projective fourier analysis for patterns abstract identifying psl 2 c as a projective group for patterns in the conformal camera model the projective harmonic analysis on its double covering group sl 2 c is presented in the noncompact and compact pictures the pictures used to study different aspects of irreducible unitary representations of semisimple lie groups bypassing technicalities of representation theory but stressing the motivation and similarities with euclidean fourier analysis each constructed picture of the projective fourier analysis includes the fourier transform plancherel s theorem and convolution property projectively covariant characteristics of the analysis in the noncompact picture allow rendering any of image projective transformations of a pattern after removing conformal distortions by using only one projective fourier transform of the original pattern what is demonstrated in a computer simulation the convolution properties in both pictures must by used to develop algorithms for projectively invariant matching of patterns work in progress on fast algorithms for computing with projective fourier transforms and for rendering image projective transformations is discussed efficient computations of the convolutions would follow from the both fast projective fourier transforms and their inverses

a class of superrigid group von neumann algebras we prove that for any group g in a fairly large class of generalized wreath product groups the associated von neumann algebra lg completely remembers the group g more precisely if lg is isomorphic to the von neumann algebra l of an arbitrary countable group then must be isomorphic to g this represents the rst superrigidity result pertaining to group von neumann algebras

the undersampled discrete gabor transform conventional studies on discrete gabor transforms have generally been confined to the cases of critical sampling and oversampling in which the gabor families span the whole signal space in this paper we investigate undersampled discrete gabor transforms for an undersampled gabor triple g a b i e a spl middot b n we show that the associated generalized dual gabor window gdgw function is the same as the one associated with the oversampled g n b n a except for the constant factor ab n computations of undersampled gabor transforms are made possible by applying the methods algorithms developed in oversampled settings the undersampled gdgw is determined then we are able to obtain the best approximation of a signal x by linear combinations of vectors in the gabor family

complex multipole beam approach to acoustic scattering problems a novel approach to reducing the matrix size associated with the boundary element moment method solution of the problem of acoustic scattering from arbitrarily shaped closed bodies is presented in this paper the key step in this approach is to represent the scattered field in terms of a series of beams produced by multipole sources located in a complex space on the scatterer boundary the fields generated by these multipole sources resemble the gabor basis functions by utilizing the properties of the gabor series guidelines for selecting the orders as well as locations of the multipole sources are developed the present approach not only reduces the number of unknowns but also generates a generalized impedance matrix with a banded structure the accuracy of the proposed method is verified by using internal accuracy checks and by comparing the numerical results with the analytic solutions for spherical scatterers

a new implementation of the mellin transform and its application to radar classification of ships a modified mellin transform for digital implementation is developed and applied to range radar profiles of naval vessels the scale invariance property of the mellin transform provides a means for extracting features from the profiles which are insensitive to the aspect angle of the radar past implementations of the mellin transform based on the fft have required exponential sampling interpolation and the computation of a correction term all of which introduce errors into the transform in addition exponential sampling results in a factor of ln n increase in the number of data points an alternate implementation developed in the paper utilizes a direct expansion of the mellin integral definition this direct mellin transform dmt eliminates the implementation problems associated with the fft approach and does not increase the number of samples a scale and translation invariant transform is developed from a modification of the dmt the mdmt applied to the fft of the radar profiles results in the desired insensitivity without having the low pass filtering characteristic that exists in other fourier mellin implementations

orbit equivalence rigidity consider a countable group acting ergodically by measure p reserving transformations on a probability space x and let r be the corresponding orbit equivalence relation on x the following rigidity phenomenon is shown there exist group actions such that the equivalence relation r on x determines the group and the action x uniquely up to finite groups the natural action of sln z on the n torus r n z n for n 2 is one of such examples the interpretation of these results in the context of von neumann algebras provides some support to the conjecture of connes on rigidity of group algebras for groups with property t our rigidity results also give examples of countable equivalence relations of type ii1 which cannot be generated mod 0 by a free action of any group this gives a negative answer to a long standing problem of feldman and moore

decentralized sequential detection a class of decentralized sequential detection problems is investigated under appropriate independence assumptions it is shown that at each time instant the optimal local strategies are given by threshold tests on the likelihood of ratios furthermore local decisions depend not only on the present and past observations but on the past local decision as well that is for each local processor a different threshold exists for every different sequence of past decisions examples computational techniques discussions of the difficulties at hand and suggestions for further exploration of the problem are presented

efficient computation of gabor filter based multiresolution responses abstract multiresolution representation in machine vision systems provides a means to detect analyze and interpret the information content of an image at multiple resolutions the pyramidal representation of images suggested by burt and crowley and the hierarchical construction of orientation and velocity tuned filters developed by fleet and jepson are some of the examples for multiresolution representation of image details in recent years gabor filter based methods have been suggested by several researchers for machine vision applications such as edge detection texture classification and optical flow estimation these applications require generating a family of gabor filters tuned to several resolutions and orientations and computing their responses the computation of gabor filter responses at multiple resolutions and orientations is a very computationally intensive task two efficient schemes for computing gabor filter based multiresolution responses are proposed the first scheme namely recursive filtering method generates a family of gabor filters and their responses starting from a high resolution and proceeding towards the lowest resolution in steps of an octave the second approach namely successive sampling method generates the same responses in the reverse order in both these methods the symmetric asymmetric and wavelet nature of gabor filters are exploited in order to speed up the computation the applicability and usefulness of the schemes are established through experimental results special purpose architectures are proposed to implement the proposed techniques in hardware in order to further speed up the computation

