asymptotics and random sampling for bci and bck lambda terms this paper presents a bijection between combinatorial maps and a class of enriched trees corresponding to a class of expression trees in some logical systems constrained lambda terms starting from two alternative definitions of combinatorial maps the classical definition by gluing half edges and a definition by non ambiguous depth first traversal we derive non trivial asymptotic expansions and efficient random generation of logic formulae syntactic trees in the bci or bck systems

a generalized depth estimation algorithm with a single image a depth estimation algorithm proposed by a p pentland 1987 is generalized in the proposed algorithm the raw image data in the vicinity of the edge is used to estimate the depth from defocus since no differentiation operation on the image data is required before the optimization process the method is less sensitive to the noise disturbance of measurements furthermore the edge orientation that was critical in pentland s approach will not be required in the case this algorithm is then applied to synthetic images containing various amounts of noise to test its performance experimental results indicate that the depth estimation errors are kept within 5 of true values on the average when it is applied to real images

classification of the ring of witt vectors and the necklace ring associated with the formal group law x y qxy abstract in this paper we classify the ring of witt vectors and the necklace ring associated with the formal group law x y q x y up to strict isomorphism as q varies over the set of integers we also introduce a q deformation of the grothendieck ring of formal power series with constant term 1 over rings in which q 1 is a unit various bijections related to witt vectors necklaces and formal power series are given as an application we provide a q analogue of the celebrated cyclotomic identity and its bijective proof

on the discrete representation of the laplacian of gaussian the laplacian of gaussian log is commonly employed as a second order edge detector in image processing and it is popular because of its attractive scaling properties however its application within a finite sampled domain is non trivial due to its infinite extent heuristics are often employed to determine the required mask size and they may lead to poor edge detection and location we derive an explicit relationship between the size of the log mask and the probability of edge detection error introduced by its approximation providing a strong basis for its stable implementation in addition we demonstrate the need for bias correction to correct the offset error introduced by truncation and derive strict bounds on the scales that may be employed by consideration of the aliasing error introduced by sampling to characterise edges a zero crossing detector is proposed which uses a bilinear surface to guarantee detection and closure of edges these issues are confirmed by experimental results which particularly emphasise the importance of bias correction as such we give a new basis for implementation of the log edge detector and show the advantages that such analysis can confer

formal group theoretic generalizations of the necklace algebra including aq deformation abstract n metropolis and g c rota adv math 50 1983 95 125 studied thenecklace polynomials and were lead to define thenecklace algebraas a combinatorial model for the classical ring ofwitt vectors which corresponds to the multiplicative formal group lawx y xy in this paper we define and study a generalized necklace algebra which is associated with an arbitrary formal group lawfover a torsion free ringa the map from the ring of witt vectors associated withfto the necklace algebra is constructed in terms of certain generalizations of the necklace polynomials we present a combinatorial interpretation for these polynomials in terms of words on a given alphabet the actions of theverschiebungandfrobeniusoperators as well as of thep typification idempotentare described and interpreted combinatorially aq analogue and other generalizations of thecyclotomic identityare also presented in general the necklace algebra can only be defined over the rationalizationa q nevertheless we show that for the family of formal group laws over the integersfq x y x y qxy q z we can define the corresponding necklace algebras over z we classify these algebras and define isomorphic ring structures on the groups of witt vectors and the groups of curves associated with the formal group lawsfq theq necklace polynomials which turn out to benumerical polynomialsin two variables can be interpreted combinatorially in terms of so calledq words and they satisfy an identity generalizing a classical one

minimum spanning trees in k dimensional space we study the problem of finding a minimum spanning tree in the complete graph on a set v of n points in k dimensional space the points are the vertices of this graph and the weight of an edge between two points is the distance between the points under some l q metric we give an o varepsilon k n log n algorithm for finding an approximate minimum spanning tree in such a graph the weight of the approximate minimum spanning tree is guaranteed to be at most 1 varepsilon times the weight of a minimum spanning tree we also present an algorithm to find a minimum spanning tree in the complete graph on v under the assumption that v consists of n random points independently and uniformly distributed in the unit k cube 0 1 k the expected running time of this minimum spanning tree algorithm is shown to be o n alpha cn n where c is a constant dependent on k and alpha is the inverse ackermann function

