an extension of pointwise circumscription abstract in this paper we generalize lifschitz s pointwise circumscription ander the first order framework the generalized version has the ability for simultaneously minimizing several predicates at finitely many pinpoints in a pointwise manner we show that if an anderlying first order theory is almost existential then the extended pointwise circumscription is complete with respect to minimal model semantics almost existential formulas are in the dual form of almost universal formulas which was proposed by lifschitz to investigate the satisfiability of circumscription this completeness result is a generalization of the result by kolaitis and papadimitriou who regarded the case of existential formulas we also give a partial answer to the question for exponential growth of the size of first order formulas equivalent to circumscription moreover we clarify that lifschitz s pointwise circumscription is complete in a slightly wider class of positive formulas

euler s elastica and curvature based inpainting image inpainting is a special image restoration problem for which image prior models play a crucial role euler s elastica was first introduced to computer vision by mumford algebraic geometry and its applications springer verlag new york 1994 pp 491 506 as a curve prior model by functionalizing the elastica energy masnou and morel proceedings of the 5th ieee international conference image processing 3 1998 pp 259 263 proposed an elastica based variational inpainting model the current paper is intended to contribute to the development of its mathematical foundation and the study of its properties and connections to the earlier works of bertalmio sapiro caselles and ballester siggraph 2000 acm press new york 2000 and chan and shen j visual comm image rep 12 2001 pp 436 449 a computational scheme based on numerical pdes is presented which allows the automatic handling of topologically complex inpainting domains

capacity of steganographic channels this work investigates a central problem in steganography that is how much data can safely be hidden without being detected to answer this question a formal definition of steganographic capacity is presented once this has been defined a general formula for the capacity is developed the formula is applicable to a very broad spectrum of channels due to the use of an information spectrum approach this approach allows for the analysis of arbitrary steganalyzers as well as nonstationary nonergodic encoder and attack channels after the general formula is presented various simplifications are applied to gain insight into example hiding and detection methodologies finally the context and applications of the work are summarized in a general discussion

active contours without edges we propose a new model for active contours to detect objects in a given image based on techniques of curve evolution mumford shah 1989 functional for segmentation and level sets our model can detect objects whose boundaries are not necessarily defined by the gradient we minimize an energy which can be seen as a particular case of the minimal partition problem in the level set formulation the problem becomes a mean curvature flow like evolving the active contour which will stop on the desired boundary however the stopping term does not depend on the gradient of the image as in the classical active contour models but is instead related to a particular segmentation of the image we give a numerical algorithm using finite differences finally we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable also the initial curve can be anywhere in the image and interior contours are automatically detected

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

universal detection of messages via finite state channels we propose a universal asymptotically optimum decision rule for deciding whether or not an observed sequence generated at the output of an unknown finite state channel corresponds to a given channel input message the hypothesized message is tested against a certain alternative message or several alternative messages under the neyman pearson criterion

the method of types information theory the method of types is one of the key technical tools in shannon theory and this tool is valuable also in other fields in this paper some key applications are presented in sufficient detail enabling an interested nonspecialist to gain a working knowledge of the method and a wide selection of further applications are surveyed these range from hypothesis testing and large deviations theory through error exponents for discrete memoryless channels and capacity of arbitrarily varying channels to multiuser problems while the method of types is suitable primarily for discrete memoryless models its extensions to certain models with memory are also discussed

a generalization of collapsible cases of circumscription abstract circumscription is a second order formula expressing the minimality of the extension of a particular predicate or set of predicates it was fashioned to capture the concept of nonmonotonic logic of human beings in some instances circumscription is equivalent to a first order formula we show that the known cases are special instances of a more general case

the computation of visible surface representations a computational theory of visible surface representations is developed the visible surface reconstruction process that computes these quantitative representations unifies formal solutions to the key problems of 1 integrating multiscale constraints on surface depth and orientation from multiple visual sources 2 interpolating dense piecewise smooth surfaces from these constraints 3 detecting surface depth and orientation discontinuities to apply boundary conditions on interpolation and 4 structuring large scale distributed surface representations to achieve computational efficiency visible surface reconstruction is an inverse problem a well posed variational formulation results from the use of a controlled continuity surface model discontinuity detection amounts to the identification of this generic model s distributed parameters from the data finite element shape primitives yield a local discretization of the variational principle the result is an efficient algorithm for visible surface reconstruction