a measurable group theoretic solution to von neumann s problem we give a positive answer in the measurable group theory context to von neumann s problem of knowing whether a non amenable countable discrete group contains a non cyclic free subgroup we also get an embedding result of the free group von neumann factor into restricted wreath product factors

mellin transform methods applied to integral evaluation taylor series and asymptotic approximations mellin transform methods have been used to obtain taylor series or asymptotic approximations to definite integrals whose integrands consist of the product of two generalized hypergeometric functions this approach has proved extremely useful in many applied physics problems including the analysis of electromagnetic propagation in a turbulent medium the main result in this article is a generalization of the method to integrands containing the product of an arbitrary number of hypergeometric functions providing a very powerful and general technique for integral evaluation with many applications in physics

the canonical coordinates method for pattern recognition ii isomorphisms with affine transformations abstract the canonical coordinates method for pattern recognition is extended conditions are examined for the existence of an isomorphism between a given deformation group and some affine transformation new invariants for many non linear deformations are derived several examples with real images are given

the canonical coordinates method for pattern deformation theoretical and computational considerations a method for the analysis of deformed patterns is presented and analyzed the image is transformed into a new set of coordinates in which the deformation has a particular simple form a number of deformations are considered the practical implementation of the method is discussed similar aspects of biological vision are also considered

orbit inequivalent actions for groups containing a copy of mathbb f _ 2 we prove that if a countable group contains a copy of mathbb f 2 then it admits uncountably many non orbit equivalent actions

rotation invariant texture classification using a complete space frequency model a method of rotation invariant texture classification based on a complete space frequency model is introduced a polar analytic form of a two dimensional 2 d gabor wavelet is developed and a multiresolution family of these wavelets is used to compute information conserving microfeatures from these microfeatures a micromodel which characterizes spatially localized amplitude frequency and directional behavior of the texture is formed the essential characteristics of a texture sample its macrofeatures are derived from the estimated selected parameters of the micromodel classification of texture samples is based on the macromodel derived from a rotation invariant subset of macrofeatures in experiments comparatively high correct classification rates were obtained using large sample sets

group cocycles and the ring of affiliated operators in this article we study cocycles of discrete countable groups with values in 2 g and the ring of affiliated operators ug we clarify properties of the first cohomology of a group g with coefficients in 2 g and answer several questions from de cornulier et al transform groups 13 1 125 147 2008 moreover we obtain strong results about the existence of free subgroups and the subgroup structure provided the group has a positive first 2 betti num ber we give numerous applications and examples of groups which satisfy our assumptions

perceptually uniform color spaces for color texture analysis an empirical evaluation rgb a nonuniform color space is almost universally accepted by the image processing community as the means for representing color on the other hand perceptually uniform spaces such as l a b as well as approximately uniform color spaces such as hsv exist in which measured color differences are proportional to the human perception of such differences this paper compares rgb with l a b and hsv in terms of their effectiveness in color texture analysis there has been a limited but increasing amount of work on the color aspects of textured images the results have shown that incorporating color into a texture analysis and recognition scheme can be very important and beneficial the presented methodology uses a family of gabor filters specially tuned to measure specific orientations and sizes within each color texture effectiveness is measured by the classification performance of each color space as well as by classifier independent measures experimental results are obtained with a variety of color texture images perceptually uniform spaces are shown to outperform rgb in many cases

some unique group measure space decomposition results using an approach emerging from the theory of closable deriva tions on von neumann algebras we exhibit a class of groups cr satisfying the following property given any groups 1 2 2 cr then any free ergodic measure preserving action on a probability space 1 2 y x gives rise to a von neumann algebra with unique group measure space cartan subalgebra pairing this result with popa s orbit equivalence superrigidity theorem we obtain new examples of w superrigid actions

analysis and synthesis of feedforward neural networks using discrete affine wavelet transformations a representation of a class of feedforward neural networks in terms of discrete affine wavelet transforms is developed it is shown that by appropriate grouping of terms feedforward neural networks with sigmoidal activation functions can be viewed as architectures which implement affine wavelet decompositions of mappings it is shown that the wavelet transform formalism provides a mathematical framework within which it is possible to perform both analysis and synthesis of feedforward networks for the purpose of analysis the wavelet formulation characterizes a class of mappings which can be implemented by feedforward networks as well as reveals an exact implementation of a given mapping in this class spatio spectral localization properties of wavelets can be exploited in synthesizing a feedforward network to perform a given approximation task two synthesis procedures based on spatio spectral localization that reduce the training problem to one of convex optimization are outlined

sequential and cooperative sensing for multi channel cognitive radios effective spectrum sensing is a critical prerequisite for multi channel cognitive radio cr networks where multiple spectrum bands are sensed to identify transmission opportunities while preventing interference to the primary users the present paper develops sequential spectrum sensing algorithms which explicitly take into account the sensing time overhead and optimize a performance metric capturing the effective average data rate of cr transmitters a constrained dynamic programming problem is formulated to obtain the policy that chooses the best time to stop taking measurements and the best set of channels to access for data transmission while adhering to hard collision constraints imposed to protect primary links given the associated lagrange multipliers the optimal access policy is obtained in closed form and the subsequent problem reduces to an optimal stopping problem a basis expansion based sub optimal strategy is employed to mitigate the prohibitive computational complexity of the optimal stopping policy a novel on line implementation based on the recursive least squares rls algorithm along with a stochastic dual update procedure is then developed to obviate the lengthy training phase of the batch scheme cooperative sequential sensing generalizations are also provided with either raw or quantized measurements collected at a central processing unit the numerical results presented verify the efficacy of the proposed algorithms