a moment based unified approach to image feature detection in this paper a novel model based approach is proposed for generating a set of image feature maps or primal sketches for each type of feature a piecewise smooth parametric model is developed to characterize the local intensity function in an image projections of the intensity profile onto a set of orthogonal zernike moment generating polynomials are used to estimate model parameters and in turn generate the desired feature map a small set of moment based detectors is identified that can extract various kinds of primal sketches from intensity as well as range images one main advantage of using parametric model based techniques is that it is possible to extract complete information i e model parameters about the underlying image feature which is desirable in many high level vision tasks experimental results are included to demonstrate the effectiveness of proposed feature detectors

subpixel edge detection of color images by principal axis analysis and moment preserving principle this paper discusses a new approach for detecting edges with sub pixel accuracy in color images using the principal axis analysis and the moment preserving principle first the principal axis of the color vectors in a three dimensional space is obtained analytically for each image block based on the projection scores the direction of the line edge is obtained by analyzing the three dimensional principal axis of a color image block next by preserving some spatial color moments of the pixels of each square block analytic formulas are derived to extract the edge feature experiments on both synthetic and real images show that the accuracy of the proposed method is comparable to other color edge detectors the proposed algorithm can be performed very fast for real time applications with no need for special hardware

detecting the wheel pattern of a vehicle using stereo images abstract this paper presents a method for detecting the wheels of a vehicle in stereo image pairs the method consists of two steps i geometrical transformation and ii circle extraction the geometrical transformation uses the disparity values obtained from a stereo image pair to calculate the parameters of the plane containing wheels of the vehicle by using these parameters we transform any elliptical wheels contained in the plane to circular ones which can be extracted by the circle extraction algorithm the circle extraction algorithm consists of 1 template matching and 2 hough transform in order to save computation and improve the results in the hough transform we employ two constraints a the neighbor region edge connectivity and b the gradient direction of each edge point to eliminate non circular edge points experimental results show that these two constraints do eliminate non circular edge points and preserve any circle embedded in edges from the final results we can observe that our method can detect and locate the wheels of a vehicle successfully

relaxation labeling in stereo image matching this paper outlines a method for solving the global stereovision matching problem using edge segments as the primitives a relaxation scheme is the technique commonly used by existing methods to solve this problem these techniques generally impose the following competing constraints similarity smoothness ordering and uniqueness and assume a bound on the disparity range the smoothness constraint is basic in the relaxation process we have verified that the smoothness and ordering constraints can be violated by objects close to the cameras and that the setting of the disparity limit is a serious problem this problem also arises when repetitive structures appear in the scene i e complex images where the existing methods produce a high number of failures we develop our approach from a relaxation labeling method 1 w j christmas j kittler m petrou structural matching in computer vision using probabilistic relaxation ieee trans pattern anal mach intell 17 8 1995 749 764 which allows us to map the above constraints the main contribution is made 1 by applying a learning strategy in the similarity constraint and 2 by introducing specific conditions to overcome the violation of the smoothness constraint and to avoid the serious problem produced by the required fixation of a disparity limit consequently we improve the stereovision matching process a better performance of the proposed method is illustrated by comparative analysis against some recent global matching methods

relaxation by hopfield network in stereo image matching abstract this paper outlines a relaxation approach using the hopfield neural network for solving the global stereovision matching problem the primitives used are edge segments the similarity smoothness and uniqueness constraints are transformed into the form of an energy function whose minimum value corresponds to the best solution of the problem we combine two methods a optimization relaxation 1 and b relaxation merit 2 with the above three constraints mapped in an energy function the main contribution is made 1 by applying a learning strategy in the similarity constraint and 2 by introducing specific conditions to overcome the violation of the smoothness constraint and to avoid the serious problem arising from the required fixation of a disparity limit so we improve the stereovision matching process a better performance of the proposed method is illustrated with a comparative analysis against a classical relaxation method