strong continuation contrast invariant inpainting with a third order optimal pde pde based image inpainting has become a very active area of research after the pioneering works of masnou and morel bertalm spl inodot spl acute o et al and ballester et al in this paper we take a different approach inspired by the excellent work of caselles et al we view the inpainting problem as a particular case of image interpolation in which we intend to propagate level lines expressing this in terms of local neighborhoods and using a taylor expansion we derive a third order pde that performs inpainting this pde is optimal in the sense that it is the most accurate third order pde which can ensure continuation of level lines the continuation is strong allowing the restoration of thin structures occluded by a wide gap the result is also contrast invariant this is a novel pde which in both its accuracy and contrast invariance outperforms the approaches cited above

circumscription completeness reviewed abstract in this paper we demonstrate that some results on the completeness of p defining theories published earlier are incorrect we point out that by restricting the original propositions to well founded theories results somewhat weaker than the original ones can be retained we also present a theorem that provides some insight into the relation between completeness and reducibility and helps to identify the theories whose minimal models can be adequately handled with circumscription

corrected proof of de buda s theorem lattice channel codes an error in de buda s see ieee j select areas commun vol 7 no 6 p 893 1989 proof on the asymptotic optimality of lattice channel codes is pointed out and corrected using a modification of de buda s approach comments are given on the correct interpretation and the limitations of this result

nested linear lattice codes for structured multiterminal binning network information theory promises high gains over simple point to point communication techniques at the cost of higher complexity however lack of structured coding schemes limited the practical application of these concepts so far one of the basic elements of a network code is the binning scheme wyner 1974 1978 and other researchers proposed various forms of coset codes for efficient binning yet these schemes were applicable only for lossless source or noiseless channel network coding to extend the algebraic binning approach to lossy source or noisy channel network coding previous work proposed the idea of nested codes or more specifically nested parity check codes for the binary case and nested lattices in the continuous case these ideas connect network information theory with the rich areas of linear codes and lattice codes and have strong potential for practical applications we review these developments and explore their tight relation to concepts such as combined shaping and precoding coding for memories with defects and digital watermarking we also propose a few novel applications adhering to a unified approach

the suprem architecture a new intelligent paradigm abstract we investigate the model theory of the notion of circumscription and find completeness theorems that provide a partial converse to a result of mccarthy we show that the circumscriptive theorems are precisely the truths of the minimal models in the case of various classes of theories and for various versions of circumscription we also present an example of commonsense reasoning in which first order circumscription does not achieve the intuitive and desired minimization

stereographiccombing a porcupine or studies on direction diffusion in image processing this paper addresses the problem of feature enhancement in noisy images when the feature is known to be constrained to a manifold as an example we approach the direction denoising problem in a general dimension via the geometric beltrami framework for image processing the spatial direction space is a fiber bundle in which the spatial part is the base manifold and the direction space is the fiber the feature direction field is represented accordingly as a section of the spatial feature fiber bundle the resulting beltrami flow is a selective smoothing process that respects the bundle s structure i e the feature constraint direction diffusion is treated as a canonical example of a non euclidean feature space the structures of the fiber spaces of interest in this paper are the unit circle s1 the unit sphere s2 and the unit hypersphere sn applications to color analysis are discussed and numerical experiments demonstrate again the benefits of the beltrami framework in comparison to other featu

orientation diffusions diffusions are useful for image processing and computer vision because they provide a convenient way of smoothing noisy data analyzing images at multiple scales and enhancing discontinuities a number of diffusions of image brightness have been defined and studied so far they may be applied to scalar and vector valued quantities that are naturally associated with intervals of either the real line or other flat manifolds some quantities of interest in computer vision and other areas of engineering that deal with images are defined on curved manifolds typical examples are orientation and hue that are defined on the circle generalizing brightness diffusions to orientation is not straightforward especially in the case where a discrete implementation is sought an example of what may go wrong is presented a method is proposed to define diffusions of orientation like quantities first a definition in the continuum is discussed then a discrete orientation diffusion is proposed the behavior of such diffusions is explored both analytically and experimentally it is shown how such orientation diffusions contain a nonlinearity that is reminiscent of edge process and anisotropic diffusion a number of open questions are proposed

coherence enhancing diffusion filtering the completion of interrupted lines or the enhancement of flow like structures is a challenging task in computer vision human vision and image processing we address this problem by presenting a multiscale method in which a nonlinear diffusion filter is steered by the so called interest operator second moment matrix structure tensor an m dimensional formulation of this method is analysed with respect to its well posedness and scale space properties an efficient scheme is presented which uses a stabilization by a semi implicit additive operator splitting aos and the scale space behaviour of this method is illustrated by applying it to both 2 d and 3 d images