some oe and w rigidity results for actions by wreath product groups we use deformation rigidity theory in the von neumann algebra framework to study probability measure preserving actions by wreath product groups in particular we single out large families of wreath product groups satisfying various types of orbit equivalence oe rigidity for instance we show that whenever h k are icc property t groups such that h and k admit stably orbit equivalent action and such that h and k are ergodic then automatically is stably orbit equivalent to and h is stably orbit equivalent to k rigidity results for von neumann algebras arising from certain actions of such groups i e w rigidity results are also obtained

orbit equivalence rigidity and bounded cohomology we establish new results and introduce new methods in the theory of measurable orbit equivalence using bounded cohomology of group representations our rigidity statements hold for a wide uncountable class of groups arising from negative curvature geometry amongst our applications are a measurable mostow type rigidity theorems for products of negatively curved groups b prime factorization results for measure equivalence c superrigidity for orbit equivalence d the first examples of continua of type ii1 equivalence relations with trivial outer automorphism group that are mutually not stably isomorphic

encoding of correlated observations an important class of engineering problems involves sensing an environment and making estimates based on the phenomena sensed in the traditional model of this problem the sensors observations are available to the estimator without alteration there is growing interest in em distributed sensing systems in which several observations are communicated to the estimator over channels of limited capacity the observations must be separately encoded so that the target can be estimated with minimum distortion two questions are addressed for a special case of this problem wherein there are two sensors which observe noisy data and communicate with a single estimator 1 if the encoder is unlimited in complexity what communication rates and distortions can be achieved 2 if the encoder must be a quantizer a mapping of a single observation sample into a digital output how can it be designed for good performance the first question is treated by the techniques of information theory it is proved that a given combination of rates and distortion is achievable if there exist degraded versions of the observations that satisfy certain formulas the second question is treated by two approaches in the first the outputs of the quantizers undergo a second stage of encoding which exploits their correlation to reduce the output rate algorithms which design the second stage are presented and tested the second approach is based on the em distributional distance a measure of dissimilarity between two probability distributions an algorithm to modify a quantizer for increased distributional distance is derived and tested

form invariant linear filtering theory and applications the form invariant filters are by definition those shift variant filters such that their output for any given input turns out to be linearly scaled implying that its form does not change whenever the input is linearly scaled in this paper the most general classes of 1 d and 2 d linear form invariant filters are derived and their properties are discussed together with their implementation techniques two main implementation approaches are considered one based on the mellin transform the other on a combination of coordinate mappings and shift invariant filtering the paper also discusses the related works of other authors covering quite different fields such as optical pattern recognition image restoration and image reconstruction from projections radar signal processing etc it is shown that the mathematics of form invariant filtering provides a common framework if not a powerful unified approach to the many signal processing techniques spread in the above mentioned works and apparently different application areas the paper ends with a processing example showing the usefulness of form invariant filtering in a pattern recognition problem that is in the area where the most promising applications of such a filtering are foreseen

motion estimation in the 3 d gabor domain motion estimation methods can be broadly classified as being spatiotemporal or frequency domain in nature the gabor representation is an analysis framework providing localized frequency information when applied to image sequences the 3 d gabor representation displays spatiotemporal spatiotemporal frequency st stf information enabling the application of robust frequency domain methods with adjustable spatiotemporal resolution in this work the 3 d gabor representation is applied to motion analysis we demonstrate that piecewise uniform translational motion can be estimated by using a uniform translation motion model in the st stf domain the resulting motion estimation method exhibits both good spatiotemporal resolution and substantial noise resistance compared to existing spatiotemporal methods to form the basis of this model we derive the signature of the translational motion in the 3 d gabor domain finally to obtain higher spatiotemporal resolution for more complex motions a dense motion field estimation method is developed to find a motion estimate for every pixel in the sequence

a theory for invariant object recognition in the frontoparallel plane we suggest a new computational theory for position size and orientation invariant recognition of planar gray scale forms in frontoparallel view the theory employs a spatial frequency representation which approximates the complex logarithmic conformally mapped wigner distribution of a gray scale image our discussion emphasizes the theoretical significance method of computation and practical utility of this powerful new representation for image pattern recognition

w superrigidity for bernoulli actions of property t groups we consider group measure space 1 factors m l x arising from bernoulli actions of icc property t groups more generally of groups containing an infinite normal subgroup with the relative property t and prove a rigidity result for homomorphisms m overbar m we deduce that the action x is w superrigid i e if y is any free ergodic measure preserving action such that the factors m l x and m l y are isomorphic then the actions x and y must be conjugate moreover we show that if p m 1 is a projection then pmp does not admit a group measure space decomposition nor a group von neumann algebra decomposition the latter under the additional assumption that is torsion free we also prove a rigidity result for homomorphisms m m this time for in a larger class of groups than above now including products of non amenable groups for certain groups e g f 2 f 2 we deduce that m does not embed into pmp for any projection p m 1 and obtain a description of the endomorphism semigroup of m

on the structural theory of ii1 factors of negatively curved groups ii actions by product groups abstract this paper contains a series of structural results for von neumann algebras arising from measure preserving actions by product groups on probability spaces expanding upon the methods used earlier by the first two authors we obtain new examples of strongly solid factors as well as von neumann algebras with unique or no cartan subalgebra for instance we show that every ii 1 factor associated with a weakly amenable group in the class s of ozawa is strongly solid there is also the following product version of this result any maximal abelian subalgebra of any ii 1 factor associated with a finite product of weakly amenable groups in the class s of ozawa has an amenable normalizing algebra finally pairing some of these results with a cocycle superrigidity result of ioana it follows that compact actions by finite products of lattices in s p n 1 n 2 are virtually w superrigid

