image sequence coding by split and merge a method is described for reducing the information contained in an image sequence while retaining the information necessary for the interpretation of the sequence by a human observer the method consists of first locating the redundant information reducing the degree of redundancy and coding the result the sequence is treated as a single 3d data volume the voxels of which are grouped into several regions obtained by a 3d split and merge algorithm the information is coded by representing the borders of the regions using a pyramidal structure in the x y t space the coefficients of the approximating polynomials are coded in a straightforward manner for 256 256 pixel 25 frame s image sequences compressions allowing transmission rates near 64 kbit s are obtained

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

hybrid image segmentation using watersheds and fast region merging a hybrid multidimensional image segmentation algorithm is proposed which combines edge and region based techniques through the morphological algorithm of watersheds an edge preserving statistical noise reduction approach is used as a preprocessing stage in order to compute an accurate estimate of the image gradient then an initial partitioning of the image into primitive regions is produced by applying the watershed transform on the image gradient magnitude this initial segmentation is the input to a computationally efficient hierarchical bottom up region merging process that produces the final segmentation the latter process uses the region adjacency graph rag representation of the image regions at each step the most similar pair of regions is determined minimum cost rag edge the regions are merged and the rag is updated traditionally the above is implemented by storing all rag edges in a priority queue we propose a significantly faster algorithm which additionally maintains the so called nearest neighbor graph due to which the priority queue size and processing time are drastically reduced the final segmentation provides due to the rag one pixel wide closed and accurately localized contours surfaces experimental results obtained with two dimensional three dimensional 2 d 3 d magnetic resonance images are presented

construction of e s 2 optimal supersaturated designs booth and cox proposed the e s 2 criterion for constructing two level supersaturated designs nguyen technometrics 38 1996 69 73 and tang and wu canad j statist 25 1997 191 201 independently derived a lower bound for e s 2 this lower bound can be achieved only when m is a multiple of n 1 where m is the number of factors and n is the run size we present a method that uses difference families to construct designs that satisfy this lower bound we also derive better lower bounds for the case where the nguyen tang wu bound is not achievable our bounds cover more cases than a bound recently obtained by butler mead eskridge and gilmour j r stat soc ser b stat methodol 63 2001 621 632 new e s 2 optimal designs are obtained by using a computer to search for designs that achieve the improved bounds

polynomial approximation and vector quantization a region based integration the paper presents an adaptive scheme for image data compression it is a region based approach that suitably integrates two different approaches to image coding vector quantization vq and polynomial approximation pa the scheme is adaptive from the point of view of the human observer the perceptually most significant areas are those near edges or details in smoothed areas pa can be used with notable results but there vq must be employed to ensure high fidelity the two techniques exhibit a complementarity in both advantages and drawbacks pa is not efficient in compressing high frequency areas but yields the best results when applied to highly correlated data vq is unable to reach high compression ratios because of its low adaptability but is quite suitable for compressing uncorrelated data the means to achieve the integration of the two techniques is a control image containing information about edge and texture locations in the paper edge encoding and restoration are also addressed which are closely related to the proposed hybrid scheme block prediction is also utilized to further reduce the residual redundancy between vq blocks the exploitation of the best features of both approaches results in high compression factors and in perceivable good quality in particular bit rates range from 0 15 to 0 07 bpp main applications of this compression scheme are in the areas of very low bit rate image transmission and image archiving

theory of j characteristics for fractional factorial designs and projection justification of minimum g2 aberration deng tang 1999 introduced the generalised resolution and minimum g aberration criteria for assessing nonregular fractional factorials in tang deng 1999 a relaxed variant of minimum g aberration called minimum g 2 aberration is proposed and studied these criteria are defined using a set of j values called j characteristics in this paper we show that a factorial design is uniquely determined by its j characteristics just as a regular factorial design is uniquely determined by its defining relation the theorem is given through an explicit formula that relates the set of design points to that of j characteristics through this formula projection justification of minimum g 2 aberration is established

sliced orthogonal array based latin hypercube designs we propose an approach for constructing a new type of design called a sliced orthogonal array based latin hypercube design this approach exploits a slicing structure of orthogonal arrays with strength two and makes use of sliced random permutations such a design achieves one and two dimensional uniformity and can be divided into smaller latin hypercube designs with one dimensional uniformity sampling properties of the proposed designs are derived examples are given for illustrating the construction method and corroborating the derived theoretical results potential applications of the constructed designs include uncertainty quantification of computer models computer models with qualitative and quantitative factors cross validation and efficient allocation of computing resources supplementary materials for this article are available online