noise removal using fourth order partial differential equation with applications to medical magnetic resonance images in space and time we introduce a new method for image smoothing based on a fourth order pde model the method is tested on a broad range of real medical magnetic resonance images both in space and time as well as on nonmedical synthesized test images our algorithm demonstrates good noise suppression without destruction of important anatomical or functional detail even at poor signal to noise ratio we have also compared our method with related pde models

quantization based methods additive attacks performance analysis the main goal of this study consists in the development of the worst case additive attack wcaa for ary quantization based data hiding methods using as design criteria the error probability and the maximum achievable rate of reliable communications our analysis focuses on the practical scheme known as distortion compensated dither modulation dc dm from the mathematical point of view the problem of the worst case attack wca design using probability of error as a cost function is formulated as the maximization of the average probability of error subject to the introduced distortion for a given decoding rule when mutual information is selected as a cost function a solution of the minimization problem should provide such an attacking noise probability density function pdf that will maximally decrease the rate of reliable communications for an arbitrary decoder structure the obtained results demonstrate that within the class of additive attacks the developed attack leads to a stronger performance decrease for the considered class of embedding techniques than the additive white gaussian or uniform noise attacks

writing on wet paper in this paper we show that the communication channel known as writing in memory with defective cells is a relevant information theoretical model for a specific case of passive warden steganography when the sender embeds a secret message into a subset c of the cover object x without sharing c with the recipient the set c which is also called the selection channel could be arbitrary determined by the sender from the cover object using a deterministic pseudo random or a truly random process we call this steganography writing on wet paper and realize it using a simple variable rate random linear code that gives the sender a convenient flexibility and control over the embedding process and is thus suitable for practical implementation the importance of the wet paper scenario for covert communication is discussed within the context of adaptive steganography and perturbed quantization steganography heuristic arguments supported by tests using blind steganalysis indicate that the wet paper steganography provides improved steganographic security and is less vulnerable to steganalytic attacks compared with existing methods with shared selection channels

universal decoding for finite state channels universal decoding procedures for finite state channels are discussed although the channel statistics are not known universal decoding can achieve an error probability with an error exponent that for large enough block length or constraint length in case of convolutional codes is equal to the random coding error exponent associated with the optimal maximum likelihood decoding procedure for the given channel the same approach is applied to sequential decoding yielding a universal sequential decoding procedure with a cutoff rate and an error exponent that are equal to those achieved by the classical sequential decoding procedure

on joint information embedding and lossy compression in the presence of a stationary memoryless attack channel we consider the problem of optimum joint public information embedding and lossy compression with respect to a fidelity criterion the decompressed composite sequence stegotext is distorted by a stationary memoryless attack resulting in a forgery which in turn is fed into the decoder whose task is to retrieve the embedded information the goal of this paper is to characterize the maximum achievable embedding rate r sub e the embedding capacity c sub e as a function of the compression composite rate r sub c and the allowed average distortion level spl delta such that the average probability of error in decoding of the embedded message can be made arbitrarily small for sufficiently large block length we characterize the embedding capacity and demonstrate how it can be approached in principle we also provide a single letter expression of the minimum achievable composite rate as a function of r sub e and spl delta below which there exists no reliable embedding scheme

on random coding error exponents of watermarking systems watermarking codes are analyzed from an information theoretic viewpoint as a game between an information hider and an active attacker while the information hider embeds a secret message watermark in a covertext message typically text image sound or video stream within a certain distortion level the attacker processes the resulting watermarked message within limited additional distortion in attempt to invalidate the watermark for the case where the covertext source is memoryless or more generally where there exists some transformation that makes it memoryless we provide a single letter characterization of the maximin game of the random coding error exponent associated with the average probability of erroneously decoding the watermark this single letter characterization is in effect because if the information hider utilizes a memoryless channel to generate random codewords for every covertext message the causal attacker will maximize the damage by implementing a memoryless channel as well partial results for the dual minimax game and the conditions for the existence of a saddle point are also presented

an information theoretic model for steganography an information theoretic model for steganography with a passive adversary is proposed the adversary s task of distinguishing between an innocent cover message c and a modified message s containing hidden information is interpreted as a hypothesis testing problem the security of a steganographic system is quantified in terms of the relative entropy or discrimination between the distributions of c and s which yields bounds on the detection capability of any adversary it is shown that secure steganographic schemes exist in this model provided the covertext distribution satisfies certain conditions a universal stegosystem is presented in this model that needs no knowledge of the covertext distribution except that it is generated from independently repeated experiments

