assigning frequencies via determinantal equations new counterexamples and invariants the problem of arbitrary pole zero assignment by fixed structure compensators has been addressed so far in terms of either necessary or sufficient conditions the strongest existing condition is based on the rank of the differential of a related map on a degenerate controller and holds true generically when the degrees of freedom of the compensator exceed the number of frequencies to be assigned mp n for the output feedback problem the complete nongeneric solvability of the problem is still open even when complex controllers are considered a simple necessary solvability condition is that the linear map appearing as a factor of the main determinantal map defining the assignment problem is onto here we examine the special problem of assignment of matrix pencil zeros via diagonal perturbations and we present a new necessary and sufficient condition for complex solvability in terms of a new invariant involving the minors of this linear map based on this result we demonstrate that for the important case where the degrees of freedom of the controller are equal to the number of frequencies to be assigned the surjectivity of this linear map although it is necessary it is not sufficient for the solvability of the problem

statistical hough transform the standard hough transform is a popular method in image processing and is traditionally estimated using histograms densities modeled with histograms in high dimensional space and or with few observations can be very sparse and highly demanding in memory in this paper we propose first to extend the formulation to continuous kernel estimates second when dependencies in between variables are well taken into account the estimated density is also robust to noise and insensitive to the choice of the origin of the spatial coordinates finally our new statistical framework is unsupervised all needed parameters are automatically estimated and flexible priors can easily be attached to the observations we show experimentally that our new modeling encodes better the alignment content of images

pole placement by static output feedback for generic linear systems we consider linear systems with m inputs p outputs and mcmillan degree n such that n mp if both m and p are even we show that there is a nonempty open in the usual topology subset u of such systems where the real pole placement map is not surjective it follows that for each system in u there exists an open set of pole configurations symmetric with respect to the real line which cannot be assigned by any real static output feedback

grassmann invariants almost zeros and the determinantal zero pole assignment problems of linear multivariable systems the strucxpects of the rationxr spaces x c x fwhere x c is the columxof the transfer function matrix g s and x f is the space associated with right matrix fracxcriptions of g s are investigated for x f gcanonixqb s grassmgesentax g x c and g x f arxd and are shown xmplete basis free invariants for x c and x f respectively the almost zeros az and almost decoupling zeros adz of g s gdefinex local minima of a normgn defix g x c and g x f respectively the computation and certain aspects of the distribution in the complex plane of azs and adzs are examined the role of azs and adzs in the determinantal zero and pole assignment problems respectively is examined next two important families of systems are defined the strongly zero non assignable szna and the strongly pole non assignable spna systems for szna and spna systems minimal radius discs dem e z r em e z and dem f zb centred at an az and adz respectively are defined it is shown that dem e r em e z contains at least one zer

the pole placement problem via pi feedback controllers in this paper we study the pole placement problem using generalized pi controllers of a fixed lag k as compensators we derive a new strong sufficiency condition which guarantees the arbitrary pole assignability of a given system having m inputs p outputs and mcmillan degree n this sufficiency condition misses the theoretical best possible necessary condition by one degree of freedom the proof of the main result can be used to derive a numerical procedure this numerical procedure is however very sensitive in the parameters and further research is required to investigate the conditions under which sensitivity occurs and whether the solution can be made more robust in this regard

generic eigenvalue assignment by memoryless real output feedback by extensive use of methods from algebraic geometry x wang proved that arbitrary pole placement by static output feedback is generically possible for strictly proper plants with n states m inputs and p outputs if n mp here we show the same result using no more of algebraic geometry than the definition of genericity

