morphological shape decomposition a technique for decomposing a binary shape into a union of simple binary shapes is presented the decomposition is shown to be unique and invariant to translation rotation and scaling the techniques used in the decomposition are based on mathematical morphology the shape description produced can be used in object recognition and in binary image coding

morphological decomposition of 2 d binary shapes into modestly overlapped octagonal and disk components one problem with several leading morphological shape representation algorithms is the heavy overlapping among the representative disks of the same size a shape component formed by grouping connected disk centers may use many heavily overlapping disks to represent a simple shape part sometimes these representative disks form complicated structures a generalized skeleton transform was recently introduced which allows a shape to be represented as a collection of modestly overlapped octagonal shape parts however the generalized skeleton transform needs to be applied many times furthermore an octagonal component is not easily matched up with another octagonal component in this paper we describe a octagon fitting algorithm which identifies a special maximal octagon for each image point in a given shape this transform leads to the development of two new shape decomposition algorithms these algorithms are more efficient to implement the octagon fitting algorithm only needs to be applied once the components generated are better characterized mathematically the disk components used in the second decomposition algorithm are more primitive than octagons and easily matched up with other disk components from another shape the experiments show that the new decomposition algorithms produce as efficient representations as the old algorithm for both exact and approximate cases a simple shape matching algorithm using disk components is also demonstrated

simultaneous adaptive control and identification via the weighted least square algorithm in this note we prove the almost sure convergence of the proposed adaptive control and identification algorithms involving a weighted least square parameter estimator the analysis presented here strengthens the previous results achieved in this context the proposed algorithm and the analysis achieve the convergence of the tracking error in a strong sense at an asymptotically arithmetic rate the stronger result is obtained under a regularity and persistency condition introduced in this note which also ensures that with probability one the algorithm affords equal weighting to all the measurements after a finite number of iterations under these conditions it is also shown that the parameter estimation error also converges to zero in the context of siso armax models it is proved that the regularity and persistency conditions are satisfied under mild mixing conditions on the noise and no pole zero cancellation in the plant input output transfer function by a random perturbation of the reference trajectory

converses for secret key agreement and secure computing we consider information theoretic secret key sk agreement and secure function computation by multiple parties observing correlated data with access to an interactive public communication channel our main result is an upper bound on the sk length which is derived using a reduction of binary hypothesis testing to multiparty sk agreement building on this basic result we derive new converses for multiparty sk agreement furthermore we derive converse results for the oblivious transfer problem and the bit commitment problem by relating them to sk agreement finally we derive a necessary condition for the feasibility of secure computation by trusted parties that seek to compute a function of their collective data using an interactive public communication that by itself does not give away the value of the function in many cases we strengthen and improve upon previously known converse bounds our results are single shot and use only the given joint distribution of the correlated observations for the case when the correlated observations consist of independent and identically distributed in time sequences we derive strong versions of previously known converses

morphological decomposition of 2 d binary shapes into conditionally maximal convex polygons mathematical morphology is an approach to image analysis based on the geometric concept of shape and size naturally it provides a very effective tool for shape analysis in this paper we present a morphological shape segmentation algorithm that decomposes a 2 d two dimensional binary shape into a collection of restricted convex polygons we use simple morphological operations to extract shape information from different skeleton subsets to form a group of conditionally maximal convex polygonal shape components then a set of more meaningful and natural convex polygonal components are constructed from these maximal components the resulting algorithm is very simple and the decomposition is always unique the components produced have well defined mathematical characterizations and they seem to be in good agreement with the nature structures of the given shapes the shape segments produced can be used to construct structural shape description and for other shape analysis purposes

a generalized discrete morphological skeleton transform with multiple structuring elements for the extraction of structural shape components a common problem shared by several leading morphological shape representation algorithms is that there is much overlapping among the representative disks of the same size a shape component represented by a group of connected disk centers sometimes uses many heavily overlapping representative disks to represent a relatively simple shape part a shape component may also contain a large number of representative disks that form a complicated structure we introduce a generalized discrete morphological skeleton transform that uses eight structuring elements to generate skeleton subsets so that no two skeletal points from the same skeleton subset are adjacent to each other each skeletal point represents a shape part that is in general an octagon with four pairs of parallel opposing sides the number of representative points needed to represent a given shape is significantly lower than that in the standard skeleton transform a collection of shape components needed to build a structural representation is easily derived from the generalized skeleton transform each shape component covers a significant area of the given shape and severe overlapping is avoided the given shape can also be accurately approximated using a small number of shape components

