that exploits several types of invariant regions as it sees fit this yields more correspondences and a system that can deal with a wider range of images to increase the robustness of the system two semi local constraints on combinations of region correspondences are derived one geometric the other photometric they allow to test the consistency of correspondences and hence to reject falsely matched regions experiments on images of real world scenes taken from substantially different viewpoints demonstrate the feasibility of the approach

coordinate independent adaptive attitude tracking control design for spacecraft robust to time varying system uncertainties abstractin this paper we consider the adaptive attitude control of spacecraft with time varying inertial properties we use a coordinate independent approach for the purpose of designing the control and estimation laws in terms of the rotation matrices representing the spacecraft body frame and reference tracking signals this method helps to overcome the difficulties regarding the attitude representation on so 3 such as ambiguities associated with quaternion representation and inherent singularities inside euler parameters we model the time variations in inertial parameters in two different ways and design adaptive control schemes for each case as the first uncertain dynamic model we consider a setting of spacecraft with multiple moving appendages and based on this model design an adaptive control scheme with three different versions where frobenious norm is used in measuring the deviation of the estimated inertia tensors from their actual values the proposed adaptive control scheme is later ex

on the effects of redundant control inputs this paper considers effects of redundant control inputs on system performance a necessary and sufficient condition for strict decrease of the quadratic performance index with input extension is introduced for the non strict decrease cases the initial state set is determined by using hamilton matrix eigenvectors and generalized eigenvectors the h 2 optimal control problem is similarly studied on the basis of state feedback and dynamic output feedback controllers both linear matrix inequality lmi and riccati equation based methods are established the guaranteed cost problem is also solved for uncertain systems with input extension an iterative optimization algorithm is presented for choosing the input matrix columns for a better performance index a satellite launch vehicle slv system is used to illustrate the results

trace bounds on the solution of the algebraic matrix riccati and lyapunov equation lower and upper bounds on the trace of the positive semidefinite solution of the algebraic matrix riccati and lyapunov equation are derived the upper trace bound obtained in this note in many cases results in a tighter bound as compared to the upper bound for the maximal eigenvalue proposed in 1 and 2

singularity complexity and quasi integrability of rational mappings we investigate global properties of the mappings entering the description of symmetries of integrable spin and vertex models by exploiting their nature of birational transformations of projective spaces we give an algorithmic analysis of the structure of invariants of such mappings we discuss some characteristic conditions for their quasi integrability and in particular its links with their singularities in the 2 plane finally we describe some of their propertiesqua dynamical systems making contact with arnol d s notion of complexity and exemplify remarkable behaviours

robust neighborhood preserving projection by nuclear l2 1 norm regularization for image feature extraction we propose two nuclear and l2 1 norm regularized 2d neighborhood preserving projection 2dnpp methods for extracting representative 2d image features 2dnpp extracts neighborhood preserving features by minimizing a frobenius norm based reconstruction error that is very sensitive noise and outliers in given data to make the distance metric more reliable and robust and encode the neighborhood reconstruction error more accurately we minimize the nuclear and l2 1 norm based reconstruction error respectively and measure it over each image technically we propose two enhanced variants of 2dnpp nuclear norm based 2dnpp and sparse reconstruction based 2dnpp besides to optimize the projection for more promising feature extraction we also add the nuclear and sparse l2 1 norm constraints on it accordingly where l2 1 norm ensures the projection to be sparse in rows so that discriminative features are learnt in the latent subspace and the nuclear norm ensures the low rank property of features by projecting data into their respective subspaces by fully considering the neighborhood preserving power using more reliable and robust distance metric and imposing the low rank or sparse constraints on projections at the same time our methods can outperform related state of the arts in a variety of simulation settings

symmetry complexity and multicritical point of the two dimensional spin glass we analyse models of spin glasses on the two dimensional square lattice by exploiting symmetry arguments the replicated partition functions of the ising and related spin glasses are shown to have many remarkable symmetry properties as functions of the edge boltzmann factors it is shown that the applications of homogeneous and hadamard inverses to the edge boltzmann matrix indicate reduced complexities when the elements of the matrix satisfy certain conditions suggesting that the system has special simplicities under such conditions using these duality and symmetry arguments we present a conjecture on the exact location of the multicritical point in the phase diagram