a closed form solution to tensor voting theory and applications we prove a closed form solution to tensor voting cftv given a point set in any dimensions our closed form solution provides an exact continuous and efficient algorithm for computing a structure aware tensor that simultaneously achieves salient structure detection and outlier attenuation using cftv we prove the convergence of tensor voting on a markov random field mrf thus termed as mrftv where the structure aware tensor at each input site reaches a stationary state upon convergence in structure propagation we then embed structure aware tensor into expectation maximization em for optimizing a single linear structure to achieve efficient and robust parameter estimation specifically our emtv algorithm optimizes both the tensor and fitting parameters and does not require random sampling consensus typically used in existing robust statistical techniques we performed quantitative evaluation on its accuracy and robustness showing that emtv performs better than the original tv and other state of the art techniques in fundamental matrix estimation for multiview stereo matching the extensions of cftv and emtv for extracting multiple and nonlinear structures are underway

dimensionality estimation manifold learning and function approximation using tensor voting we address instance based learning from a perceptual organization standpoint and present methods for dimensionality estimation manifold learning and function approximation under our approach manifolds in high dimensional spaces are inferred by estimating geometric relationships among the input instances unlike conventional manifold learning we do not perform dimensionality reduction but instead perform all operations in the original input space for this purpose we employ a novel formulation of tensor voting which allows an n d implementation tensor voting is a perceptual organization framework that has mostly been applied to computer vision problems analyzing the estimated local structure at the inputs we are able to obtain reliable dimensionality estimates at each instance instead of a global estimate for the entire data set moreover these local dimensionality and structure estimates enable us to measure geodesic distances and perform nonlinear interpolation for data sets with varying density outliers perturbation and intersections that cannot be handled by state of the art methods quantitative results on the estimation of local manifold structure using ground truth data are presented in addition we compare our approach with several leading methods for manifold learning at the task of measuring geodesic distances finally we show competitive function approximation results on real data

robust adaptive scale parametric model estimation for computer vision robust model fitting essentially requires the application of two estimators the first is an estimator for the values of the model parameters the second is an estimator for the scale of the noise in the inlier data indeed we propose two novel robust techniques the two step scale estimator tsse and the adaptive scale sample consensus assc estimator tsse applies nonparametric density estimation and density gradient estimation techniques to robustly estimate the scale of the inliers the assc estimator combines random sample consensus ransac and tsse using a modified objective function that depends upon both the number of inliers and the corresponding scale assc is very robust to discontinuous signals and data with multiple structures being able to tolerate more than 80 percent outliers the main advantage of assc over ransac is that prior knowledge about the scale of inliers is not needed assc can simultaneously estimate the parameters of a model and the scale of the inliers belonging to that model experiments on synthetic data show that assc has better robustness to heavily corrupted data than least median squares lmeds residual consensus resc and adaptive least kth order squares alks we also apply assc to two fundamental computer vision tasks range image segmentation and robust fundamental matrix estimation experiments show very promising results

decentralized pole assignment and product grassmannians the pole assignment problems of linear systems by decentralized static output feedback are considered in this paper a compactification of decentralized static feedback space product grassmannians is introduced in this paper its degree under plucker segre embedding is computed sufficient conditions for arbitrary and almost arbitrary pole assignability are given it is also proved that the generic m times p system of mcmillan degree n has arbitrary pole assignability by r channel decentralized static output with m i inputs and p i outputs on the i th channel if sum i 1 r m ip i geq n when the degree of the product grassmannians is odd or if sum i 1 r m ip i n and the local channels have either the same numbers of inputs or the same numbers of outputs when the degree of the product grassmannians is even

necessary and sufficient conditions for zero assignment by constant squaring down the problem of zero assignment by constant squaring down czap is studied for minimal systems described by a transfer function g s rm l s m l using tools from exterior algebra and algebraic geometry conditions for its solvability are given in terms of the numbers m l the forney dynamical order and the rank of the plucker matrix p for the cases l 1 or l m 1 it is shown that g s is completely zero assignable cza if and only if 1 for the cases l 1 m 1 it is proved that g s is cza or generically zero assignable gza under a complex squaring down if and only if l m l 1 and 1 the latter conditions also provide necessary conditions for the existence of a real solution for a generic g s sufficient conditions for solvability of czap by a real squaring down are that l m l 1 and that the number g a0 al 1 1 a0 al 1 i j ai aj is odd for some set a0 al 1 satisfying 1 l 1i 0ai l l 1 2 and 0 a0 a1 al 1 m 1 apart from the existence results the present approach also allows the computation of the solutions whenever they exist finally it is proved that the only fixed zeros of czap are the zeros of g s and a procedure for computing the solutions of czap whenever such solutions exist based on an optimization problem is given