diffusion of general data on non flat manifolds viaharmonic maps theory the direction diffusion case in a number of disciplines directional data provides a fundamental source of information a novel framework for isotropic and anisotropic diffusion of directions is presented in this paper the framework can be applied both to denoise directional data and to obtain multiscale representations of it the basic idea is to apply and extend results from the theory of harmonic maps and in particular harmonic maps in liquid crystals this theory deals with the regularization of vectorial data while satisfying the intrinsic unit norm constraint of directional data we show the corresponding variational and partial differential equations formulations for isotropic diffusion obtained from an l 2 norm and edge preserving diffusion obtained from an l norm in general and an l 1 norm in particular in contrast with previous approaches the framework is valid for directions in any dimensions supports non smooth data and gives both isotropic and anisotropic formulations in addition the framework of harmonic maps here described can be used to diffuse and analyze general image data defined on general non flat manifolds that is functions between two general manifolds we present a number of theoretical results open questions and examples for gradient vectors optical flow and color images

multiterminal source encoding with one distortion criterion the authors unify earlier investigations concerning the encoding of two correlated sources x sub k y sub k by means of separate encoders decoding is done by a single decoder which receives the outputs from both encoders the reconstruction of x sub k is required to be perfect in the usual shannon sense the authors determine the admissible rate region r d where d is the distortion of the reconstruction of y sub k the binary hamming case is investigated explicitly

on the satisfiability of circumscription abstract etherington mercer and reiter showed on the basis of ideas of bossu and siegel that circumscription cannot lead to inconsistency for universal formulas we extend this result in three directions to formulas of a more general syntactic form to circumscription with some predicate symbols allowed to vary and to prioritized circumscription

numerical methods for p harmonic flows and applications to image processing we propose in this paper an alternative approach for computing p harmonic maps and flows instead of solving a constrained minimization problem on sn 1 we solve an unconstrained minimization problem on the entire space of functions this is possible using the projection on the sphere of any arbitrary function then we show how this formulation can be used in practice for problems with both isotropic and anisotropic diffusion with applications to image processing using a new finite difference scheme

orientation matching minimization for image denoising and inpainting in this paper we propose an orientation matching functional minimization for image denoising and image inpainting following the two step tv stokes algorithm rahman et al in scale space and variational methods in computer vision pp 473 482 springer heidelberg 2007 tai et al in image processing based on partial differential equations pp 3 22 springer heidelberg 2006 bertalmio et al in proc conf comp vision pattern rec pp 355 362 2001 a regularized tangential vector field with zero divergence condition is first obtained then a novel approach to reconstruct the image is proposed instead of finding an image that fits the regularized normal direction from the first step we propose to minimize an orientation matching cost measuring the alignment between the image gradient and the regularized normal direction this functional yields a new nonlinear partial differential equation pde for reconstructing denoised and inpainted images the equation has an adaptive diffusivity depending on the orientation of the regularized normal vector field providing reconstructed images which have sharp edges and smooth regions the additive operator splitting aos scheme is used for discretizing euler lagrange equations we present the results of various numerical experiments that illustrate the improvements obtained with the new functional

perfectly secure steganography capacity error exponents and code constructions an analysis of steganographic systems subject to the following perfect undetectability condition is presented in this paper following embedding of the message into the covertext the resulting stegotext is required to have exactly the same probability distribution as the covertext then no statistical test can reliably detect the presence of the hidden message we refer to such steganographic schemes as perfectly secure a few such schemes have been proposed in recent literature but they have vanishing rate we prove that communication performance can potentially be vastly improved specifically our basic setup assumes independent and identically distributed i i d covertext and we construct perfectly secure steganographic codes from public watermarking codes using binning methods and randomized permutations of the code the permutation is a secret key shared between encoder and decoder we derive positive capacity and random coding exponents for perfectly secure steganographic systems the error exponents provide estimates of the code length required to achieve a target low error probability in some applications steganographic communication may be disrupted by an active warden modeled here by a compound discrete memoryless channel dmc the transmitter and warden are subject to distortion constraints we address the potential loss in communication performance due to the perfect security requirement this loss is the same as the loss obtained under a weaker order 1 steganographic requirement that would just require matching of first order marginals of the covertext and stegotext distributions furthermore no loss occurs if the covertext distribution is uniform and the distortion metric is cyclically symmetric steganographic capacity is then achieved by randomized linear codes our framework may also be useful for developing computationally secure steganographic systems that have near optimal communication performance

some computational aspects of circumscription the effects of circumscribing first order formulas are explored from a computational standpoint first extending work of v lifschitz it is shown that the circumscription of any existential first order formula is equivalent to a first order formula after this it is established that a set of universal horn clauses has a first order circumscription if and only if it is bounded when considered as a logic program thus it is undecidable to tell whether such formulas have first order circumscription finally it is shown that there arefirst order formulas whode circumscription has a conp complete model checking problem