on bipartite drawings and the linear arrangement problem the bipartite crossing number problem is studied and a connection between this problem and the linear arrangement problem is established a lower bound and an upper bound for the optimal number of crossings are derived where the main terms are the optimal arrangement values two polynomial time approximation algorithms for the bipartite crossing number are obtained the performance guarantees are o log n and o log2 n times the optimal respectively for a large class of bipartite graphs on n vertices no polynomial time approximation algorithm which could generate a provably good solution had been known for a tree a formula is derived that expresses the optimal number of crossings in terms of the optimal value of the linear arrangement and the degrees resulting in an o n1 6 time algorithm for computing the bipartite crossing number the problem of computing a maximum weight biplanar subgraph of an acyclic graph is also studied and a linear time algorithm for solving it is derived no polynomial time algorithm for this problem was known and the unweighted version of the problem had been known to be np hard even for planar bipartite graphs of degree at most 3

3 d information derivation from a pair of binocular images abstract a new scheme using a pair of stereo images for 3 d information derivation about a scene is presented first we establish a triangulation geometry between two camera models and a point in 3 d scene in this scheme the successful implementation of a matching algorithm of features in images is considered as the key step of stereovision analysis after a brief discussion of feature extraction representation and internal implementation an efficient stereo feature matching algorithm is proposed finally some results obtained by applying the matching algorithm to several pairs of stereo images are shown in the paper

modeling edges at subpixel accuracy using the local energy approach in this paper we describe a new technique for id and 2d edge feature extraction to subpixel accuracy using edge models and the local energy approach a candidate edge is modeled as one of a number of parametric edge models and the fit is refined by a least squared error fitting technique

self similarity in the combinatorics of orthogonal polynomials resume dans cet article nous construisons des structures combinatoires invariantes sous l action d une permutation donnee dans certains cas le poids de ces dernieres correspon a des polynomes orthogonaux dont on a ajuste convenablement les parametres on examine ici de ces structures associees aux polynomes de hermite laguerre krawtchouk meixner meixner pollaczek et de jacobi

active tracking strategy for monocular depth inference over multiple frames the extraction of depth information from a sequence of images is investigated an algorithm that exploits the constraint imposed by active motion of the camera is described within this framework in order to facilitate measurement of the navigation parameters a constrained egomotion strategy was adopted in which the position of the fixation point is stabilized during the navigation in an anthropomorphic fashion this constraint reduces the dimensionality of the parameter space without increasing the complexity of the equations a further distinctive point is the use of two sampling rates the faster related to the computation of the instantaneous optical flow is fast enough to allow the local operator to sense the passing edge or in other words to allow the tracking of moving contour points while the slower used to perform the triangulation procedure necessary to derive depth is slow enough to provide a sufficiently large baseline for triangulation experimental results on real image sequences are presented

witt vectors and the algebra of necklaces where u is the classical mobius function m a n is called a necklace polynomial we shall be concerned with some remarkable identities satisfied by the polynomials m a n which apparently have not been previously noticed specifically we prove that m a n can be expressed as a quadratic polynomial in m a i and mj that m a n can be expressed linearly and integrally in terms of m a i the proofs given below of these identities are entirely combinatorial theorems l 6