adaptive split and merge segmentation based on piecewise least square approximation the performance of the classic split and merge segmentation algorithm is severely hampered by its rigid split and merge processes which are insensitive to the image semantics the author proposes efficient algorithms and data structures to optimize the split and merge processes by piecewise least square approximation of image intensity functions this optimization aims at the unification of segment finding and edge detection the optimized split and merge algorithm is shown to be adaptive to the image semantics and hence improves the segmentation validity of the previous algorithms this algorithm also appears to work well on noisy sources since the optimization is done within the split and merge framework the better segmentation performance is achieved at the same order of time complexity as the previous algorithms

localizing with respect to self maps of the circle we describe a general procedure to construct idempotent functors on the pointed homotopy category of connected cw complexes some of which extend localization of nilpotent spaces at a set of primes p we focus our attention on one such functor whose local objects are cw complexes x for which the pth power map on the loop space qx is a self homotopy equiv alence if p p we study its algebraic properties its behaviour on certain spaces and its relation with other functors such as bousfield s homology local ization bousfield kan completion and quillen s plus construction

columnwise pairwise algorithms with applications to the construction of supersaturated designs motivated by the construction of supersaturated designs we develop a class of algorithms called columnwise pairwise exchange algorithms they differ from the k exchange algorithms in two respects 1 they exchange columns instead of rows of the design matrix and 2 they employ a pairwise adjustment in the search for a better column the proposed algorithms perform very well in the construction of supersaturated designs both for a single criterion and for multiple criteria they are also applicable to the construction of designs that are not supersaturated

an algorithm for the design of labeled transition finite state vector quantizers a finite state vector quantizer fsvq is a switched vector quantizer where the sequence of quantizers selected by the encoder can be tracked by the decoder it can be viewed as an adaptive vector quantizer with backward estimation a vector generalization of an aqb system recently a family of algorithms for the design of fsvq s for waveform coding application has been introduced these algorithms first design an initial set of vector quantizers together with a next state function giving the rule by which the next quantizer is selected the codebooks of this initial fsvq are then iteratively improved by a natural extension of the usual memoryless vector quantizer design algorithm the next state function however is not modified from its initial form in this paper we present two extensions of the fsvq design algorithms first the algorithm for fsvq design for waveform coders is extended to fsvq design of linear predictive coded lpc speech parameter vectors using an itakura saito distortion measure second we introduce a new technique for the iterative improvement of the next state function based on an algorithm from adaptive stochastic automata theory the design algorithms are simulated for an lpc fsvq and the results are compared with each other and to ordinary memoryless vector quantization several open problems suggested by the simulation results are presented

k circulant supersaturated designs a class of supersaturated designs called k circulant designs is explored these designs are constructed from cyclic generators by cycling k elements at a time the class of designs includes many es2 optimal designs some of which are already known and some of which are more efficient than known designs for model estimation under factor sparsity generators for the most efficient designs are listed and projection properties of some of the designs are explored we also illustrate that some k circulant supersaturated designs can be augmented with interaction columns to produce efficient designs for a larger number of factors or for estimating interactions

on the existence of saturated and nearly saturated asymmetrical orthogonal arrays we develop a combinatorial condition necessary for the existence of a saturated asymmetrical orthogonal array of strength 2 this condition limits the choice of integral solutions to the system of equations in the bose bush approach and can thus strengthen considerably the bose bush approach as applied to a symmetrical part of such an array as a consequence several nonexistence results follow for saturated and nearly saturated orthogonal arrays of strength 2 one of these leads to a partial settlement of an issue left open in a paper by wu zhang and wang nonexistence of a class of saturated asymmetrical orthogonal arrays of strength 4 is briefly discussed

a low complexity region based video coder using backward morphological motion field segmentation we introduce a novel region based video compression framework based on morphology to efficiently capture motion correspondences between consecutive frames in an image sequence our coder is built on the observation that the motion field associated with typical image sequences can be segmented into component motion subfield clusters associated with distinct objects or regions in the scene and further that these clusters can be efficiently captured using morphological operators in a backward framework that avoids the need to send region shape information region segmentation is performed directly on the motion field by introducing a small core for each cluster that captures the essential features of the cluster and reliably represents its motion behavior cluster matching is used in lieu of the conventional block matching methods of standard video coders to define a cluster motion representation paradigm furthermore a region based pel recursive approach is applied to find the refinement motion field for each cluster and the cluster motion prediction error image is coded by a novel adaptive scalar quantization method experimental results reveal a 10 20 reduction in prediction error energy and 1 3 db gain in the final reconstructed peak signal to noise ratio psnr over the standard mpeg 1 coder at typical bit rates of 500 kb s to 1 mb s on standard test sequences while also requiring lower computational complexity

