robust pole clustering of structured uncertain systems in union of disjointed circular regions abstract this paper presents a systematic procedure for depicting the robust pole clustering of a system with structured uncertainties different from many previous researches on connected region a union of disjointed circular regions on the complex plane containing either a single nominal pole or multi nominal poles is obtained utilizing matrix operation in addition a criterion for determining the allowable perturbation bounds of the structured uncertain system such that the pole clusters remain within certain pre specified circular regions is also proposed the validity of the proposed approach is confirmed by way of numerical examples

structure selective depth superresolution for rgb d cameras this paper describes a method for high quality depth superresolution the standard formulations of image guided depth upsampling using simple joint filtering or quadratic optimization lead to texture copying and depth bleeding artifacts these artifacts are caused by inherent discrepancy of structures in data from different sensors although there exists some correlation between depth and intensity discontinuities they are different in distribution and formation to tackle this problem we formulate an optimization model using a nonconvex regularizer a nonlocal affinity established in a high dimensional feature space is used to offer precisely localized depth boundaries we show that the proposed method iteratively handles differences in structure between depth and intensity images this property enables reducing texture copying and depth bleeding artifacts significantly on a variety of range data sets we also propose a fast alternating direction method of multipliers algorithm to solve our optimization problem our solver shows a noticeable speed up compared with the conventional majorize minimize algorithm extensive experiments with synthetic and real world data sets demonstrate that the proposed method is superior to the existing methods

a fast approximation of the bilateral filter using a signal processing approach the bilateral filter is a nonlinear filter that smoothes a signal while preserving strong edges it has demonstrated great effectiveness for a variety of problems in computer vision and computer graphics and fast versions have been proposed unfortunately little is known about the accuracy of such accelerations in this paper we propose a new signal processing analysis of the bilateral filter which complements the recent studies that analyzed it as a pde or as a robust statistical estimator the key to our analysis is to express the filter in a higher dimensional space where the signal intensity is added to the original domain dimensions importantly this signal processing perspective allows us to develop a novel bilateral filtering acceleration using downsampling in space and intensity this affords a principled expression of accuracy in terms of bandwidth and sampling the bilateral filter can be expressed as linear convolutions in this augmented space followed by two simple nonlinearities this allows us to derive criteria for downsampling the key operations and achieving important acceleration of the bilateral filter we show that for the same running time our method is more accurate than previous acceleration techniques typically we are able to process a 2 megapixel image using our acceleration technique in less than a second and have the result be visually similar to the exact computation that takes several tens of minutes the acceleration is most effective with large spatial kernels furthermore this approach extends naturally to color images and cross bilateral filtering

robustness in the presence of mixed parametric uncertainty and unmodeled dynamics continuing the development of the structured singular value approach to robust control design the authors investigate the problem of computing mu in the case of mixed real parametric and complex uncertainty the problem is shown to be equivalent to a smooth constrained finite dimensional optimization problem in view of the fact that the functional to be maximized may have several local extrema an upper bound on mu whose computation is numerically tractable is established this leads to a sufficient condition of robust stability and performance a historical perspective on the development of the mu theory is included

stereo matching with color weighted correlation hierarchical belief propagation and occlusion handling in this paper we formulate a stereo matching algorithm with careful handling of disparity discontinuity and occlusion the algorithm works with a global matching stereo model based on an energy minimization framework the global energy contains two terms the data term and the smoothness term the data term is first approximated by a color weighted correlation then refined in occluded and low texture areas in a repeated application of a hierarchical loopy belief propagation algorithm the experimental results are evaluated on the middlebury data sets showing that our algorithm is the top performer among all the algorithms listed there

multiple structures with arbitrarily large projective dimension supported on linear subspaces abstract let k be an algebraically closed field there has been much interest in characterizing multiple structures in p k n defined on a linear subspace of small codimension under additional assumptions e g cohen macaulay we show that no such finite characterization of multiple structures is possible if one only assumes unmixedness specifically we prove that for any positive integers h e 2 with h e 2 2 and p 5 there is a homogeneous ideal i in a polynomial ring over k such that 1 the height of i is h 2 the hilbert samuel multiplicity of r i is e 3 the projective dimension of r i is at least p and 4 the ideal i is primary to a linear prime x 1 x h this result is in stark contrast to manolache s characterization of cohen macaulay multiple structures in codimension 2 and multiplicity at most 4 and also to engheta s characterization of unmixed ideals of height 2 and multiplicity 2