orthogonal moment operators for subpixel edge detection abstract a new approach to detect step edges with subpixel accuracy is presented the proposed approach is based on a set of orthogonal complex moments of the image known as zernike moments an ideal two dimensional 2d step edge is modeled in terms of four parameters the background gray level the step size the distance of the edge from the center of the mask and the orientation of the edge discrete zernike moments are used to obtain a total of three complex masks to compute all the edge parameters for subpixel detection for pixel level edge detection only two masks one real and one complex are required the theoretical analysis of the influence of noise on the location and the orientation of an edge is presented this analysis reveals that the accuracy of the proposed approach is virtually unaffected by the additive noise the technique is effective in detecting both the pixel level and subpixel level edges experimental results are presented to demonstrate the efficacy of the proposed technique

fuzzy cognitive maps for stereovision matching this paper outlines a method for solving the stereovision matching problem using edge segments as the primitives in stereovision matching the following constraints are commonly used epipolar similarity smoothness ordering and uniqueness we propose a new matching strategy under a fuzzy context in which such constraints are mapped the fuzzy context integrates both fuzzy clustering and fuzzy cognitive maps with such purpose a network of concepts nodes is designed each concept represents a pair of primitives to be matched each concept has associated a fuzzy value which determines the degree of the correspondence the goal is to achieve high performance in terms of correct matches the main findings of this paper are reflected in the use of the fuzzy context that allows building the network of concepts where the matching constraints are mapped initially each concept value is loaded via the fuzzy clustering and then updated by the fuzzy cognitive maps framework this updating is achieved through the influence of the remainder neighboring concepts until a good global matching solution is achieved under this fuzzy approach we gain quantitative and qualitative matching correspondences this method works as a relaxation matching approach and its performance is illustrated by comparative analysis against some existing global matching methods

one pixel wide closed boundary identification an appropriate space of one pixel wide closed opwc boundary configurations is explicitly defined and an automatic algorithm to obtain opwc contour estimates from a segmented image is presented the motivation is to obtain a reasonable starting estimate for a markov chain monte carlo based mcmc based boundary optimization algorithm

a generalized cyclotomic identity abstract in this paper we prove a generalization of the cyclotomic identity for each group g satisfying suitable finiteness conditions we prove this generalized cyclotomic identity by counting coloured g set structures the cyclotomic identity corresponds to taking g the free abelian group of rank one for the free abelian group of rank two for example we get an analogous identity involving the generating function of the partition function interalia we show that studying g set structures gives a unified and conceptually simple approach to other classical combinatorial identities not to the author s knowledge previously linked in the literature

image smoothing and edge detection by hermite integration in the present paper we propose hermite polynomial integration method for gaussian and gaussian derivatives filtering in image smoothing and edge detection hermite integration method for one dimensional 1d gaussian filtering is at first introduced and its performance is analysed the hermite method is then generalized to gaussian derivative filtering and to multi dimensional cases application for edge detection with a subpixel precision is presented as well experimental results which confirm the theoretical analysis are reported

r analogue of the burnside ring of profinite groups and free lie algebras abstract let r be a finite dimensional torsion free special ring in this paper we generalize the results in dress and siebeneicher adv in math 70 1988 89 78 1989 1 by constructing r analogue r g of the burnside ring of profinite groups g in particular we remark that the grothendieck lie module denominator identity of free lie algebras in oh necklace rings and logarithmic functions preprint kias 2003 is closely related to the canonical isomorphism between r g and grothendieck s ring of formal power series with coefficients in r and constant term 1

detection of intensity changes with subpixel accuracy using laplacian gaussian masks we present a system that takes a gray level image as input locates edges with subpixel accuracy and links them into lines edges are detected by finding zero crossings in the convolution of the image with laplacian of gaussian log masks the implementation differs markedly from m i t s as we decompose our masks exactly into a sum of two separable filters instead of the usual approximation by a difference of two gaussians dog subpixel accuracy is obtained through the use of the facet model 1 we also note that the zero crossings obtained from the full resolution image using a space constant for the gaussian and those obtained from the 1 n resolution image with 1 n pixel accuracy and a space constant of n for the gaussian are very similar but the processing times are very different finally these edges are grouped into lines using the technique described in 2