skeleton based morphological coding of binary images this paper presents new properties of the discrete morphological skeleton representation of binary images along with a novel coding scheme for lossless binary image compression that is based on these properties following a short review of the theoretical background two sets of new properties of the discrete morphological skeleton representation of binary images are proved the first one leads to the conclusion that only the radii of skeleton points belonging to a subset of the ultimate erosions are needed for perfect reconstruction this corresponds to a lossless sampling of the quench function the second set of new properties is related to deterministic prediction of skeletonal information in a progressive transmission scheme based on the new properties a novel coding scheme for binary images is presented the proposed scheme is suitable for progressive transmission and fast implementation computer simulations also presented show that the proposed coding scheme substantially improves the results obtained by previous skeleton based coders and performs better than classical coders including run length huffman quadtree and chain coders for facsimile images its performance can be placed between the modified read mr method k 4 and modified modified read mmr method

morphological reversible contour representation in this paper a novel morphological reversible contour representation of discrete binary images is proposed a binary image is represented by a set of nonoverlapping multilevel contours and a residual image in this proposed representation the total number of pixels representing an image is far less than the total number of pixels obtained by the seed based morphological contour skeleton lossless representation the proposed contour representation is simple unique and general without restrictions on the binary image to be represented the resulting multicontour image component is robust to noise an efficient differential chain contour coding scheme is employed to further compress the represented image the proposed method yields very low bit rates compared to the existing morphological techniques an automatic filling procedure which properly fills a proper multicontour image according to its topological structure without need of seed points is proposed

discrete time stochastic adaptive control this paper establishes global convergence of a stochastic adaptive control algorithm for discrete time linear systems it is shown that with probability one the algorithm will ensure the system inputs and outputs are sample mean square bounded and the conditional mean square output tracking error achieves its global minimum possible value for linear feedback control thus asymptotically the adaptive control algorithm achieves the same performance as could be achieved if the system parameters were known

adaptive control with recursive identification for stochastic linear systems this paper presents a stochastic adaptive control algorithm which is shown to possess the following properties when applied to a possibly unstable inverse stable linear stochastic system with unknown parameters whenever that system satisfies a certain positive real condition on its moving average noise dynamics 1 the adaptive control part of the algorithm stabilizes and asymptotically optimizes the behavior of the system in the sense that the limit of the sample mean square variation of the output around a given demand level equals that of a minimum variance control strategy implemented with known parameters this optimal behavior is subject to an offset 2where 2is the variance of a dither signal added to the control action in order to produce a continually disturbed control for mu 2 0 it is shown that the input output process satisfies a persistent excitation property and hence subject to a simple identifiability condition the next property holds 2 the observed input and output of the controlled system may be taken as inputs to an approximate maximum likelihood algorithm aml which generates strongly consistent estimates of the system s parameters results are presented for the scalar and multivariable cases

on the decomposition of binary shapes into meaningful parts abstract a novel decomposition scheme for binary shapes is proposed based on a newly developed notion of maximal approximately convex subpart macs macss are first derived from concepts of integral geometry and it is argued that macss are the simplest possible constituents of a decomposition an algorithm is developed that utilizes the notion of macss to achieve a decomposition into possibly overlapping parts the developed algorithm is based on concepts of mathematical morphology which have been extended by an elongation and a fattening operation the validity of the chosen approach is shown by applying it to several examples synthetic as well as real objects thus corroborating as well the validity of the initial concept of macss

empirical distribution of good channel codes with nonvanishing error probability this paper studies several properties of channel codes that approach the fundamental limits of a given discrete or gaussian memoryless channel with a nonvanishing probability of error the output distribution induced by an capacity achieving code is shown to be close in a strong sense to the capacity achieving output distribution relying on the concentration of measure isoperimetry property enjoyed by the latter it is shown that regular lipschitz functions of channel outputs can be precisely estimated and turn out to be essentially nonrandom and independent of the actual code it is also shown that the output distribution of a good code and the capacity achieving one cannot be distinguished with exponential reliability the random process produced at the output of the channel is shown to satisfy the asymptotic equipartition property