robust stability of state space models with structured uncertainties a method for robust eigenvalue location analysis of linear state space models affected by structured real parametric perturbations is proposed the approach based on algebraic matrix properties deals with state space models in which system matrix entries are perturbed by polynomial functions of a set of uncertain physical parameters a method converting the robust stability problem into nonsingularity analysis of a suitable matrix is proposed the method requires a check of the positivity of a multinomial form over a hyperrectangular domain in parameter space this problem which can be reduced to finding the real solutions of a system of polynomial equations simplifies considerably when cases with one or two uncertain parameters are considered for these cases necessary and sufficient conditions for stability are given in terms of the solution of suitable real eigenvalue problems

stack filters and selection probabilities based on the fact that the output of a given stack filter can be determined if the ranks of the samples in the input window are known and that this output always equals one of the samples in the input window rank and sample selection probabilities are defined the output distribution of the stack filter of size n with independent identically distributed i i d inputs can be expressed as a weighted sum of the ith i 1 2 n order statistics where the rank selection probabilities are the weights the sample selection probabilities equal the impulse response coefficients of a finite impulse response fir filter whose output spectrum is closest of all linear filters to that of the stack filter for i i d gaussian inputs results are also derived for correlated inputs robustness and detail preserving properties of stack filters are related to the selection probabilities other statistical properties are also derived finally methods to compute the selection probabilities of the stack filter from its positive boolean function and the selection probabilities of the weighted median filter from its weights are given in detail

depth superresolution by transduction this paper presents a depth superresolution sr method that uses both of a low resolution lr depth image and a high resolution hr intensity image we formulate depth sr as a graph based transduction problem in particular the hr intensity image is represented as an undirected graph in which pixels are characterized as vertices and their relations are encoded as an affinity function when the vertices initially labeled with certain depth hypotheses from the lr depth image are regarded as input queries all the vertices are scored with respect to the relevances to these queries by a classifying function each vertex is then labeled with the depth hypothesis that receives the highest relevance score we design the classifying function by considering the local and global structures of the hr intensity image this approach enables us to address a depth bleeding problem that typically appears in current depth sr methods furthermore input queries are assigned in a probabilistic manner making depth sr robust to noisy depth measurements we also analyze existing depth sr methods in the context of transduction and discuss their theoretic relations intensive experiments demonstrate the superiority of the proposed method over state of the art methods both qualitatively and quantitatively

nonlocal image and movie denoising neighborhood filters are nonlocal image and movie filters which reduce the noise by averaging similar pixels the first object of the paper is to present a unified theory of these filters and reliable criteria to compare them to other filter classes a ccd noise model will be presented justifying the involvement of neighborhood filters a classification of neighborhood filters will be proposed including classical image and movie denoising methods and discussing further a recently introduced neighborhood filter nl means in order to compare denoising methods three principles will be discussed the first principle method noise specifies that only noise must be removed from an image a second principle will be introduced noise to noise according to which a denoising method must transform a white noise into a white noise contrarily to method noise this principle which characterizes artifact free methods eliminates any subjectivity and can be checked by mathematical arguments and fourier analysis noise to noise will be proven to rule out most denoising methods with the exception of neighborhood filters this is why a third and new comparison principle the statistical optimality is needed and will be introduced to compare the performance of all neighborhood filters the three principles will be applied to compare ten different image and movie denoising methods it will be first shown that only wavelet thresholding methods and nl means give an acceptable method noise second that neighborhood filters are the only ones to satisfy the noise to noise principle third that among them nl means is closest to statistical optimality a particular attention will be paid to the application of the statistical optimality criterion for movie denoising methods it will be pointed out that current movie denoising methods are motion compensated neighborhood filters this amounts to say that they are neighborhood filters and that the ideal neighborhood of a pixel is its trajectory unfortunately the aperture problem makes it impossible to estimate ground true trajectories it will be demonstrated that computing trajectories and restricting the neighborhood to them is harmful for denoising purposes and that space time nl means preserves more movie details