on the location error of curved edges in low pass filtered 2 d and 3 d images the authors study the location error of curved edges in two and three dimensional images after analog and digital low pass filtering the zero crossing of a second derivative filter is a well known edge localization criterion the second derivative in gradient direction sdgd produces a predictable bias in edge location towards the centers of curvature while the linear laplace filter produces a shift in the opposite direction their sum called plus plus laplace sdgd leads to an edge detector that finds curved edges one order more accurately than its constituents this argument holds irrespective of the dimension the influence of commonly used low pass filters such as the psf originating from diffraction limited optics using incoherent light 2 d the gaussian filter with variable cutoff point d d and the isotropic uniform filter d d is studied

on achievable accuracy in edge localization edge localization occurs when an edge detector determines the location of an edge in an image the authors use statistical parameter estimation techniques to derive bounds on achievable accuracy in edge localization these bounds known as the cramer rao bounds reveal the effect on localization of factors such as signal to noise ratio snr extent of edge observed scale of smoothing filter and a priori uncertainty about edge intensity by using continuous values for both image coordinates and intensity the authors focus on the effect of these factors prior to sampling and quantization they also analyze the canny algorithm and show that for high snr its mean squared error is only a factor of two higher than the lower limit established by the cramer rao bound although this is very good the authors show that for high snr the maximum likelihood estimator which is also derived virtually achieves the lower bound

q deformation of witt burnside rings in this paper we construct a q deformation of the witt burnside ring of a profinite group over a commutative ring where q ranges over the set of integers when q 1 it coincides with the witt burnside ring introduced by dress and siebeneicher adv math 70 87 132 1988 to achieve our goal we first show that there exists a q deformation of the necklace ring of a profinite group over a commutative ring as in the classical case i e the case q 1 q deformed witt burnside rings and necklace rings always come equipped with inductions and restrictions we also study their properties as a byproduct we prove a conjecture due to lenart j algebra 199 703 732 1998 finally we classify mathbb w g q up to strict natural isomorphism in case where g is an abelian profinite group

building surfaces of evolution the weaving wall this paper describes a three dimensional surface construction process designed for the analysis of image sequences named the weaving wall the process operates over images as they arrive from a sensor knitting together along a parallel frontier connected descriptions of images as they evolve over time although the weaving wall was developed to support a tracking mechanism for recovering the three dimensional structure of a scene being traversed other applications of the surface building process have since become apparent these include rendering and computation on tomographic medical data display of higher dimensional analytic functions edge detection on the scale space surface and display and analysis of material fracture data more generally the weaving wall may be of use in representing the evolution of any two dimensional imagery varying in a nearly continuous manner along a third dimension we are currently looking into extending the processing to higher dimensions

q analog of the mobius function and the cyclotomic identity associated to a profinite group abstract let g be a profinite group and q an indeterminate in this paper we introduce and study a q analog of the mobius function and the cyclotomic identity arising from the lattice of open subgroups of g when q is any integer we show that they have close connections with the functors w g q nr g q and nr g q introduced in y t oh q deformation of witt burnside rings math z 257 2007 151 191 in particular we interpret the multiplicative property of the inverse of the table of marks and the mobius function of g as a composition property of certain functors classification of w g q nr g q and nr g q up to strict natural isomorphism as q varies over the set of integers and its application will be dealt with too

edge detection and linear feature extraction using a 2 d random field model the edge detection problem is posed as one of detecting step discontinuities in the observed correlated image using directional derivatives estimated with a random field model specifically the method consists of representing the pixels in a local window by a 2 d causal autoregressive ar model whose parameters are adaptively estimated using a recursive least squares algorithm the directional derivatives are functions of parameter estimates an edge is detected if the second derivative in the direction of the estimated maximum gradient is negatively sloped and the first directional derivative and a local estimate of variance satisfy some conditions because the ordered edge detector may not detect edges of all orientations well the image scanned in four different directions and the union of the four edge images is taken as the final output the performance of the edge detector is illustrated using synthetic and real images comparisons to other edge detectors are given a linear feature extractor that operates on the edges produced by the ar model is presented