a decomposition framework for image denoising algorithms in this paper we consider an image decomposition model that provides a novel framework for image denoising the model computes the components of the image to be processed in a moving frame that encodes its local geometry directions of gradients and level lines then the strategy we develop is to denoise the components of the image in the moving frame in order to preserve its local geometry which would have been more affected if processing the image directly experiments on a whole image database tested with several denoising methods show that this framework can provide better results than denoising the image directly both in terms of peak signal to noise ratio and structural similarity index metrics

filling in by joint interpolation of vector fields and gray levels a variational approach for filling in regions of missing data in digital images is introduced the approach is based on joint interpolation of the image gray levels and gradient isophotes directions smoothly extending in an automatic fashion the isophote lines into the holes of missing data this interpolation is computed by solving the variational problem via its gradient descent flow which leads to a set of coupled second order partial differential equations one for the gray levels and one for the gradient orientations the process underlying this approach can be considered as an interpretation of the gestaltist s principle of good continuation no limitations are imposed on the topology of the holes and all regions of missing data can be simultaneously processed even if they are surrounded by completely different structures applications of this technique include the restoration of old photographs and removal of superimposed text like dates subtitles or publicity examples of these applications are given we conclude the paper with a number of theoretical results on the proposed variational approach and its corresponding gradient descent flow

universal wyner ziv coding for distortion constrained general side information we investigate the wyner ziv coding in which the statistics of the principal source is known but the statistics of the channel generating the side information is unknown except that it is in a certain class the class consists of channels such that the distortion between the principal source and side information is smaller than a threshold but channels may be neither stationary nor ergodic in this situation we define a new rate distortion function as the minimum rate such that there exists a wyner ziv code that is universal for every channel in the class then we show an upper bound and a lower bound on the rate distortion function and derive a matching condition such that the upper and lower bounds coincide the relation between the new rate distortion function and rate distortion function of the heegard berger problem is also discussed

on joint information embedding and lossy compression we consider the problem of optimum joint information embedding and lossy compression with respect to a fidelity criterion the goal is to find the minimum achievable compression composite rate r sub c as a function of the embedding rate r sub e and the average distortion level spl delta allowed such that the average probability of error in decoding of the embedded message can be made arbitrarily small for sufficiently large block length we characterize the minimum achievable composite rate for both the public and the private versions of the problem and demonstrate how this minimum can be approached in principle we also provide an alternative single letter expression of the maximum achievable embedding rate embedding capacity as a function of r sub c and spl delta above which there exist no reliable embedding schemes

on information embedding when watermarks and covertexts are correlated in this correspondence a new digital watermarking scenario is studied where watermarks and covertexts are correlated with each other a necessary and sufficient condition is derived under which a watermark is first embedded and can later be recovered with high probability at the output of a public watermark decoder after the watermarked signal is disturbed by a fixed memoryless attack channel interestingly the condition also implies that the shannon separation theorem does not hold in this scenario

a short time beltrami kernel for smoothing images and manifolds we introduce a short time kernel for the beltrami image enhancing flow the flow is implemented by convolving the image with a space dependent kernel in a similar fashion to the solution of the heat equation by a convolution with a gaussian kernel the kernel is appropriate for smoothing regular flat 2 d images for smoothing images painted on manifolds and for simultaneously smoothing images and the manifolds they are painted on the kernel combines the geometry of the image and that of the manifold into one metric tensor thus enabling a natural unified approach for the manipulation of both additionally the derivation of the kernel gives a better geometrical understanding of the beltrami flow and shows that the bilateral filter is a euclidean approximation of it on a practical level the use of the kernel allows arbitrarily large time steps as opposed to the existing explicit numerical schemes for the beltrami flow in addition the kernel works with equal ease on regular 2 d images and on images painted on parametric or triangulated manifolds we demonstrate the denoising properties of the kernel by applying it to various types of images and manifolds

an efficient method for eliminating varying predicates from a circumscription abstract circumscription appears to be the most powerful and well studied technique used in formalizing common sense reasoning the general form of predicate circumscription allows for fixed and varying floating predicates we show that the inference problem under this form of circumscription is efficiently reducible to inferencing under circumscription without varying predicates in fact we transform this problem even into circumscription without fixed and varying predicates that is where all predicates are minimized thus any theorem prover or algorithm for inferencing under circumscription without fixed and varying predicates is able to handle inferencing under the general form of predicate circumscription as a consequence algorithms that compute circumscription for an inference task can be simplified