efficient morphological shape representation mathematical morphology is well suited to capturing geometric information hence morphology based approaches have been popular for object shape representation the two primary morphology based approaches the morphological skeleton and the morphological shape decomposition msd each represent an object as a collection of disjoint sets a practical shape representation scheme though should give a representation that is computationally efficient to use unfortunately little work has been done for the morphological skeleton and the msd to address efficiency we propose a flexible search based shape representation scheme that typically gives more efficient representations than the morphological skeleton and msd our method decomposes an object into a number of simple components based on homothetics of a set of structuring elements to form the representation the components are combined using set union and set difference operations we use three constituent component types and a thorough cost based search strategy to find efficient representations we also consider allowing object representation error which may yield even more efficient representations

a generalized morphological skeleton transform using both internal and external skeleton points the morphological skeleton transform mst is a leading morphological shape representation scheme in the mst a given shape is represented as the union of all the maximal disks contained in the shape the concept of external skeleton points and external maximal disks has been used for shape description and characterization purposes in this paper we develop a generalized morphological skeleton transform that combines the concepts of internal and external maximal disks into a unified framework in this framework a shape is described in terms of disk components that need to be added as well as disk components that need to be removed the procedures and formulae describing the extraction of the disk components and the reconstruction of the original shape from these components are developed the correctness of the procedures and formulae is established this new framework seems to provide a more powerful and more natural way of modeling the approximation and reconstruction of binary shapes using primitive shape components

a new shape decomposition scheme for graph based representation nowadays the part based representation of a given shape plays a significant role in shape related applications such as those involving content based retrieval object recognition and so on in this paper to represent both 2 d and 3 d shapes as a relational structure i e a graph a new shape decomposition scheme which recursively performs constrained morphological decomposition cmd is proposed the cmd method adopts the use of the opening operation with the ball shaped structuring element and weighted convexity to select the optimal decomposition for the sake of providing a compact representation the merging criterion is applied using the weighted convexity difference therefore the proposed scheme uses the split and merge approach finally we present experimental results for various modified 2 d shapes as well as 3 d shapes represented by triangular meshes based on the experimental results it is believed that the decomposition of a given shape coincides with that based on human insight for both 2 d and 3 d shapes and also provides robustness to scaling rotation noise shape deformation and occlusion

efficient morphological shape representation with overlapping disk components this paper proposes a new morphological shape representation algorithm in which a two dimensional 2 d binary shape is represented as a union of certain disks contained in the given shape the representative disks of different sizes may overlap but excessive overlapping between them is avoided the algorithm combines the advantages of the morphological skeleton transform mst and the morphological shape decomposition msd the representative disks have simple and well defined mathematical characterizations the algorithm is simple and efficient to implement the experimental results show that the number of representative disks used by our algorithm is significant lower than that used by the msd the overlapping level between the representative disks is much lower than that of the mst a simple procedure can be used to combine the representative disks into more meaningful shape components these shape components seem to correspond better to the natural shape parts than those generated by the msd it is also possible to build a good approximation for a given shape using only a small number of major components

shape decomposition and representation using a recursive morphological operation abstract this paper presents a recursive morphological operation developed in order to perform efficient shape representation this operation uses a structuring element as a geometrical primitive to evaluate the shape of an object it results in a set of loci of the translated structuring elements that are included in the object but which do not overlap the analysis of its computational complexity shows that it is usually less time consuming than morphological erosion by using this operation an object decomposition algorithm is then developed for shape representation it decomposes an object into a union of simple and non overlapping object components the object is represented by the sizes and loci of its object components this representation is information preserving shift and scale invariant and non rebundant it has been compared with skeletons morphological decomposition chain codes and quatrees in terms of compression ability and image processing facility experimental results shows that it is very compact especially if information loss is allowed because of the non overlap between object components many image processing tasks can be easily performed by directly using this shape representation

brief paper stochastic adaptive control using a modified least squares algorithm recent papers on stochastic adaptive control have established global convergence for algorithms using a stochastic approximation iteration however to date global convergence has not been established for algorithms incorporating a least squares iteration this paper establishes global convergence for a slightly modified least squares stochastic adaptive control algorithm it is shown that with probability one the algorithm will ensure that the system inputs and outputs are sample mean square bounded and the mean square output tracking error achieves its global minimum possible value for linear feedback control