a new learning strategy for stereo matching derived from a fuzzy clustering method this paper presents an approach to the local stereo correspondence problem the primitives or features used are groups of collinear connected edge points called segments each segment has several associated attributes or properties we have verified that the differences of the attributes for the true matches cluster in a cloud around a center then for each current pair of primitives we compute a distance between the difference of its attributes and the cluster center the correspondence is established in the basis of the minimum distance criterion similarity constraint we have designed an image understanding system to learn the best representative cluster center for such purpose a new learning method is derived from the fuzzy c means fcm algorithm where the dispersion of the true samples in the cluster is taken into account through the mahalanobis distance this is the main contribution of this paper a better performance of the proposed local stereo matching learning method is illustrated with a comparative analysis between classical local methods without learning

upper bounds for sorting integers on random access machines two models of random access machines suitable for sorting integers are presented our main results show that i a ram with addition subtraction multiplication and integer division can sort n integers in the range 0 2 cn in o n log c n steps ii a ram with addition subtraction and left and right shifts can sort any n integers in linear time iii a ram with addition subtraction and left and right shifts can sort n integers in the range 0 n c in o n log c n steps where all intermediate results are bounded in value by the largest input

nested witt vectors and their q deformation abstract let n n be a truncation set we study the ring of n nested witt vectors and its q deformation given two arbitrary integers q and r we provide a necessary and sufficient condition of a so that w n q a and w n r a should be strictly isomorphic to each other also an isomorphism of functors w n q w m q w m n q will be established for coprime truncation sets m and n as a byproduct we deal with interesting connections between nested witt vectors and other areas such as generalized mobius functions and numerical polynomials i e polynomials which take integral values at integer arguments

on the edge location error for local maximum and zero crossing edge detectors examines the localization criterion for edge detection and determine the probability density function describing the edge location error canny 1986 defines the measure of localization as the reciprocal of the root mean square edge location error and formulates an expression of this measure for local maximum detectors however tagare and defigueiredo 1990 point out that an incorrect assumption is made in the calculation the same procedure is used by sarkar and boyer 1991 for their localization measure for zero crossing detectors we modify the analysis and obtain a closed form solution of the probability density function of the edge location error examination of the density function indicates the variance of the edge location error does not exist and hence cannot be used directly as a measure of localization

two results on linear embeddings of complete binary trees given a binary tree t with n vertices we want to embed t onto a given set a of n points on the line so as to minimize the total embedded edge length polynomial time algorithms for the two following special cases of this problem can be found in the literature 1 when t is arbitrary but a 1 n 2 when t is a complete binary tree and a is arbitrary to the best of our knowledge the complexity of the general problem is open in this paper we deal with case 2 bern et al presented an algorithm for this case that runs in time o n5 76 and uses o n3 2 space they also considered the naive embedding which maps the root r of t into the middle point a of a and then embeds recursively the left and right subtrees of r to the left and right of a respectively this is equivalent to embedding t from left to right according to the inorder traversal they prove that this naive algorithm approximates the optimal solution within the factor of 3 the main results of this paper are i the proof that the approximation ratio of this naive algorithm is exactly 73 and ii a more efficient algorithm for computing minimum embeddings of complete binary trees our algorithm runs in time o n1 log 3 o n2 59 and uses o n space where o f o f logcn for some constant c 0

une theorie combinatoire des series formelles abstract this paper presents a combinatorial theory of formal power series the combinatorial interpretation of formal power series is based on the concept of species of structures a categorical approach is used to formulate it a new proof of cayley s formula for the number of labelled trees is given as well as a new combinatorial proof due to g labelle of lagrange s inversion formula polya s enumeration theory of isomorphism classes of structures is entirely renewed recursive methods for computing cycle index polynomials are described a combinatorial version of the implicit function theorem is stated and proved the paper ends with general considerations on the use of coalgebras in combinatorics