experiments on estimating egomotion and structure parameters using long monocular image sequences this paper presents a simple but robust model based approach to estimating the kinematics of a moving camera and the structure of the objects in a stationary environment using long noisy monocular image sequences both batch and recursive algorithms are presented and the problem due to occlusion is addressed the approach is based on representing the constant translational velocity and constant angular velocity of the camera motion using nine rectilinear motion parameters which are 3 d vectors of the position of the rotation center linear and angular velocities the structure parameters are 3 d coordinates of the salient feature points in the inertial coordinate system due to redundancies in parameterization the total number of independent parameters to be estimated is 3m 7 wherem is the number of feature points the image plane coordinates of these feature points in each frame are first detected and matched over the frames these noisy image coordinates serve as the input to our algorithms due to the nonlinear nature of perspective projection a nonlinear least squares method is formulated for the batch algorithm and a conjugate gradient method is then applied to find the solution a recursive method using an iterated extended kalman filter iekf for incremental estimation of motion and structure is also presented since the plant model is simple in our formulation closed form solutions for the state and covariance transition equations are easily derived experimental results for simulated imagery as well as several real image sequences are included

automatic surface inspection using wavelet reconstruction abstract in this paper we present a multiresolution approach for the inspection of local defects embedded in homogeneous textured surfaces the proposed method does not rely on the extraction of local textural features in a pixel by pixel basis it is based on an efficient image restoration scheme using the wavelet transforms by properly selecting the smooth subimage or the combination of detail subimages in different decomposition levels for backward wavelet transform the reconstructed image will remove regular repetitive texture patterns and enhance only local anomalies then a simple thresholding can be used to discriminate between defective regions and homogeneous regions in the reconstructed image this converts the difficult defect detection in complicated textured images into a simple binary thresholding in nontextured images effects of different wavelet bases the number of multiresolution levels the decomposed subimages used for reconstruction and the change in image rotation on defect detection are thoroughly evaluated and discussed based on the experiment on a variety of real textures including machined surfaces natural wood textile fabrics sandpaper and leather

wide band proportional bandwidth wigner ville analysis the wigner ville w v distribution is a time frequency representation that yields a highly accurate estimate of instantaneous frequency it is related to the narrow band ambiguity function by an internal transform and it can be used in a variety of detection and estimation problems a spectrogram constructed with constant bandwidth filters can be obtained by convolving two w v distributions or by forming a magnitude squared narrow band cross ambiguity function the wide band ambiguity function represents the doppler effect with dilation or compression rather than with frequency shift as in the narrow band approximation the q distributions a modified w v representation that is related to the wide band ambiguity function by an integral transform is defined a spectrogram constructed with proportional bandwidth or constant q filters can be obtained by a convolution like operation involving two q distributions or by forming a magnitude squared wide band cross ambiguity function the q distribution is thus a wide band version of the w v distribution properties of the q distribution indicate that it may prove useful for detection and parameter estimation as well as for tomographic measurement of wideband scattering functions with relatively few transmitted waveforms

unsupervised texture segmentation using gabor filters abstract this paper presents a texture segmentation algorithm inspired by the multi channel filtering theory for visual information processing in the early stages of human visual system the channels are characterized by a bank of gabor filters that nearly uniformly covers the spatial frequency domain and a systematic filter selection scheme is proposed which is based on reconstruction of the input image from the filtered images texture features are obtained by subjecting each selected filtered image to a nonlinear transformation and computing a measure of energy in a window around each pixel a square error clustering algorithm is then used to integrate the feature images and produce a segmentation a simple procedure to incorporate spatial information in the clustering process is proposed a relative index is used to estimate the true number of texture categories

recognition of distorted patterns by invariance kernels abstract a novel method for the recognition of deformed patterns is presented it is shown that for planar deformations generated by lie transformation groups there exist kernels such that the associated integral transforms are invariant under the deformations many examples of deformations and the corresponding kernels are given

l 2 rigidity in von neumann algebras we introduce the notion of l2 rigidity for von neumann algebras a generalization of property t which can be viewed as an analogue for the vanishing of 1 cohomology into the left regular representation of a group we show that l2 rigidity passes to normalizers and is satisfied by nonamenable ii1 factors which are non prime have property or are weakly rigid as a consequence we obtain that if m is a free product of diffuse von neumann algebras or if m l where is a finitely generated group with 1 2 0 then any nonamenable regular subfactor of m is prime and does not have properties or t in particular this gives a new approach for showing solidity for a free group factor thus recovering a well known recent result of n ozawa

one cohomology and the uniqueness of the group measure space decomposition of a ii1 factor we provide a unified and self contained treatment of several of the recent uniqueness theorems for the group measure space decomposition of a ii1 factor we single out a large class of groups characterized by a one cohomology property and prove that for every free ergodic probability measure preserving action of the associated ii1 factor has a unique group measure space cartan subalgebra up to unitary conjugacy our methods follow closely a recent article of chifan peterson but we replace the usage of peterson s unbounded derivations by thomas sinclair s dilation into a malleable deformation by a one parameter group of automorphisms

measure equivalence rigidity of the mapping class group we show that the mapping class group of a compact orientable surface with higher complexity satisfies the following rigidity in the sense of measure equivalence if the mapping class group is measure equivalent to a discrete group then they are commensurable up to finite kernels moreover we describe all locally compact second countable groups containing a lattice isomorphic to the mapping class group we obtain similar results for finite direct products of mapping class groups