ordered structural shape matching with primitive extraction by mathematical morphology abstract structural shape matching procedures begin by decomposing the shapes to be matched into primitive parts and extracting the properties of and relationships among these primitives the resultant structural descriptions are matched to structural models usually via a tree search whose time is exponential in the number of primitives in this paper we introduce a new fast method of structural shape matching called ordered structural matching which has polynomial time complexity instead of exponential the approach presented also uses mathematical morphology to rapidly decompose the shapes into primitives to be used in the matching the primitives so produced are pieces of the original shape but not necessarily those pieces that a human would select the method has been tested on the toy task of determining which plastic shapes match the shapes of the holes in a child s six sided toy box it is also directly applicable to the inspection and manipulation of certain airplane parts

common randomness in information theory and cryptography ii cr capacity for pt i see ibid vol 39 p 1121 1993 the common randomness cr capacity of a two terminal model is defined as the maximum rate of common randomness that the terminals can generate using resources specified by the given model we determine cr capacity for several models including those whose statistics depend on unknown parameters the cr capacity is shown to be achievable robustly by common randomness of nearly uniform distribution no matter what the unknown parameters are our cr capacity results are relevant for the problem of identification capacity and also yield a new result on the regular transmission capacity of arbitrarily varying channels with feedback

channel coding rate in the finite blocklength regime this paper investigates the maximal channel coding rate achievable at a given blocklength and error probability for general classes of channels new achievability and converse bounds are given which are tighter than existing bounds for wide ranges of parameters of interest and lead to tight approximations of the maximal achievable rate for blocklengths n as short as 100 it is also shown analytically that the maximal rate achievable with error probability isclosely approximated by c v n q 1 where c is the capacity v is a characteristic of the channel referred to as channel dispersion and q is the complementary gaussian cumulative distribution function

self tuning trackers we examine the problem of obtaining adaptive control laws which tune themselves to control laws minimizing the variance of the tracking error between the output of the linear armax system and a specified reference trajectory if the reference trajectory is sufficiently rich of order greater than or equal to the sum of the degrees of the control and noise polynomials in the armax system then an adaptive controller is exhibited for which the parameter estimates are strongly consistent for the linear model following problem where the trajectory to be tracked is generated as the output of a linear system it is enough for the order of sufficient richness to be greater than the degree of the noise polynomial alone further if the order of sufficient richness is even smaller as is often the case then a lower dimensional adaptive controller which does not attempt to estimate all the coefficients of the noise polynomial is self tuning

secret key agreement general capacity and second order asymptotics we revisit the problem of secret key agreement using interactive public communication for two parties and propose a new secret key agreement protocol the protocol attains the secret key capacity for general observations and attains the second order asymptotic term in the maximum length of a secret key for independent and identically distributed observations in contrast to the previously suggested secret key agreement protocols the proposed protocol uses interactive communication in fact the standard one way communication protocol used prior to this paper fails to attain the asymptotic results above our converse proofs rely on a recently established upper bound for secret key lengths both our lower and upper bounds are derived in a single shot setup and the asymptotic results are obtained as corollaries

strong secrecy from channel resolvability we analyze physical layer security based on the premise that the coding mechanism for secrecy over noisy channels is tied to the notion of channel resolvability instead of considering capacity based constructions which associate to each message a subcode that operates just below the capacity of the eavesdropper s channel we consider channel resolvability based constructions which associate to each message a subcode that operates just above the resolvability of the eavesdropper s channel building upon the work of csiszar and hayashi we provide further evidence that channel resolvability is a powerful and versatile coding mechanism for secrecy by developing results that hold for strong secrecy metrics and arbitrary channels specifically we show that at least for symmetric wiretap channels random capacity based constructions fail to achieve the strong secrecy capacity while channel resolvability based constructions achieve it we then leverage channel resolvability to establish the secrecy capacity region of arbitrary broadcast channels with confidential messages and a cost constraint for strong secrecy metrics finally we specialize our results to study the secrecy capacity of wireless channels with perfect channel state information csi mixed channels and compound channels with receiver csi as well as the secret key capacity of source models for secret key agreement by tying secrecy to channel resolvability we obtain achievable rates for strong secrecy metrics with simple proofs