topological median filters this paper describes the definition and testing of a new type of median filter for images the topological median filter implements some existing ideas and some new ideas on fuzzy connectedness to improve over a conventional median filter the extraction of edges in noise the concept of spl alpha connectivity is defined and used to create an algorithm for computing the degree of connectedness of a pixel to all the other pixels in an arbitrary neighborhood the resulting connectivity map of the neighborhood effectively disconnects peaks in the neighborhood that are separated from the center pixel by a valley in the brightness topology the median of the connectivity map is an estimate of the median of the peak or plateau to which the center pixel belongs unlike the conventional median filter the topological median is relatively unaffected by disconnected features in the neighborhood of the center pixel four topological median filters are defined qualitative and statistical analyses of the four filters are presented it is demonstrated that edge detection can be more accurate on topologically median filtered images than on conventionally median filtered images

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

a new class of detail preserving filters for image processing a new class of median type filters for image processing is proposed in the filters linear fir substructures are used in conjunction with the median operation the root signals and noise attenuation properties of the fir median hybrid filters are analyzed and compared to representative edge preserving filtering operations the concept of multilevel median operation is introduced to improve the detail preserving property of conventional median and the fir median hybrid filters in the multilevel filters there exists a tradeoff between noise attenuation and detail preservation the analysis and examples indicate that fir median hybrid filters preserve details better and are computationally much more efficient than the conventional median and the k nearest neighbor averaging filters

the fuzzy transformation and its applications in image processing the spatial and rank sr orderings of samples play a critical role in most signal processing algorithms the recently introduced fuzzy ordering theory generalizes traditional or crisp sr ordering concepts and defines the fuzzy spatial samples fuzzy order statistics fuzzy spatial indexes and fuzzy ranks here we introduce a more general concept the fuzzy transformation fzt which refers to the mapping of the crisp samples order statistics and sr ordering indexes to their fuzzy counterparts we establish the element invariant and order invariant properties of the fzt these properties indicate that fuzzy spatial samples and fuzzy order statistics constitute the same set and under commonly satisfied membership function conditions the sample rank order is preserved by the fzt the fzt also possesses clustering and symmetry properties which are established through analysis of the distributions and expectations of fuzzy samples and fuzzy order statistics these properties indicate that the fzt incorporates sample diversity into the ordering operation which can be utilized in the generalization of conventional filters here we establish the fuzzy weighted median fwm fuzzy lower upper middle flum and fuzzy identity filters as generalizations of their crisp counterparts the advantage of the fuzzy generalizations is illustrated in the applications of dct coded image deblocking impulse removal and noisy image sharpening

regularity of prime ideals we answer several natural questions which arise from a recent paper of mccullough and peeva providing counterexamples to the eisenbud goto regularity conjecture we give counterexamples using rees algebras and also construct counterexamples that do not rely on the mayr meyer construction furthermore examples of prime ideals for which the difference between the maximal degree of a minimal generator and the maximal degree of a minimal first syzygy can be made arbitrarily large are given using a result of ananyan hochster we show that there exists an upper bound on regularity of prime ideals in terms of the multiplicity alone

stability robustness bounds for linear state space models with structured uncertainty in this note we consider the robust stability analysis problem in linear state space models we consider systems with structured uncertainty some lower bounds on allowable perturbations which maintain the stability of a nominally stable system are derived these bounds are shown to be less conservative than the existing ones

stereo matching using belief propagation in this paper we formulate the stereo matching problem as a markov network and solve it using bayesian belief propagation the stereo markov network consists of three coupled markov random fields that model the following a smooth field for depth disparity a line process for depth discontinuity and a binary process for occlusion after eliminating the line process and the binary process by introducing two robust functions we apply the belief propagation algorithm to obtain the maximum a posteriori map estimation in the markov network other low level visual cues e g image segmentation can also be easily incorporated in our stereo model to obtain better stereo results experiments demonstrate that our methods are comparable to the state of the art stereo algorithms for many test cases

on the projective dimension and the unmixed part of three cubics let r be a polynomial ring over a field in an unspecified number of variables we prove that if j r is an ideal generated by three cubic forms and the unmixed part of j contains a quadric then the projective dimension of r j is at most 4 to this end we show that if k r is a three generated ideal of height two and l r an ideal linked to the unmixed part of k then the projective dimension of r k is bounded above by the projective dimension of r l plus one