gromov s measure equivalence and rigidity of higher rank lattices in this paper the notion of measure equivalence me of countable groups is studied me was introduced by gromov as a measure theoretic analog of quasi isometries all lattices in the same locally compact group are measure equivalent this is one of the motivations for this notion the main result of this paper is me rigidity of higher rank lattices any countable group which is me to a lattice in a simple lie group g of higher rank is commensurable to a lattice in g

distributed structures sequential optimization and quantization for detection in the design of distributed quantization systems one inevitably confronts two types of constraints those imposed by a distributed system s structure and those imposed by how the distributed system is optimized structural constraints are inherent properties of any distributed quantization system and are normally summarized by functional relationships defining the inputs and outputs of their component quantizers the use of suboptimal optimization methods are often necessitated by the computational complexity encountered in distributed problems this correspondence briefly explores the impact and interplay of these two types of constraints in the context of distributed quantization for detection we introduce two structures that exploit interquantizer communications and that represent extremes in terms of their structural constraints we then develop a sequential optimization scheme that maximizes the kullback leibler divergence takes advantage of statistical dependencies in the distributed system s output variables and leads to simple parameterizations of the component quantization rules we present an illustrative example from which we draw insights into how these constraints influence the quantization boundaries and affect performance relative to lower and upper bounds

oversampling in the gabor scheme a method for calculating the coefficients of the gabor expansion in the case of oversampling is presented the method is based on the concept of frames and utilizes the zak transform as such the zak transform highlights the meaning and importance of frames in the context of oversampling and other aspects of signal representation by means of nonorthogonal bases

w superrigidity for arbitrary actions of central quotients of braid groups for any n geqslant 4 let tilde b n b n z b n be the quotient of the braid group b n through its center we prove that any free ergodic probability measure preserving pmp action tilde b n curvearrowright x mu is virtually hbox w superrigid in the following sense if l infty x rtimes tilde b n cong l infty y rtimes lambda for an arbitrary free ergodic pmp action lambda curvearrowright y nu then the actions tilde b n curvearrowright x lambda curvearrowright y are virtually conjugate moreover we prove that the same holds if tilde b n is replaced with a finite index subgroup of the direct product tilde b n 1 times cdots times tilde b n k for some n 1 ldots n k geqslant 4 the proof uses the dichotomy theorem for normalizers inside crossed products by free groups from popa and vaes 212 141 198 2014 in combination with the oe superrigidity theorem for actions of mapping class groups from kida 131 99 109 2008 similar techniques allow us to prove that if a group gamma is hyperbolic relative to a finite family of proper finitely generated residually finite infinite subgroups then the hbox ii 1 factor l infty x rtimes gamma has a unique cartan subalgebra up to unitary conjugacy for any free ergodic pmp action gamma curvearrowright x mu

bargmann transform zak transform and coherent states it is well known that completeness properties of sets of coherent states associated with lattices in the phase plane can be proved by using the bargmann representation or by using the kq representation which was introduced by j zak in this paper both methods are considered in particular in connection with expansions of generalized functions in what are called gabor series the setting consists of two spaces of generalized functions tempered distributions and elements of the class s which appear in a natural way in the context of the bargmann transform also a thorough mathematical investigation of the zak transform is given this paper contains many comments and complements on existing literature in particular connections with the theory of interpolation of entire functions over the gaussian integers are given

a class of ii1 factors with many non conjugate cartan subalgebras abstract we construct a class of ii 1 factors m that admit unclassifiably many cartan subalgebras in the sense that the equivalence relation of being conjugate by an automorphism of m is complete analytic in particular non borel we also construct a ii 1 factor that admits uncountably many non isomorphic group measure space decompositions all involving the same group g so g is a group that admits uncountably many non stably orbit equivalent actions whose crossed product ii 1 factors are all isomorphic

computationally attractive real gabor transforms we present a gabor transform for real discrete signals and present a computationally attractive method for computing the transform for the critically sampled case we derive a biorthogonal function which is very localized in the time domain therefore truncation of this biorthogonal function allows us to compute approximate expansion coefficients with significantly reduced computational requirements further truncation does not degrade the numerical stability of the transform we present a tight upper bound on the reconstruction error incurred due to use of a truncated biorthogonal function and summarize computational savings for example the expense of transforming a length 2048 signal using length 16 blocks is reduced by a factor of 26 over similar fft based methods with at most 0 04 squared error in the reconstruction

gabor filter based edge detection abstract it is common practice to utilize evidence from biological and psychological vision experiments to develop computational models for low level feature extraction the receptive profiles of simple cells in mammalian visual systems have been found to closely resemble gabor filters daugman proved that gabor filters achieve joint minimal joint uncertainty these results led researchers to develop computational models based on gabor filters for several low level vision applications such as edge detection texture classification optical flow estimation and data compression in this paper the performance of a gabor odd filter based edge detector is investigated using the measures proposed by canny based on this performance analysis a design criterion for one dimensional 1d gabor filter based edge detector is derived it is shown that this design criterion also holds good for a two dimensional 2d gabor filter based edge detector experimental results are presented to demonstrate the performance of the gabor filter based edge detector

unique cartan decomposition for ii1 factors arising from arbitrary actions of free groups we prove that for any free ergodic probability measure preserving action mathbb f n curvearrowright x mu of a free group on n generators mathbb f n 2 leq n leq infty the associated group measure space ii1 factor l infty x rtimes mathbb f n has l x as its unique cartan subalgebra up to unitary conjugacy we deduce that group measure space ii1 factors arising from actions of free groups with different number of generators are never isomorphic we actually prove unique cartan decomposition results for ii1 factors arising from arbitrary actions of a much larger family of groups including all free products of amenable groups and their direct products