random coding lower bounds for the error exponent of joint quantization and watermarking systems we establish random coding lower bounds to the error exponent of discrete and gaussian joint quantization and private watermarking systems in the discrete system both the covertext and the attack channel are memoryless and have finite alphabets in the gaussian system the covertext is memoryless gaussian and the attack channel has additive memoryless gaussian noise in both cases our bounds on the error exponent are positive in the interior of the achievable quantization and watermarking rate region

regularized laplacian zero crossings as optimal edge integrators we view the fundamental edge integration problem for object segmentation in a geometric variational framework first we show that the classical zero crossings of the image laplacian edge detector as suggested by marr and hildreth inherently provides optimal edge integration with regard to a very natural geometric functional this functional accumulates the inner product between the normal to the edge and the gray level image gradient along the edge we use this observation to derive new and highly accurate active contours based on this functional and regularized by previously proposed geodesic active contour geometric variational models we also incorporate a 2d geometric variational explanation to the haralick edge detector into the geometric active contour framework

writing on dirty paper corresp a channel with output y x s z is examined the state s sim n 0 qi and the noise z sim n 0 ni are multivariate gaussian random variables i is the identity matrix the input x in r n satisfies the power constraint l n sum i 1 n x i 2 leq p if s is unknown to both transmitter and receiver then the capacity is frac 1 2 ln 1 p n q nats per channel use however if the state s is known to the encoder the capacity is shown to be c ast frac 1 2 ln 1 p n independent of q this is also the capacity of a standard gaussian channel with signal to noise power ratio p n therefore the state s does not affect the capacity of the channel even though s is unknown to the receiver it is shown that the optimal transmitter adapts its signal to the state s rather than attempting to cancel it

a modified tv stokes model for image processing we introduce and investigate the modified total variation tv stokes model for two classical image processing tasks i e image restoration and image inpainting the modified tv stokes model is a two step model based on a tv minimization in each step and the use of geometric information of the image in the first step a smoothed and divergence free tangential field of the given image is recovered and in the second step the image is reconstructed from the corresponding normals the existence and the uniqueness of the solution to the minimization problems are established for both steps of the model numerical examples and comparisons are presented to illustrate the effectiveness of the model

rate distortion for correlated sources with partially separated encoders we resolve some open problems concerning the encoding of a pair of correlated sources with respect to a fidelity criterion two encoders are used one encoder observes only the output of the first source while the other is supplied both with the second source output and with partial information about the first source at some predetermined rate a general coding theorem is proved which established that cal s ast a certain region defined in terms of single letter information theoretic quantities is an inner bound to the region of all attainable vectors of rates and distortions for certain cases of interest the converse is proved too thereby establishing the rate distortion region for these cases

on the error exponent and capacity games of private watermarking systems watermarking systems are analyzed as a game between an information hider a decoder and an attacker the information hider is allowed to cause some tolerable level of distortion to the original data within which the message is hidden and the resulting distorted data can suffer some additional amount of distortion caused by an attacker who aims at erasing the message two games are investigated the error exponent game and the coding capacity game motivated by a worst case approach we assume that the attacker is informed of the hiding strategy taken by the information hider and the decoder which are uninformed of the attacking scheme this approach leads to the maximin error exponent and maximin coding capacity as objective functions it is assumed that the host data is drawn from a finite alphabet memoryless stationary source and its realization side information is available at the encoder and the decoder a single letter expression for the maximin error exponent is found under large deviations distortion constraints moreover we find an asymptotically optimal random coding distribution a universal decoder and a worst case attack channel it is proved that there is a saddle point in the asymptotic exponent and that the minimax and the maximin error exponents are equal finally a single letter expression for the coding capacity i e the maximin reliable information rate is found

joint watermarking and compression using scalar quantization for maximizing robustness in the presence of additive gaussian attacks in joint watermarking and compression jwc a key process is quantization which embeds watermarks into a host signal while digitizing the host signal subject to requirements on the embedding rate compression rate quantization distortion and robustness using fixed rate scalar quantization for watermarking and compression in this paper we mainly consider how to design binary jwc systems to maximize the robustness of the systems in the presence of additive gaussian attacks under constraints on the compression rate and quantization distortion we first investigate optimum decoding of a binary jwc system and demonstrate by experiments that in the distortion to noise ratio dnr region of practical interest the minimum distance md decoder achieves performance comparable to that of the maximum likelihood decoder in addition to having advantages of low computation complexity and being independent of the statistics of the host signal we then present optimum binary jwc encoding schemes using fixed rate scalar quantization and the md decoder simulation results show that optimum binary jwc systems using nonuniform quantization are better than optimum binary jwc systems using uniform quantization furthermore in comparison with separate watermarking and compression systems optimum binary jwc systems using nonuniform quantization achieve significant dnr gains in the dnr region of practical interest finally spread transform dither modulation is applied to improving the robustness of the jwc systems at low dnrs