in defense of the eight point algorithm the fundamental matrix is a basic tool in the analysis of scenes taken with two uncalibrated cameras and the eight point algorithm is a frequently cited method for computing the fundamental matrix from a set of eight or more point matches it has the advantage of simplicity of implementation the prevailing view is however that it is extremely susceptible to noise and hence virtually useless for most purposes this paper challenges that view by showing that by preceding the algorithm with a very simple normalization translation and scaling of the coordinates of the matched points results are obtained comparable with the best iterative algorithms this improved performance is justified by theory and verified by extensive experiments on real images

global asymptotic linearisation of the pole placement map a closed form solution for the constant output feedback problem abstract the problem of pole assignment by constant output feedback controllers is studied for minimal systems described by a proper transfer function matrix g s r m p s with mcmillan degree n a new method is presented based on asymptotic linearisation around a degenerate point of the pole placement map related to the problem the essence of the present approach is to reduce the multilinear nature of the problem to one of solving a linear set of equations and this is achieved without losing any of the degrees of freedom in the controller the solution is given in closed form in terms of a one parameter family of static feedback compensators for which the closed loop poles approach the required ones as 0 conditions for the generic as well as exact solvability of the arbitrary pole placement problem are given in terms of the numbers m p n and the rank of a new system invariant the d restricted plucker matrix it is shown that the method works generically when mp n which along with the boundary case mp n is the best possible condition as far as the number of states of the open loop system is concerned for achieving arbitrary pole placement via constant output feedback

homoclinic solutions for autonomous ordinary differential equations with nonautonomous perturbations nonautomonous ordinary differential equations depending on two parameters 1 and 2 are considered in rn it is assumed that when both parameters are zero the differential equation is autonomous with a hyperbolic equilibrium and a homoclinic solution no restriction is placed on the dimension of the phase space rn or on the dimension of intersection of the stable and unstable manifolds by means of the method of lyapunov schmidt a bifurcation function h is constructed between two finite dimensional spaces where the zeros of h correspond to homoclinic solutions at nonzero parameter values the independent variables of h consist of scalars 1 2 and a vector where is a phase angle and corresponds to directions other than along the original homoclinic solution tangent to both the stable and unstable manifolds when is fixed the equation h 0 yields in general several bifurcation curves through the origin in the 1 2 plane along which there exists a homoclinic solution when is varied these become a number of wedge shaped regions the theory is applied to two examples one in r6 where the invariant manifolds meet in dimension three and a second in r4 where these manifolds agree

simultaneous two view epipolar geometry estimation and motion segmentation by 4d tensor voting we address the problem of simultaneous two view epipolar geometry estimation and motion segmentation from nonstatic scenes given a set of noisy image pairs containing matches of n objects we propose an unconventional efficient and robust method 4d tensor voting for estimating the unknown n epipolar geometries and segmenting the static and motion matching pairs into n independent motions by considering the 4d isotropic and orthogonal joint image space only two tensor voting passes are needed and a very high noise to signal ratio up to five can be tolerated epipolar geometries corresponding to multiple rigid motions are extracted in succession only two uncalibrated frames are needed and no simplifying assumption such as affine camera model or homographic model between images other than the pin hole camera model is made our novel approach consists of propagating a local geometric smoothness constraint in the 4d joint image space followed by global consistency enforcement for extracting the fundamental matrices corresponding to independent motions we have performed extensive experiments to compare our method with some representative algorithms to show that better performance on nonstatic scenes are achieved results on challenging data sets are presented