multipliers of the fourier algebras of some simple lie groups and their discrete subgroups for any amenable locally compact group g the space of multipliers ma g of the fourier algebra a g coincides with the space b g of functions on g that are linear combinations of continuous positive definite functions we prove that ma g b g 0 for many non amenable connected groups more specifically we prove that moa g b g 0 for the classical complex lie groups and the general lorentz groups soo n 1 n 2 moa g is a certain subspace of ma g which we call the space of completely bounded multipliers of a g unlike ma g the space moa g has nice stability properties with respect to direct products of groups it is known that the fourier algebra of the free group on n generators n 2 2 admits an unbounded approximate unit pn which is bounded in the multiplier norm we extend this result to any closed subgroup of the general lorentz group soo n 1 moreover we show that for these groups pn can be chosen to be bounded with respect to the moa g norm by a duality argument we obtain that the reduced c algebra of every discrete subgroup of soo n 1 has the completely bounded approximation property in particular this property holds for c f2 the reduced c algebra of the free group on two generators we also prove

sequential scalar quantization of vectors an analysis proposes an efficient vector quantization vq technique called sequential scalar quantization ssq the scalar components of the vector are individually quantized in a sequence with the quantization of each component utilizing conditional information from the quantization of previous components unlike conventional independent scalar quantization isq ssq has the ability to exploit intercomponent correlation at the same time since quantization is performed on scalar rather than vector variables ssq offers a significant computational advantage over conventional vq techniques and is easily amenable to a hardware implementation in order to analyze the performance of ssq the authors appeal to asymptotic quantization theory where the codebook size is assumed to be large closed form expressions are derived for the quantizer mean squared error mse these expressions are used to compare the asymptotic performance of ssq with other vq techniques the authors also demonstrate the use of asymptotic theory in designing ssq for a practical application color image quantization where the codebook size is typically small theoretical and experimental results show that ssq far outperforms isq with respect to mse while offering a considerable reduction in computation over conventional vq at the expense of a moderate increase in mse

wave propagation and sampling theory part ii sampling theory and complex waves morlet et al 1982 this issue showed the advantages of using complex values for both waves and characteristics of the media we simulated the theoretical tools we present here using the goupillaud kunetz algorithm now we present sampling methods for complex signals or traces corresponding to received waves and sampling methods for complex characterization of multilayered or heterogeneous media regarding the complex signals we present a twodimecsional 2 d method of sampling in the time frequency domain using a special or extended gabor expansion on a set of basic wavelets adapted to phase preservation such a 2 d expansion permits us to handle in a proper manner instantaneous frequency spectra we show the differences between wavelet resolution and sampling grid resolution we also show the importance of phase preservation in high resolution seismic regarding the media we show how analytical studies of wave propagation in periodic structured layers could help when trying to characterize the physical properties of the layers and their large scale granularity as a result of complex deconvolution analytical studies of wave propagation in periodic structures are well known in solid state physics and lead to the so called bloch waves the introduction of complex waves leads to replacing the classical wave equation by a schriidinger equation finally we show that complex wave equations gabor expansion and bloch waves are three different ways of introducing the tools of quantum mechanics in highresolution seismic gabor 1946 kittel 1976 morlet 1975 and conversely the goupillaud kunetz algorithm and an extended gabor expansion may be of some use in solid state physics

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

measure equivalence rigidity and bi exactness of groups we get three types of results on measurable group theory direct product groups of ozawa s class s groups wreath product groups and amalgamated free products we prove measure equivalence factorization results on direct product groups of ozawa s class s groups as consequences monod shalom type orbit equivalence rigidity theorems follow we prove that if two wreath product groups a g b of non amenable exact direct product groups g with amenable bases a b are measure equivalent then g and are measure equivalent we get bass serre rigidity results on amalgamated free products of non amenable exact direct product groups

cocycle superrigidity and bounded cohomology for negatively curved spaces we introduce new techniques to extend superrigidity theory beyond the scope of lie or algebraic groups we construct a cohomological invariant which accounts for and generalizes all known superrigidity results for actions on negatively curved spaces together with a new vanishing result and the machinery of bounded cohomology this enables us to prove a general superrigidity theorem for actions of irreducible lattices on spaces of negative curvature we also prove a cocycle version a la zimmer

wave propagation and sampling theory part i complex signal and scattering in multilayered media from experimental studies in digital processing of seismic reflection data geophysicists know that a seismic signal does vary in amplitude shape frequency and phase versus propagation time to enhance the resolution of the seismic reflection method we must investigate these variations in more detail we present quantitative results of theoretical studies on propagation of plane waves for normal incidence through perfectly elastic multilayered media as wavelet shapes we use zero phase cosine wavelets modulated by a gaussian envelope and the corresponding complex wavelets a finite set of such wavelets for an appropriate sampling of the frequency domain may be taken as the basic wavelets for a gabor expansion of any signal or trace in a two dimensional 2 d domain time and frequency we can then compute the wave propagation using complex functions and thereby obtain quantitative results including energy and phase of the propagating signals these results appear as complex 2 d functions of time and frequency i e as instantaneous frequency spectra choosing a constant sampling rate on the logarithmic scale in the frequency domain leads to an appropriate sampling method for phase preservation of the complex signals or traces for this purpose we developed a gabor expansion involving basic wavelets with a constant time duration mean period ratio for layered media as found in sedimentary basins