post critical set and non existence of preserved meromorphic 2 forms we present a family of birational transformations in cp2 depending on two or three parameters which do not generically preserve meromorphic 2 forms with the introduction of the orbit of the critical set vanishing condition of the jacobian also called the post critical set we get some new structures some non analytic 2 form which reduce to meromorphic 2 forms for particular subvarieties in the parameter space on these subvarieties the iterates of the critical set have a polynomial growth in the degrees of the parameters while one has an exponential growth out of these subspaces the analysis of our birational transformation in cp2 is first carried out using the diller favre criterion in order to find the complexity reduction of the mapping the integrable cases are found the identification between the complexity growth and the topological entropy is once again verified we perform plots of the post critical set as well as calculations of lyapunov exponents for many orbits confirming that generically no meromorphic 2 form can be preserved for this mapping these birational transformations in cp2 which generically do not preserve any meromorphic 2 form are extremely similar to other birational transformations we previously studied which do preserve meromorphic 2 forms we note that these two sets of birational transformations exhibit totally similar results as far as topological complexity is concerned but drastically different results as far as a more probabilistic approach of dynamical systems is concerned lyapunov exponents with these examples we see that the existence of a preserved meromorphic 2 form explains most of the numerical discrepancies between the topological and probabilistic approaches of dynamical systems

accurate object recognition with shape masks in this paper we propose an object recognition approach that is based on shape masks generalizations of segmentation masks as shape masks carry information about the extent outline of objects they provide a convenient tool to exploit the geometry of objects we apply our ideas to two common object class recognition tasks classification and localization for classification we extend the orderless bag of features image representation in the proposed setup shape masks can be seen as weak geometrical constraints over bag of features those constraints can be used to reduce background clutter and help recognition for localization we propose a new recognition scheme based on high dimensional hypothesis clustering shape masks allow to go beyond bounding boxes and determine the outline approximate segmentation of the object during localization furthermore the method easily learns and detects possible object viewpoints and articulations which are often well characterized by the object outline our experiments reveal that shape masks can improve recognition accuracy of state of the art methods while returning richer recognition answers at the same time we evaluate the proposed approach on the challenging natural scene graz 02 object classes dataset

integrability versus non integrability hard hexagons and hard squares compared in this paper we compare the integrable hard hexagon model with the nonintegrable hard squares model by means of partition function roots and transfer matrix eigenvalues we consider partition functions for toroidal cylindrical and free free boundary conditions up to sizes 40 40 and transfer matrices up to 30 sites for all boundary conditions the hard squares roots are seen to lie in a bounded area of the complex fugacity plane along with the universal hard core line segment on the negative real fugacity axis the density of roots on this line segment matches the derivative of the phase difference between the eigenvalues of largest and equal moduli and exhibits much greater structure than the corresponding density of hard hexagons we also study the special point z 1 of hard squares where all eigenvalues have unit modulus and we give several conjectures for the value at z 1 of the partition functions

real and complex dynamics of a family of birational maps of the plane the golden mean subshift we describe the real dynamics of a family of birational mappings of the plane by combining complex intersection theory and techniques from smooth dynamical systems we are able to give an essentially complete account of the behavior of both wandering and nonwandering orbits in particular the golden mean subshift provides a topological model for the dynamics on the nonwandering set while the mappings are not hyperbolic they are shown to possess many of the structures associated with hyperbolicity

localizing overlapping parts by searching the interpretation tree this paper discusses how local measurements of positions and surface normals may be used to identify and locate overlapping objects the objects are modeled as polyhedra or polygons having up to six degrees of positional freedom relative to the sensors the approach operates by examining all hypotheses about pairings between sensed data and object surfaces and efficiently discarding inconsistent ones by using local constraints on distances between faces angles between face normals and angles relative to the surface normals of vectors between sensed points the method described here is an extension of a method for recognition and localization of nonoverlapping parts previously described in 18 and 15

integrable mappings and polynomial growth abstract we describe birational representations of discrete groups generated by involutions having their origin in the theory of exactly solvable vertex models in lattice statistical mechanics these involutions correspond respectively to two kinds of transformations on q q matrices the inversion of the q q matrix and an involutive permutation of the entries of the matrix we concentrate on the case where these permutations are elementary transpositions of two entries in this case the birational transformations fall into six different classes for each class we analyze the factorization properties of the iteration of these transformations these factorization properties enable to define some canonical homogeneous polynomials associated with these factorization properties some mappings yield a polynomial growth of the complexity of the iterations for three classes the successive iterates for q 4 actually lie on elliptic curves this analysis also provides examples of integrable mappings in arbitrary dimension even infinite moreover for two classes the homogeneous polynomials are shown to satisfy non trivial non linear recurrences the relations between factorizations of the iterations the existence of recurrences on one or several variables as well as the integrability of the mappings are analyzed