iterative image restoration combining total variation minimization and a second order functional a noise removal technique using partial differential equations pdes is proposed here it combines the total variational tv filter with a fourth order pde filter the combined technique is able to preserve edges and at the same time avoid the staircase effect in smooth regions a weighting function is used in an iterative way to combine the solutions of the tv filter and the fourth order filter numerical experiments confirm that the new method is able to use less restrictive time step than the fourth order filter numerical examples using images with objects consisting of edge flat and intermediate regions illustrate advantages of the proposed model

optimal watermark embedding and detection strategies under limited detection resources an information theoretic approach is proposed to watermark embedding and detection under limited detector resources first the attack free scenario is considered under which asymptotically optimal decision regions in the neyman pearson sense are proposed along with the optimal embedding rule later the case of zero mean independent and identically distributed i i d gaussian covertext distribution is explored with unknown variance under the attack free scenario for this case a lower bound on the exponential decay rate of the false negative probability is proposed it is proven that the optimal embedding and detecting strategy is superior to the customary linear additive embedding strategy in the exponential sense finally these results are extended to the case of memoryless attacks and general worst case attacks optimal decision regions and embedding rules are offered and the worst attack channel is identified

a relationship between quantization and watermarking rates in the presence of additive gaussian attacks a system which embeds watermarks in n dimensional gaussian data and distributes them in compressed form is studied the watermarked compressed data have to satisfy a distortion constraint and the watermark has to be recoverable in a private scenario in which the original data are available at the watermark detector the performance of the system in the presence of additive gaussian attacks is considered and the region of achievable quantization and watermarking rate pairs r sub q r sub w is established moreover two surprising facts are demonstrated 1 at low r sub q the maximum achievable r sub w is the same as when there are no attacks and 2 at high but finite r sub q the maximum achievable r sub w is the same as when there is no compression r sub q spl infin finally the performance of related schemes is also discussed

variations on information embedding in multiple access and broadcast channels information embedding ie is the transmission of information within a host signal subject to a distortion constraint there are two types of embedding methods namely irreversible ie and reversible ie depending upon whether or not the host as well as the message is recovered at the decoder in irreversible ie only the embedded message is recovered at the decoder and in reversible ie both the message and the host are recovered at the decoder in this paper combinations of irreversible and reversible ie in multiple access channels mac and physically degraded broadcast channels bc are considered in this paper mac ie in which separate encoders embed their messages into their host signals subject to distortion constraints is considered the embedded signals from the two encoders are transmitted to a single decoder across a mac for the mac ie model the following three cases are considered a no host recovery at the decoder b lossless recovery of one host at the decoder and c lossless recovery of both hosts at the decoder for the cases a and b inner bounds on the respective capacity regions are developed for the case c inner and outer bounds on the capacity region are developed and the capacity region is obtained if the hosts are independent in this paper bc ie in which two messages intended for separate decoders are embedded into a given host sequence by a single encoder subject to a distortion constraint is also considered for the bc ie model the following four cases are considered a lossless recovery of the host sequence at neither of the decoders b lossless recovery of the host sequence at only the better decoder c lossless recovery of the host sequence at both decoders and d lossless recovery of the host sequence at only the worse decoder for cases a and b inner and outer bounds on the respective capacity regions are developed for cases c and d the identical capacity regions are obtained

capacity and random coding exponents for channel coding with side information capacity formulas and random coding exponents are derived for a generalized family of gel fand pinsker coding problems these exponents yield asymptotic upper bounds on the achievable log probability of error in our model information is to be reliably transmitted through a noisy channel with finite input and output alphabets and random state sequence and the channel is selected by a hypothetical adversary partial information about the state sequence is available to the encoder adversary and decoder the design of the transmitter is subject to a cost constraint two families of channels are considered 1 compound discrete memoryless channels cdmc and 2 channels with arbitrary memory subject to an additive cost constraint or more generally to a hard constraint on the conditional type of the channel output given the input both problems are closely connected the random coding exponent is achieved using a stacked binning scheme and a maximum penalized mutual information decoder which may be thought of as an empirical generalized maximum a posteriori decoder for channels with arbitrary memory the random coding exponents are larger than their cdmc counterparts applications of this study include watermarking data hiding communication in presence of partially known interferers and problems such as broadcast channels all of which involve the fundamental idea of binning