a joint frequency position domain structure identification of nonlinear discrete time systems by neural networks a new technique is proposed to identify the structure and the parameters of nonlinear discrete time system models the structure is represented in a frequency position domain of gabor basis functions gbfs a simplification to the gbf is also presented where the spatial gaussian envelope of gbf is replaced with a triangular one a modification to the gbf has also been introduced in order to suppress the effects of noise on the procedure a three layered neural network augmented with nonuniform sampling is described for solving the system identification problem

a unified approach to boundary perception edges textures and illusory contours a model consisting of a multistage system which extracts and groups salient features in the image at different spatial scales or frequencies is used in the first stage a gabor wavelet decomposition provides a representation of the image which is orientation selective and has optimal localization properties in space and frequency this decomposition is useful in detecting significant features such as step and line edges at different scales and orientations in the image following the wavelet transformation local competitive interactions are introduced to reduce the effects of noise and changes in illumination interscale interactions help in localizing the line ends and corners and play a crucial role in boundary perception the final stage groups similar features aiding in boundary completion the different stages can be identified with processing by simple complex and hypercomplex cells in the visual cortex of mammals experimental results demonstrate the performance of this model in detecting boundaries both real and illusory in real and synthetic images

gaussian networks for direct adaptive control a direct adaptive tracking control architecture is proposed and evaluated for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible the architecture uses a network of gaussian radial basis functions to adaptively compensate for the plant nonlinearities under mild assumptions about the degree of smoothness exhibit by the nonlinear functions the algorithm is proven to be globally stable with tracking errors converging to a neighborhood of zero a constructive procedure is detailed which directly translates the assumed smoothness properties of the nonlinearities involved into a specification of the network required to represent the plant to a chosen degree of accuracy a stable weight adjustment mechanism is determined using lyapunov theory the network construction and performance of the resulting controller are illustrated through simulations with example systems

on the superrigidity of malleable actions with spectral gap some of the most interesting aspects of the dynamics of measure preserving actions of countable groups on probability spaces v rx x are revealed by the study of group measure space von neumann algebras l x x t mvnl and the classification of actions up to orbit equivalence oe i e up to isomorphism of probability spaces carrying the orbits of actions onto each other although one is in von neumann algebras and the other in ergodic theory the two problems are closely related as an oe of actions v rx x a rxy has been shown to implement an algebra isomorphism l x x t l y x a taking l x onto l y and vice versa si dy fm in particular the isomorphism class of l x xi t only depends on the equivalence relation 7 r t gt 1t x g t thus von neumann equivalence vne of group actions requiring isomorphism of their group measure space algebras is weaker than oe since there are exam ples of non oe actions whose associated von neumann algebras are all isomorphic cj1 it is in general strictly weaker on the other hand oe is manifestly weaker than classical conjugacy which for free actions r rx x a rx y requires isomor phism of probability spaces a x p y v satisfying ar a 1 a so in particular r a how much weaker vne and oe can be with respect to conju gacy is best seen in the amenable case where by a celebrated theorem of connes all free ergodic actions of all infinite amenable groups give rise to the same hi factor cl and by dy ow cfw they are undistinguishable under oe as well also any embedding of algebras l x xi t c l y x a with a amenable forces t to be amenable but the non amenable case is extremely complex and for many years progress has been slow mvn2 dy me c2 cw sc even after the discovery of the first rigidity phenomena by connes in von neumann algebras c3 c4 and by zimmer in oe ergodic theory zi z2 this changed dramatically over the last 7 8 years with the advent of a variety of striking rigidity results ful gl g2 mosh h hk p1 p8 see p9 for a survey also sh for a survey on oe rigidity our aim in this paper is to investigate the most extreme such phenomena called strong rigidity which show that for certain classes of source group actions

the generalized gabor scheme of image representation in biological and machine vision a scheme suitable for visual information representation in a combined frequency position space is investigated through image decomposition into a finite set of two dimensional gabor elementary functions gef the scheme is generalized to account for the position dependent gabor sampling rate oversampling logarithmic frequency scaling and phase quantization characteristic of the visual system comparison of reconstructed signal highlights the advantages of the generalized gabor scheme in coding typical bandlimited images it is shown that there exists a tradeoff between the number of frequency components used per position and the number of such clusters sampling rate utilized along the spatial coordinate

oe and w superrigidity results for actions by surface braid groups we show that several important normal subgroups of the mapping class group of a surface satisfy the following property any free ergodic probability measure preserving action y x is stablyoe superrigid these include the central quotients of most surface braid groups and most torelli groups and johnson kernels in addition we show that all these groups satisfy the measure equivalence rigidity and we describe all their lattice embeddings using these results in combination with previous results from cik13 we deduce that any free ergodic probabilitymeasure preserving action of almost any surface braid group is stablyw superrigid i e it can be completely reconstructed from its vonneumann algebra

on image analysis by the methods of moments various types of moments have been used to recognize image patterns in a number of applications a number of moments are evaluated and some fundamental questions are addressed such as image representation ability noise sensitivity and information redundancy moments considered include regular moments legendre moments zernike moments pseudo zernike moments rotational moments and complex moments properties of these moments are examined in detail and the interrelationships among them are discussed both theoretical and experimental results are presented

invariant pattern recognition using the rfm descriptor a pattern descriptor invariant to rotation scaling translation rst and robust to additive noise is proposed by using the radon fourier and mellin transforms the radon transform converts the rst transformations applied on a pattern image into transformations in the radial and angular coordinates of the pattern s radon image these beneficial properties of the radon transform make it an useful intermediate representation for the extraction of invariant features from pattern images for the purpose of indexing matching in this paper invariance to rst is obtained by applying the 1d fourier mellin and discrete fourier transforms on the radial and angular coordinates of the pattern s radon image respectively the implementation of the proposed descriptor is reasonably fast and correct based mainly on the fusion of the radon and fourier transforms and on a modification of the mellin transform theoretical arguments validate the robustness of the proposed descriptor to additive noise and empirical evidence on both occlusion deformation and noisy datasets shows its effectiveness