rational dynamical zeta functions for birational transformations we propose a conjecture for the exact expression of the unweighted dynamical zeta function for a family of birational transformations of two variables depending on two parameters this conjectured function is a simple rational expression with integer coecients this yields an algebraic value for the topological entropy furthermore the generating function for the arnold complexity is also conjectured to be a rational expression with integer coecients with the same singularities as for the dynamical zeta function this leads at least in this example to an equality between the asymptotic of the arnold complexity and the exponential of the topological entropy we also give a semi numerical method to eectively compute the arnold complexity c 1999 published by elsevier science b v all rights reserved

the combinatorics of object recognition in cluttered environments using constrained search abstract the problem of recognizing rigid objects from noisy sensory data has been successfully attacked in previous work by using a constrained search approach empirical investigations have shown the method to be very effective when recognizing and localizing isolated objects but less effective when dealing with occluded objects where much of the sensory data arises from objects other than the one of interest when clustering techniques such as the hough transform are used to isolate likely subspaces of the search space empirical performance in cluttered scenes improves considerably in this note we establish formal bounds on the combinatorics of this approach under some simple assumptions we show that the expected complexity of recognizing isolated objects is quadratic in the number of model and sensory fragments but that the expected complexity of recognizing objects in cluttered environments is exponential in the size of the correct interpretation we also provide formal bounds on the efficacy of using the hough transform to preselect likely subspaces showing that the problem remains exponential but that in practical terms the size of the problem is significantly decreased

eigenvalue inequalities for matrix product we present a family of eigenvalue inequalities for the product of a hermitian matrix and a positive semidefinite matrix our theorem contains or extends some existing results on trace and eigenvalues

factorization properties of birational mappings abstract we analyse birational mappings generated by transformations on q q matrices which correspond respectively to two kinds of transformations the matrix inversion and a permutation of the entries of the q q matrix remarkable factorization properties emerge for quite general involutive permutations it is shown that factorization properties do exist even for birational transformations associated with noninvolutive permutations of entries of q q matrices and even for more general transformation which are rational transformations but no longer birational the existence of factorization relations independent of q the size of the matrices is underlined the relations between the polynomial growth of the complexity of the iterations the existence of recursions in a single variable and the integrability of the mappings are sketched for the permutations yielding these properties all these results show that permutations of the entries of the matrix yielding factorization properties are not so rare in contrast the occurrence of recursions in a single variable or of the polynomial growth of the complexity are of course less frequent but not completely exceptional

discrete symmetry groups of vertex models in statistical mechanics we analyze discrete symmetry groups of vertex models in lattice statistical mechanics represented as groups of birational transformations they can be seen as generated by involutions corresponding respectively to two kinds of transformations onq q matrices the inversion of theq q matrix and an involutive permutation of the entries of the matrix we show that the analysis of the factorizations of the iterations of these transformations is a precious tool in the study of lattice models in statistical mechanics this approach enables one to analyze two dimensionalq4 state vertex models as simply as three dimensional vertex models or higher dimensional vertex models various examples of birational symmetries of vertex models are analyzed a particular emphasis is devoted to a three dimensional vertex model the 64 state cubic vertex model which exhibits a polynomial growth of the complexity of the calculations a subcase of this general model is seen to yield integrable recursion relations we also concentrate on a specific two dimensional vertex model to see how the generic exponential growth of the calculations reduces to a polynomial growth when the model becomes yang baxter integrable it is also underlined that a polynomial growth of the complexity of these iterations can occur even for transformations yielding algebraic surfaces or higher dimensional algebraic varieties

singularity confinement and chaos in discrete systems we present a number of second order maps which pass the singularity confinement test commonly used to identify integrable discrete systems but which nevertheless are non integrable as a more sensitive integrability test we propose the analysis of the complexity algebraic entropy of the map using the growth of the degree of its iterates integrability is associated with polynomial growth while the generic growth is exponential for chaotic systems

local grayvalue invariants for image retrieval this paper addresses the problem of retrieving images from large image databases the method is based on local grayvalue invariants which are computed at automatically detected interest points a voting algorithm and semilocal constraints make retrieval possible indexing allows for efficient retrieval from a database of more than 1 000 images experimental results show correct retrieval in the case of partial visibility similarity transformations extraneous features and small perspective deformations

spectral norm and trace bounds of algebraic matrix riccati equations upper bounds on spectral norm and trace for the solution of continuous algebraic matrix riccati equations are proposed the proposed bounds are based on a form of the general analytic solution it is shown that in many cases the spectral norm and the trace bounds are better than other results