a new class of supersaturated designs supersaturated designs are useful in situations in which the number of active factors is very small compared to the total number of factors being considered in this article a new class of supersaturated designs is constructed using half fractions of hadamard matrices when a hadamard matrix of order n is used such a design can investigate up to n 2 factors in n 2 runs results are given for n 60 extension to larger n is straightforward these designs are superior to other existing supersaturated designs and are easy to construct an example with real data is used to illustrate the ideas

homotopical localizations of spaces for a map f of spaces dror farjoun and the author have constructed an f localization functor where a space y is called f local when map f y is an equivalence this very general construction gives all known idempotent homotopy functors of spaces the main theorem of this paper shows that f localization functors always preserve fiber sequences of connected h spaces up to small error terms for instance the localization with respect to the n th morava k theory preserves such fiber sequences up to error terms with at most three nontrivial homotopy groups this implies for example that a k 1 homology equivalence of h spaces must induce an isomorphism of v 1 periodic homotopy groups results are also obtained on the a nullification or a periodization functors which are just the f localization functors for the maps f from spaces a to points two spaces are said to have the same nullity when they give the same nullification functors and it is shown that arbitrary sets of nullity classes have both least upper bounds and greatest lower bounds the a nullifications of nilpotent postnikov spaces are completely determined

subband coding of images subband coding has become quite popular for the source encoding of speech this paper presents a simple yet efficient extension of this concept to the source coding of images we specify the constraints for a set of two dimensional quadrature mirror filters qmf s for a particular frequency domain partition and show that these constraints are satisfied by a separable combination of one dimensional qmf s bits are then optimally allocated among the subbands to minimize the mean squared error for dpcm coding of the subbands also an adaptive technique is developed to allocate the bits within each subband by means of a local variance mask optimum quantization is employed with quantizers matched to the laplacian distribution subband coded images are presented along with their signal to noise ratios snr s the snr performance of the subband coder is compared to that of the adaptive discrete cosine transform dct vector quantization and differential vector quantization for bit rates of 0 67 1 0 and 2 0 bits per pixel for 256 256 monochrome images the adaptive subband coder has the best snr performance

nearly orthogonal arrays mappable into fully orthogonal arrays we develop a method for construction of arrays which are nearly orthogonal in the sense that each column is orthogonal to a large proportion of the other columns and which are convertible to fully orthogonal arrays via a mapping of the symbols in each column to a possibly smaller set of symbols these arrays can be useful in computer experiments as designs which accommodate a large number of factors and enjoy attractive space filling properties our construction allows both the mappable nearly orthogonal array and the consequent fully orthogonal array to be either symmetric or asymmetric resolvable orthogonal arrays play a key role in the construction

generalized minimum aberration for asymmetrical fractional factorial designs by studying treatment contrasts and anova models we propose a generalized minimum aberration criterion for comparing asymmetrical fractional factorial designs the criterion is independent of the choice of treatment contrasts and thus model free it works for symmetrical and asymmetrical designs regular and nonregular designs in particular it reduces to the minimum aberration criterion for regular designs and the minimum g 2 aberration criterion for two level nonregular designs in addition by exploring the connection between factorial design theory and coding theory we develop a complementary design theory for general symmetrical designs which covers many existing results as special cases

generating systematic supersaturated designs practitioners are routinely faced with distinguishing between factors that have real effects and those whose apparent effects are due to random error when there are many factors the usual advice given is to run so called main effect designs resolution iii designs in the orthogonal case that require at least k 1 runs for investigating k factors this may be wasteful however if the goal is only to detect those active factors this is particularly true when the number of factors is large in such situations a supersaturated design can often save considerable cost a supersaturated design is a fraction of a factorial design composed of n observations where n k 1 when such a design is used the abandonment of orthogonality is inevitable this article examines the maximum number of factors that can be accommodated when the degree of the nonorthogonality is specified furthermore interesting properties of systematic supersaturated designs are revealed for example such a design may be adequate

on the homotopy type of p completions of infra nilmanifolds infra nilmanifolds are compact k g 1 manifolds with g a torsion free finitely generated virtually nilpotent group motivated by previous results of various authors on p completions of k g 1 spaces with g a finite or a nilpotent group we study the homotopy type of p completions of infra nilmanifolds for any prime p we prove that the p completion of an infra nilmanifold is a virtually nilpotent space which is either aspherical or has infinitely many nonzero homotopy groups the same is true for p localization moreover we show by means of examples that rationalizations of infra nilmanifolds may be elliptic or hyperbolic