multivariable nyquist criteria root loci and pole placement a geometric viewpoint classical control theory is concerned with the topics in our title in the context of single input single output systems there is now a large and growing literature on the extension of these ideas to the multiinput multioutput case this development has posed certain difficulties some due to the intrinsic nature of the problem and some we would argue due to an inadequate reflection on what the multivariable problem calls for in this paper we describe what seems to us to be the natural multivariable analogs of these concepts from classical control theory a rather satisfactory generalization of the nyquist criterion will be described and a clear analog of the asymptotic properties of the root locus will be obtained in the multiparameter case however an example is given which illustrates the quite surprising fact that the root locus map is not always continuous at infinite gains this calls for a new ingredient a compactification of the space of gains and perhaps the most interesting new feature in this circle of ideas comes in the area of pole placement this problem is difficult in the multivariable case but by establishing a correspondence with a classical set of problems in geometry we are able to understand its main aspects and to derive results on pole placement by output feedback over the real field

least median of squares regression abstract classical least squares regression consists of minimizing the sum of the squared residuals many authors have produced more robust versions of this estimator by replacing the square by something else such as the absolute value in this article a different approach is introduced in which the sum is replaced by the median of the squared residuals the resulting estimator can resist the effect of nearly 50 of contamination in the data in the special case of simple regression it corresponds to finding the narrowest strip covering half of the observations generalizations are possible to multivariate location orthogonal regression and hypothesis testing in linear models

pole placement and matrix extension problems a common point of view this paper studies a general inverse eigenvalue problem which generalizes many well studied pole placement and matrix extension problems it is shown that the problem corresponds geometrically to a so called central projection from some projective variety the degree of this variety represents the number of solutions the inverse problem has in the critical dimension we are able to compute this degree in many instances and we provide upper bounds in the general situation

bifurcation from homoclinic to periodic solutions in ordinary differential equations with multivalued perturbations the existence of periodic solutions are studied for certain differential inclusions applications are given to ordinary differential equations with multivalued perturbations embodying also dry friction problems singularly perturbed differential inclusions are investigated as well

on output feedback via grassmannians the output feedback pole placement map chi has been studied by using the central projection model necessary and sufficient conditions for chi being dominant are given 2 times 2 systems of mcmillan degree 4 and 2 times 3 systems of mcmillan degree 6 are studied intensively

zero assignment of matrix pencils by additive structured transformations abstract matrix pencil models are natural descriptions of linear networks and systems changing the values of elements of networks that is redesigning them implies changes in the zero structure of the associated pencil and this is achieved by structured additive transformations the paper examines the problem of zero assignment of regular matrix pencils by a special type of structured additive transformations for a certain family of network redesign problems the additive perturbations may be described as diagonal perturbations and such modifications are considered here this problem has certain common features with the pole assignment of linear systems by structured static compensators and thus the new powerful methodology of global linearization j leventides n karcanias sufficient conditions for arbitrary pole assignment by constant decentralised output feedback mathematics of control for signals and systems 8 1995 222 240 j leventides n karcanias global asymptotic linearisation of the pole placement map a closed form solution for the constant output feedback problem automatica 31 1995 1303 1309 can be used for regular pencils with infinite zeros families of structured degenerate additive transformations are defined and parameterized and this lead to the derivation of conditions for zero structure assignment as well as methodology for computing such solutions the case of regular pencils with no infinite zeros is also considered and conditions of zero assignment are developed the results here provide the means for studying problems of linear network redesign by modification of the non dynamic elements

robust adaptive segmentation of range images we propose a novel image segmentation technique using the robust adaptive least kth order squares alks estimator which minimizes the kth order statistics of the squares of residuals the optimal value of k is determined from the data and the procedure detects the homogeneous surface patch representing the relative majority of the pixels the alks shows a better tolerance to structured outliers than other recently proposed similar techniques the performance of the new fully autonomous range image segmentation algorithm is compared to several other methods