on the convergence of the self tuning algorithms based on nonmodified least squares self tuning servo control based on a nonmodified least squares algorithm is considered the fundamental result of the analysis is that the passivity of the two time varying operators depending on the noise process dynamics regression vector and the ponderation matrix sequence of the algorithm is essential for the global stability of the self tuning regulator the methodology can be applied to problems of adaptive prediction based on a nonmodified least squares algorithm and system parameter identification by a least squares algorithm with a priori prediction

convergence of adaptive minimum variance algorithms via weighting coefficient selection weighted least squares and related stochastic approximation algorithms are studied for parameter estimation adaptive state estimation adaptive n step ahead prediction and adaptive control in both white and colored noise environments for the fundamental algorithm which is the basis for the various applications the step size in the stochastic approximation versions and the weighting coefficient in the weighted least squares schemes are selected according to a readily calculated stability measure associated with the estimator the selection is guided by the convergence theory in this way strong global convergence of the parameter estimates state estimates and prediction or tracking errors is not only guaranteed under the appropriate noise passivity and stability or minimum phase conditions but the convergence is also as fast as it appears reasonable to achieve given the simplicity of the adaptive scheme

on the convergence of self tuning stochastic servo algorithms based on stochastic approximation the problem of the adaptive tracking of stochastic reference signals is considered supposing that the process can be represented by an armax model with arbitrary time delay and the reference signal by an arma model two algorithms of the stochastic approximation type providing adaptation to both process and reference characteristics are proposed they differ by the incorporated a priori knowledge about the optimal regulator parameters global stability asymptotic optimally convergence of the adaptive control law in a cesaro sense and the strong consistency of the parameter estimates are proved the persistence of excitation condition is analyzed

decomposition of convex polygonal morphological structuring elements into neighborhood subsets a discussion is presented of the decomposition of convex polygon shaped structuring elements into neighborhood subsets such decompositions will lead to efficient implementation of corresponding morphological operations on neighborhood processing based parallel image computers it is proved that all convex polygons are decomposable efficient decomposition algorithms are developed for different machine structures an o 1 time algorithm with respect to the image size is developed for the four neighbor connected mesh machines a linear time algorithm for determining the optimal decomposition is provided for the machines that can quickly perform 3 3 morphological operations

efficient morphological shape representation by varying overlapping levels among representative disks abstract the morphological skeleton transform the morphological shape decomposition and the overlapped morphological shape decomposition are three basic morphological shape representation schemes in this paper we propose a new way of generalizing these basic representation algorithms to improve representational efficiency in all three basic algorithms a fixed overlapping policy is used to control the overlapping relationships among representative disks of different sizes in our new algorithm different overlapping policies are used to generate shape components that have different overlapping relationships among themselves the overlapping policy is selected dynamically according to local shape features experiments show that compared to the three basic algorithms our algorithm produces more efficient representations with lower numbers of representative points

a simple proof of the blowing up lemma corresp the blowing up lemma says that if the probability with respect to a product measure of a set a subseteq cal x n cal x finite n large is not exponentially small then its l n neighborhood has probability almost one for some l n o n here an information theoretic proof of the blowing up lemma generalizing it to continuous alphabets is given

convergence rate of least squares identification and adaptive control for stochastic systems the strong consistency and the convergence rate of least squares identification for the multidimensional armax model are established under some decaying excitation conditions which are satisfied if both input and output do not grow too fast and the attenuating excitation technique is applied the parameter identification results are applied to adaptive control systems with a quadratic loss function the rate of convergence of the loss function to its minimum is also obtained

morphological decomposition of 2 d binary shapes into convex polygons a heuristic algorithm in many morphological shape decomposition algorithms either a shape can only be decomposed into shape components of extremely simple forms or a time consuming search process is employed to determine a decomposition in this paper we present a morphological shape decomposition algorithm that decomposes a two dimensional 2 d binary shape into a collection of convex polygonal components a single convex polygonal approximation for a given image is first identified this first component is determined incrementally by selecting a sequence of basic shape primitives these shape primitives are chosen based on shape information extracted from the given shape at different scale levels additional shape components are identified recursively from the difference image between the given image and the first component simple operations are used to repair certain concavities caused by the set difference operation the resulting hierarchical structure provides descriptions for the given shape at different detail levels the experiments show that the decomposition results produced by the algorithm seem to be in good agreement with the natural structures of the given shapes the computational cost of the algorithm is significantly lower than that of an earlier search based convex decomposition algorithm compared to nonconvex decomposition algorithms our algorithm allows accurate approximations for the given shapes at low coding costs