noise removal using smoothed normals and surface fitting in this work we use partial differential equation techniques to remove noise from digital images the removal is done in two steps we first use a total variation filter to smooth the normal vectors of the level curves of a noise image after this we try to find a surface to fit the smoothed normal vectors for each of these two stages the problem is reduced to a nonlinear partial differential equation finite difference schemes are used to solve these equations a broad range of numerical examples are given in the paper

achievable error exponents for the private fingerprinting game fingerprinting systems in the presence of collusive attacks are analyzed as a game between a fingerprinter and a decoder on the one hand and a coalition of two or more attackers on the other hand the fingerprinter distributes to different users different fingerprinted copies of a host data covertext drawn from a memoryless stationary source embedded with different fingerprints the coalition members create a forgery of the data while aiming at erasing the fingerprints in order not to be detected their action is modeled by a multiple access channel mac we analyze the performance of two classes of decoders associated with different kinds of error events the decoder of the first class aims at detecting the entire coalition whereas the second is satisfied with the detection of at least one member of the coalition both decoders have access to the original covertext data and observe the forgery in order to identify member s of the coalition motivated by a worst case approach we assume that the coalition of attackers is informed of the hiding strategy taken by the fingerprinter and the decoder while they are uninformed of the attacking scheme achievable single letter expressions for the two kinds of error exponents are obtained single letter lower bounds are also derived for the subclass of constant composition codes these lower and the upper bounds coincide for the error exponent of the first class further for the error of the first kind a decoder that is optimal is introduced and the worst case attack channel is characterized

an information theoretic and game theoretic study of timing channels this paper focuses on jammed timing channels pure delay jammers with a maximum delay constraint an average delay constraint or a maximum buffer size constraint are explored for continuous time or discrete time packet waveforms fluid waveform approximations of each of these classes of waveforms are employed to aid in analysis channel capacity is defined and an information theoretic game based on mutual information rate is studied min max optimal jammers and max min optimal input processes are sought bounds on the min max and max min mutual information rates are described and numerical examples are given for maximum delay constrained mdc jammers with continuous time packet waveforms saddle point input and jammer strategies are identified the capacity of the maximum delay constrained jamming channel with continuous time packet waveforms is shown to equal the mutual information rate of the saddle point for mdc jammers with discrete time packet waveforms saddle point strategies are shown to exist jammers which have quantized batch departures at regular intervals are shown to perform well input processes with batches at regular intervals perform well for mdc or maximum buffer size constrained jammers

an algorithm to compute circumscription abstract mccarthy s theory of circumscription appears to be the most powerful among various formalizations of nonmonotonic reasoning designed to handle incomplete and negative information in knowledge representation systems in this paper we describe a query answering algorithm for circumscriptive theories the closed world assumption cwa and its generalizations the generalized closed world assumption gcwa and the extended closed world assumption ecwa can be considered as special forms of circumscription consequently our algorithm also applies to answering queries in theories using the closed world assumption and its generalizations similarly since prioritized circumscription is equivalent to a conjunction of parallel circumscriptions our algorithm can be used to answer queries in theories circumscribed by prioritized circumscription

mathematical models for local nontexture inpaintings dedicated to stanley osher on the occasion of his 60th birthday abstract inspired by the recent work of bertalmio et al on digital inpaintings siggraph 2000 we develop general mathematical models for local inpaintings of nontexture images on smooth regions inpaintings are connected to the harmonic and biharmonic extensions and inpainting orders are analyzed for inpaintings involving the recovery of edges we study a variational model that is closely connected to the classical total variation tv denoising model of rudin osher and fatemi phys d 60 1992 pp 259 268 other models are also discussed based on the mumford shah regularity comm pure appl math xlii 1989 pp 577 685 and curvature driven diffusions cdd of chan and shen j visual comm image rep 12 2001 the broad applications of the inpainting models are demonstrated through restoring scratched old photos disocclusion in vision analysis text removal digital zooming and edge based image coding

detection of hiding in the least significant bit in this paper we apply the theory of hypothesis testing to the steganalysis or detection of hidden data in the least significant bit lsb of a host image the hiding rate if data is hidden and host probability mass function pmf are unknown our main results are as follows a two types of tests are derived a universal over choices of host pmf method that has certain asymptotic optimality properties and methods that are based on knowledge or estimation of the host pmf and hence an appropriate likelihood ratio lr b for a known host pmf it is shown that the composite hypothesis testing problem corresponding to an unknown hiding rate reduces to a worst case simple hypothesis testing problem c using the results for a known host pmf practical tests based on the estimation of the host pmf are obtained these are shown to be superior to the state of the art in terms of receiver operating characteristics as well as self calibration across different host images estimators for the hiding rate are also developed