orthogonalization of circular stationary vector sequences and its application to the gabor decomposition certain vector sequences in hermitian or in hilbert spaces can be orthogonalized by a fourier transform in the finite dimensional case the discrete fourier transform dft accomplishes the orthogonalization the property of a vector sequence which allows the orthogonalization of the sequence by the dft called circular stationarity cs is discussed in this paper applying the dft to a given cs vector sequence results in an orthogonal vector sequence which has the same span as the original one in order to obtain coefficients of the decomposition of a vector upon a particular nonorthogonal cs vector sequence the decomposition is first found upon the equivalent dft orthogonalized one and then the required coefficients are found through the dft it is shown that the sequence of discrete gabor 1946 basis functions with periodic kernel and with a certain inner product on the space of n periodic discrete functions satisfies the cs condition the theory of decomposition upon cs vector sequences is then applied to the gabor basis functions to produce a fast algorithm for calculation of the gabor coefficients

extremal properties of likelihood ratio quantizers m hypotheses and a random variable y with a different probability distribution under each hypothesis are considered a quantizer is applied to form a quantized random variable gamma y the extreme points of the set of possible probability distributions of gamma y as gamma ranges over all quantizers is characterized optimality properties of likelihood ratio quantizers are established for a very broad class of quantization problems including problems involving the maximization of an ali silvey 1966 distance measure and the neyman pearson variant of the decentralized detection problem

an fft based technique for translation rotation and scale invariant image registration this correspondence discusses an extension of the well known phase correlation technique to cover translation rotation and scaling fourier scaling properties and fourier rotational properties are used to find scale and rotational movement the phase correlation technique determines the translational movement this method shows excellent robustness against random noise

compact actions and uniqueness of the group measure space decomposition of ii1 factors abstract we prove that any ii1 factor l x arising from a compact free ergodic probability measure preserving action of a countable group with positive first l 2 betti number 1 2 0 has a unique group measure space cartan subalgebra up to unitary conjugacy

analysis of multichannel narrow band filters for image texture segmentation a model for texture analysis and segmentation using multiple oriented channel filters is analyzed in the general framework several different arguments are applied leading to the conclusion that the two dimensional gabor filters possess strong optimality properties for this task properties of the multiple channel segmentation approach are analyzed in particular perturbations of textures from an ideal model are found to have important effects on the segmentation that can usually be ameliorated by simply preceding the segmentation process by a logarithmic operation and using a low pass postfilter prior to making region assignments the difficult problems of space variant textures and multiple component textures are also considered local spatial frequency estimation approaches are suggested that use the responses as constraints in estimating the locally emergent texture frequencies complex texture aggregates containing multiple shared frequency components can be analyzed if the textures are distinct and few in number

quantization for decentralized hypothesis testing under communication constraints in a decentralized hypothesis testing network several peripheral nodes observe an environment and communicate their observations to a central node for the final decision the presence of capacity constraints introduces theoretical and practical problems the following problem is addressed given that the peripheral encoders that satisfy these constraints are scalar quantizers how should they be designed in order that the central test to be performed on their output indices is most powerful the scheme is called cooperative design separate encoding since the quantizers process separate observations but have a common goal they seek to maximize a system wide performance measure the bhattacharyya distance of the joint index space as such a criterion is suggested and a design algorithm to optimize arbitrarily many quantizers cyclically is proposed a simplified version of the algorithm namely an independent design separate encoding scheme where the correlation is either absent or neglected for the sake of simplicity is outlined performances are compared through worked examples

an image representation algorithm compatible with neural associative processor based hardware recognition systems a robust image representation algorithm compatible with the vlsi matching engine based image recognition system has been developed the spatial distributions of four principal direction edges in a 64 spl times 64 pels gray scale image are coded to form a 64 dimension feature vector since the 2d edge information is reduced to a feature vector by projecting edge flags to the principal directions it is named the projected principal edge distribution pped representation the pped vectors very well preserve the human perception of similarity among images in the vector space while achieving a substantial dimensionality reduction in the image data the pped algorithm has been applied to medical radiograph analysis which was taken as a test vehicle for algorithm optimization the robust nature of the pped representation has been confirmed by the recognition results comparable to the diagnosis by experts having several years of experience in a university hospital dedicated digital vlsi circuits have been developed for pped vector generation in order to expedite the processing a test hardware recognition system was constructed using the vector generation circuits where the analog neural associative processor chip developed in a separate project was employed as a vector matching engine as a result a successful medical radiograph analysis has been experimentally demonstrated using the hardware system feasibility of a very low power operation of the system has been also demonstrated

nonuniform image representation in area of interest systems this paper is concerned with image representation by data distributed nonuniformly and in particular with a representation scheme suitable for area of interest imaging the class of signals under consideration whose information density varies with position can be represented according to a nonuniform sampling scheme position varying projection operators are presented as simple low pass filtering operations in a fourier like domain sequential projections are used for pyramidal representation of nonuniformly sampled images it is shown that irregular random sampling prevents under certain mild restrictions aliasing effects

strong solidity of group factors from lattices in so n 1 and su n 1 abstract we show that the group factors l where is an icc lattice in either so n 1 or su n 1 n 2 are strongly solid in the sense of ozawa and popa 2010 13 this strengthens a result of ozawa and popa 2010 14 showing that these factors do not have cartan subalgebras