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

image coding using vector quantization a review a review of vector quantization techniques used for encoding digital images is presented first the concept of vector quantization is introduced then its application to digital images is explained spatial predictive transform hybrid binary and subband vector quantizers are reviewed the emphasis is on the usefulness of the vector quantization when it is combined with conventional image coding techniques or when it is used in different domains

on the p adic completions of nonnilpotent spaces this paper deals with the p adic completion f p x developed by bousfield kan for a space x and prime p a space x is called f p good when the map x f p x is a mod p homology equivalence and called f p bad otherwise general examples of f p good spaces are established beyond the usual nilpotent or virtually nilpotent ones these include the polycyclic by finite spaces however the wedge of a circle with a sphere of positive dimension is shown to be f p bad this provides the first example of an f p bad space of finite type and implies that the p profinite completion of a free group on two generators must have nontrivial higher mod p homology as a discrete group

region based hierarchical image matching this paper presents an approach to region based hierarchical image matching where given two images the goal is to identify the largest part in image 1 and its match in image 2 having the maximum similarity measure defined in terms of geometric and photometric properties of regions e g area boundary shape and color as well as region topology e g recursive embedding of regions to this end each image is represented by a tree of recursively embedded regions obtained by a multiscale segmentation algorithm this allows us to pose image matching as the tree matching problem to overcome imaging noise one to one many to one and many to many node correspondences are allowed the trees are first augmented with new nodes generated by merging adjacent sibling nodes which produces directed acyclic graphs dags then transitive closures of the dags are constructed and the tree matching problem reformulated as finding a bijection between the two transitive closures on dags while preserving the connectivity and ancestor descendant relationships of the original trees the proposed approach is validated on real images showing similar objects captured under different types of noise including differences in lighting conditions scales or viewpoints amidst limited occlusion and clutter

a general method of constructing e s2 optimal supersaturated designs there has been much recent interest in supersaturated designs and their application in factor screening experiments supersaturated designs have mainly been constructed by using the e s 2 optimality criterion originally proposed by booth and cox in 1962 however until now e s 2 optimal designs have only been established with certainty for n experimental runs when the number of factors m is a multiple of n 1 and in adjacent cases where m q n 1 r r 2 q an integer a method of constructing e s 2 optimal designs is presented which allows a reasonably complete solution to be found for various numbers of runs n including n 8 12 16 20 24 32 40 48 64

construction of optimal multi level supersaturated designs author s xu hongquan wu cfj abstract a supersaturated design is a design whose run size is not large enough for estimating all the main effects the goodness of multi level supersaturated designs can be judged by the generalized minimum aberration criterion proposed by xu and wu 2001 optimal supersaturated designs are shown to have a periodic property and general methods for constructing optimal multilevel supersaturated designs are proposed inspired by the addelman kempthorne construction of orthogonal arrays optimal multi level supersaturated designs are given in an explicit form columns are labeled with linear or quadratic polynomials and rows are points over a finite field additive characters are used to study the properties of resulting designs some small optimal supersaturated designs of 3 4 and 5 levels are listed with their properties

construction of supersaturated designs through partially aliased interactions summary an n x n hadamard matrix can be used to construct a saturated 2 n 1 design with n runs furthermore if an interaction column for two of the columns of the matrix is not fully aliased with any column of the matrix this interaction column can be used as a supplementary column for studying an additional factor for some small hadamard matrices studied by plackett burman 1946 the number of such interaction columns is very large thus allowing the construction of supersaturated designs whose number of factors far exceeds the number of runs a general method of construction along these lines is proposed the efficiency of the constructed designs is studied by using three criteria

localization and genus in group theory we provide a unifying category theoretical framework to discuss various kinds of local global phenomena specializing to localization of groups at sets of primes p we identify a large class of groups for which localization supports a passage from local information to global information local global principles for groups in this class are established and used to calculate certain homomorphism sets as well as splittings of epimorphisms and monomorphisms from local data

centroidal voronoi tessellations applications and algorithms a centroidal voronoi tessellation is a voronoi tessellation whose generating points are the centroids centers of mass of the corresponding voronoi regions we give some applications of such tessellations to problems in image compression quadrature finite difference methods distribution of resources cellular biology statistics and the territorial behavior of animals we discuss methods for computing these tessellations provide some analyses concerning both the tessellations and the methods for their determination and finally present the results of some numerical experiments