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

growth complexity spectrum of some discrete dynamical systems we first study the iteration of birational mappings generated by the composition of the matrix inversion and of a permutation of the entries of 3 3 matrices and consider the degree d n of the numerators or denominators of the corresponding successive rational expressions for the nth iterate the growth of this degree is generically exponential with n d n n is called the growth complexity we introduce a semi numerical analysis which enables to compute these growth complexities for all the 9 possible birational transformations these growth complexities correspond to a spectrum of eighteen algebraic values we then drastically generalize these results replacing permutations of the entries by homogeneous polynomial transformations of the entries possibly depending on many parameters again it is shown that the associated birational or even rational transformations yield algebraic values for their growth complexities 1999 elsevier science b v all rights reserved

a trace inequality for matrix product we extend to arbitrary hermitian matrices a well known trace inequality for positive semidefinite matrices when using this result for the product of two matrices when only one is hermitian we improve a recent trace inequality given by fanf et al 1994

let s baxterise we recall the concept of baxterisation of an r matrix or of a monodromy matrix which corresponds to build from one point in the r matrix parameter space the algebraic variety where the spectral parameter s live we show that the baxterisation which amounts to studying the iteration of a birational transformation is a win win strategy it enables to discard efficiently the non integrable situations focusing directly on the two interesting cases where the algebraic varieties are of the so called general type finite order iteration or are abelian varieties infinite order iteration we emphasize the heuristic example of the sixteen vertex model and provide a complete description of the finite order iterations situations for the baxter model we show that the baxterisation procedure can be introduced in much larger frameworks where the existence of some underlying yang baxter structure is not used we baxterise l operators local quantum lax matrices and quantum hamiltonians

an inequality for the trace of matrix product new bounds for the trace of the product of an arbitrary real matrix a and a nonnegative definite symmetric matrix b are derived in each case where the symmetric part of a is an indefinite matrix these bounds are substantial improvements over the bounds known in the literature

comments on a matrix inequality associated with bounds on solutions of algebraic riccati and lyapunov equation by j m saniuk and i b rhodes improved inequalities over the ones reported by j m saniuk and i b rhodes 1987 in the above mentioned paper ibid vol 32 p 739 40 1987 are obtained following the reasoning developed thereby relations are presented that demonstrate the improvement asserted by the commenter

simultaneous object recognition and segmentation from single or multiple model views we present a novel object recognition approach based on affine invariant regions it actively counters the problems related to the limited repeatability of the region detectors and the difficulty of matching in the presence of large amounts of background clutter and particularly challenging viewing conditions after producing an initial set of matches the method gradually explores the surrounding image areas recursively constructing more and more matching regions increasingly farther from the initial ones this process covers the object with matches and simultaneously separates the correct matches from the wrong ones hence recognition and segmentation are achieved at the same time the approach includes a mechanism for capturing the relationships between multiple model views and exploiting these for integrating the contributions of the views at recognition time this is based on an efficient algorithm for partitioning a set of region matches into groups lying on smooth surfaces integration is achieved by measuring the consistency of configurations of groups arising from different model views experimental results demonstrate the stronger power of the approach in dealing with extensive clutter dominant occlusion and large scale and viewpoint changes non rigid deformations are explicitly taken into account and the approximative contours of the object are produced all presented techniques can extend any view point invariant feature extractor

a new trace bound for a general square matrix product using the correlated properties between the diagonal element and the singular value of the matrix we propose new trace bounds for the product of two arbitrary real square matrices and improve the recent results