some results on distributed source coding for interactive function computation a two terminal interactive distributed source coding problem with alternating messages for function computation at both locations is studied for any number of messages a computable characterization of the rate region is provided in terms of single letter information measures while interaction is useless in terms of the minimum sum rate for lossless source reproduction at one or both locations the gains can be arbitrarily large for function computation even when the sources are independent for a class of sources and functions interaction is shown to be useless even with infinite messages when a function has to be computed at only one location but is shown to be useful if functions have to be computed at both locations for computing the boolean and function of two independent bernoulli sources at both locations an achievable infinite message sum rate with infinitesimal rate messages is derived in terms of a 2 d definite integral and a rate allocation curve the benefit of interaction is highlighted in multiterminal function computation problem through examples for networks with a star topology multiple rounds of interactive coding is shown to decrease the scaling law of the total network rate by an order of magnitude as the network grows

feedback does not affect the reliability function of a dmc at rates above capacity corresp asymptotically coincident upper and lower bounds on the exponent of the largest possible probability of correct decoding for block codes of any given rate above capacity have been given by dueck and korner their method is extended to show that the same bounds also hold in the presence of noiseless feedback

recursive system identification and adaptive control by use of the modified least squares algorithm in this paper we first use a weaker than persistent excitation condition to establish the strong consistency of mls for mimo stochastic systems without monitoring and give a comparison between various conditions for consistency then we show the global convergence for adaptive tracking based on mls and finally the adaptive tracking and strong consistency results are combined

a proof of the strong converse theorem for gaussian broadcast channels via the gaussian poincare inequality we prove that the gaussian broadcast channel with two destinations admits the strong converse property this implies that for every sequence of block codes operated at a common rate pair with an asymptotic average error probability 1 the rate pair must lie within the capacity region derived by cover and bergmans the main mathematical tool required for our analysis is a logarithmic sobolev inequality known as the gaussian poincare inequality

strong converse using change of measure arguments the strong converse for a coding theorem shows that the optimal asymptotic rate possible with vanishing error cannot be improved by allowing a fixed error building on a method introduced by gu and effros for centralized coding problems we develop a general and simple recipe for proving strong converse that is applicable for distributed problems as well heuristically our proof of strong converse mimics the standard steps for proving a weak converse except that we apply those steps to a modified distribution obtained by conditioning the original distribution on the event that no error occurs a key component of our recipe is the replacement of the hard markov constraints implied by the distributed nature of the problem with a soft information cost using a variational formula introduced by oohama we illustrate our method by providing a short proof of the strong converse for the wyner ziv problem and strong converse theorems for interactive function computation common randomness and secret key agreement and the wiretap channel the latter three strong converse problems were open prior to this work

binary shape recognition using the morphological skeleton transform abstract binary image representation by its morphological skeleton transform has been proposed in the past as an information preserving representation in this paper this skeleton representation is adopted as the start point for the development of a binary shape recognition scheme a skeleton matching algorithm is presented that efficiently characterizes the similarity between two skeletons as a distance measure this skeleton matching algorithm resembles the well known from speech processing elastic matching technique

information spectrum approach to second order coding rate in channel coding in this paper second order coding rate of channel coding is discussed for general sequence of channels the optimum second order transmission rate with a constant error constraint epsiv is obtained by using the information spectrum method we apply this result to the discrete memoryless case the discrete memoryless case with a cost constraint the additive markovian case and the gaussian channel case with an energy constraint we also clarify that the gallager bound does not give the optimum evaluation in the second order coding rate

morphological shape representation abstract a new approach for shape representation is described which provides a general scheme for object description and unifies some of the existing representation techniques the proposed method has the advantage that it is based on the use of simple geometric objects which are intuitively used by humans in their perception of shapes furthermore its unifying framework can be used both in computer graphics and computer vision thus providing a tool to close the existing gap between object modeling and object recognition in certain applications