detail preserving ranked order based filters for image processing the theoretical analysis of multistage median filters is developed it is shown that multistage median filters are a combination of max median and min median filters since multistage median filters belong to the class of two dimensional stack filters they have threshold decomposition attributes making their theoretical analysis simple statistical threshold decomposition is applied to derive the statistical characteristics of these filters and the results are used to evaluate the performance of these two types of multistage filters finally a quantitative and qualitative comparison of the multistage filters and of other efficient detail preserving filters is presented the comparisons are made using the mean squared error and the mean absolute error criteria

fusion of median and bilateral filtering for range image upsampling we present a new upsampling method to enhance the spatial resolution of depth images given a low resolution depth image from an active depth sensor and a potentially high resolution color image from a passive rgb camera we formulate it as an adaptive cost aggregation problem and solve it using the bilateral filter the formulation synergistically combines the median and bilateral filters thus it better preserves the depth edges and is more robust to noise numerical and visual evaluations on a total of 37 middlebury data sets demonstrate the effectiveness of our method a real time high resolution depth capturing system is also developed using commercial active depth sensor based on the proposed upsampling method

polynomial weighted median filtering this paper extends weighted median wm filters to the class of polynomial weighted median pwm filters traditional polynomial filtering theory based on linear combinations of polynomial terms is able to approximate important classes of nonlinear systems the linear combination of polynomial terms however yields poor performance in environments characterized by heavy tailed distributions weighted median filters in contrast are well known for their outlier suppression and detail preservation properties the weighted median sample selection methodology is naturally extended to the polynomial sample case yielding a filter structure that exploits the higher order statistics of the observed samples while simultaneously being robust to outliers moreover the pwm filter class is well motivated by an analysis of cross and square term statistics a presented probability density function analysis shows that these terms have heavier tails than the observed samples indicating that robust combination methods should be utilized to avoid undue influence of outliers further analysis shows weighted median processing of polynomial terms is justified from a maximum likelihood perspective the established pwm filter class is statistically analyzed through the determination of the filter output distribution and breakdown probability filter parameter optimization procedures are also presented finally the effectiveness of pwm filters is demonstrated through simulations that include temporal spectrum and bispectrum analysis

the effect of median filtering on edge estimation and detection in this paper we consider the effect of median prefiltering on the subsequent estimation and detection of edges in digital images where possible a quantitative statistical comparison is made for a number of filters defined with two dimensional geometries in some cases one dimensional analyses are required to illustrate certain points noise images prefiltered by median filters defined with a variety of windowing geometries are used to support the analysis and it is found that median prefiltering improves the performance of both thresholding and zero crossing based edge detectors

median power and median correlation theory we show that the maximum likelihood ml estimate of location under the laplacian model which forms the basis for weighted median filters can be generalized to correlation estimates based on weighted medians much like linear sample correlations the resultant median correlation estimates have a surprisingly simple structure unlike linear correlations median correlations are robust to data contamination notably weights in this framework do not assume fixed values as with weighted median filters but take on random values determined by the underlying data itself the underlying parameters associated with the sample median correlations are obtained leading to well defined expressions that can be used in subspace based signal processing algorithms the properties of median correlations are illustrated through a number of simulations where the multiple signal classification music algorithm is applied on linear and median sample correlation matrices for real valued frequency estimation applications this paper thus unveils new and powerful capabilities of weighted medians for use in modern signal processing applications

streaking in median filtered images this paper presents a probabilistic analysis of the streaking or blotching effect commonly observed in median filtered signals in both one and two dimensions the effcts are identified as runs of equal or nearly equal values which create visual impressions that have no visual correlate for one dimensional discrete iid random signals with continuous input probability densities the probability of a streak of length l occurring is computed and shown to be independent of the input probability distribution expressions for the first and second moments of the streak length are also derived and certain asymptotic results are given as the analysis and definition of the analogous effect in two dimensions is less tractable the probability that medians taken from distinct overlapping windows will take the same value is derived for various filter geometries the analytic results are supported by examples using both one and two dimensional signals

computation of stability robustness bounds for state space models with structured uncertainty this paper makes two contributions related to computing a bound on the size of structured real parameter perturbations under which a nominally stable matrix remains stable first a more efficient method is presented for computing existing bounds requiring less time and storage than other methods the second contribution is a means of computing tighter bounds although at a higher computational cost