keypoints and local descriptors of scalar functions on 2d manifolds this paper addresses the problem of describing surfaces using local features and descriptors while methods for the detection of interest points in images and their description based on local image features are very well understood their extension to discrete manifolds has not been well investigated we provide a methodological framework for analyzing real valued functions defined over a 2d manifold embedded in the 3d euclidean space e g photometric information local curvature etc our work is motivated by recent advancements in multiple camera reconstruction and image based rendering of 3d objects there is a growing need for describing object surfaces matching two surfaces or tracking them over time considering polygonal meshes we propose a new methodological framework for the scale space representations of scalar functions defined over such meshes we propose a local feature detector meshdog and region descriptor meshhog unlike the standard image features the proposed surface features capture both the local geometry of the underlying manifold and the scale space differential properties of the real valued function itself we provide a thorough experimental evaluation the repeatability of the feature detector and the robustness of feature descriptor are tested by applying a large number of deformations to the manifold or to the scalar function

inequalities for the trace of matrix product to obtain estimates of solutions of lyapunov and riccati equations which frequently occur in the stability analysis and optimal control design in linear control theory many researchers have attempted to determine upper and lower bounds for the product of two matrices in terms of the trace of one matrix and the eigenvalues of the other baksalary and puntanen claimed an inequality for the trace of matrix product ibid vol 37 no 2 p 239 40 1992 that they had obtained a better estimate for the trace of the product of two matrices the purpose of this note is to point out that their main result is incorrect and a counterexample is presented

new integrable cases of a cremona transformation a finite order orbits analysis we analyse the properties of a particular birational mapping of two variables cremona transformation depending on two free parameters e and associated with the action of a discrete group of non linear birational transformations on the entries of a q q matrix this mapping originates from the analysis of birational transformations obtained from very simple algebraic calculations namely taking the inverse of q q matrices and permuting some of the entries of these matrices it has been seen to yield weak chaos and integrability we have found new integrable cases of this cremona transformation corresponding to the values of 0 when e 12 13 1 besides the already known values e 0 and e 1 and also arbitrary when e 0 for these cases one has a foliation of the parameter space in elliptic curves we give the equations of these elliptic curves based on this very example we show how one can find these integrability cases of the cremona transformation and actually integrate it using a method based on the systematic study of the finite order conditions of the cremona transformation the method is shown to be efficient and straightforward the various integrability cases are revisited using many different representations of this very mapping birational transformations recursion in one variable

real topological entropy versus metric entropy for birational measure preserving transformations abstract we consider a family of birational measure preserving transformations of two complex variables depending on one parameter for which simple rational expressions for the dynamical zeta function have been conjectured together with an equality between the topological entropy and the logarithm of the arnold complexity divided by the number of iterations similar results have been obtained for the adaptation of these two concepts to dynamical systems of real variables yielding to introduce a real topological entropy and a real arnold complexity we try to compare here the kolmogorov sinai metric entropy and this real arnold complexity or real topological entropy on this particular example of a one parameter dependent birational transformation of two variables more precisely we analyze using an infinite precision calculation the lyapunov characteristic exponents for various values of the parameter of the birational transformation in order to compare these results with the ones for the real arnold complexity we find a quite surprising result for this very birational example and in fact for a large set of birational measure preserving mappings generated by involutions the lyapunov characteristic exponents seem to be equal to zero or at least extremely small for all the orbits we have considered and for all values of the parameter birational measure preserving transformations generated by involutions could thus allow to better understand the difference between the topological description and the probabilistic description of discrete dynamical systems many birational measure preserving transformations generated by involutions seem to provide examples of discrete dynamical systems which can be topologically chaotic while they are metrically almost quasi periodic heuristically this can be understood as a consequence of the fact that their orbits seem to form some kind of transcendental foliation of the two dimensional space of variables

a birational mapping with a strange attractor post critical set and covariant curves we consider some two dimensional birational transformations one of them is a birational deformation of the henon map for some of these birational mappings the post critical set i e the iterates of the critical set is infinite and we show that this gives straightforwardly the algebraic covariant curves of the transformation when they exist these covariant curves are used to build the preserved meromorphic 2 form one may also have an infinite post critical set yielding a covariant curve which is not algebraic transcendental for two of the birational mappings considered the post critical set is finite and we claim that there is no algebraic covariant curve and no preserved meromorphic 2 form for these two mappings with finite post critical sets attracting sets occur and we show that they pass the usual tests lyapunov exponents and the fractal dimension for being strange attractors the strange attractor of one of these two mappings is unbounded