subpixel measurements using a moment based edge operator recent results in precision measurements using computer vision are presented an edge operator based on two dimensional spatial moments is given the operator can be implemented for virtually any size of window and has been shown to locate edges in digitized images to a twentieth of a pixel this accuracy is unaffected by additive or multiplicative changes to the data values the precision is achieved by correcting for many of the deterministic errors caused by nonideal edge profiles using a lookup table to correct the original estimates of edge orientation and location this table is generated using a synthesized edge which is located at various subpixel locations and various orientations the operator is extended to accommodate nonideal edge profiles and rectangularly sampled pixels the technique is applied to the measurement of imaged machined metal parts theoretical and experimental noise analyses show that the operator has relatively small bias in the presence of noise

fast convolution with laplacian of gaussian masks we present a technique for computing the convolution of an image with log laplacian of gaussian masks it is well known that a log of variance a can be decomposed as a gaussian mask and a log of variance 1 we take advantage of the specific spectral characteristics of these filters in our computation the log is a bandpass filter we can therefore fold the spectrum of the image after low pass filtering without loss of information which is equivalent to reducing the resolution we present a complete evaluation of the parameters involved together with a complexity analysis that leads to the paradoxical result that the computation time decreases when increases we illustrate the method on two images

transdichotomous results in computational geometry i point location in sublogarithmic time given a planar subdivision whose coordinates are integers bounded by u leq2 w we present a linear space data structure that can answer point location queries in o min lg n lg lg n sqrt lg u lg lg u time on the unit cost random access machine ram with word size w this is the first result to beat the standard theta lg n bound for infinite precision models as a consequence we obtain the first o n lg n randomized algorithms for many fundamental problems in computational geometry for arbitrary integer input on the word ram including constructing the convex hull of a three dimensional 3d point set computing the voronoi diagram or the euclidean minimum spanning tree of a planar point set triangulating a polygon with holes and finding intersections among a set of line segments higher dimensional extensions and applications are also discussed though computational geometry with bounded precision input has been investigated for a long time improvements have been limited largely to problems of an orthogonal flavor our results surpass this long standing limitation answering for example a question of willard soda 92

decomposition of the witt burnside ring and burnside ring of an abelian profinite group abstract let g h be abelian profinite groups whose orders are coprime and assume that q ranges over the set of integers the aim of this paper is to establish an isomorphism of functors w g q w h q w g h q where w g q denotes the q deformed witt burnside ring functor of g introduced in y t oh q deformation of witt burnside rings math z 207 1 2007 151 191 to do this we first establish an isomorphism of functors b g q b h q b g h q where b g q denotes the q deformed burnside ring functor of g which was also introduced in y t oh q deformation of witt burnside rings math z 207 1 2007 151 191 as an application we derive a pseudo multiplicative property of the q mobius function associated to the lattice of open subgroups of the direct sum of g and h

witt vectors and tambara functors abstract we give a combinatorial description of the ring of g witt vectors on a polynomial algebra over the integers for every finite group g using this description we show that the functor which takes a commutative ring with trivial action of g to its ring of witt vectors coincides with the left adjoint of the algebraic functor from the category of g tambara functors to the category of commutative rings with an action of g

directional analysis of images in scale space the authors propose a computational technique for the directional analysis of piecewise linear patterns in images based on the notion of zero crossings in gradient images a given image is preprocessed by a sequence of filters that are second derivatives of 2 d gaussian functions with different scales this gives a set of zero crossing maps the scale space from which a stability map is generated significant linear patterns are detected from measurements on the stability map information regarding orientation of the linear patterns in the image and the area covered by the patterns in specific directions is then computed the performance of the method is illustrated through applications to a simple test image made up of straight bar patterns as well as to scanning electron microscope images of collagen fibrils in rabbit ligaments the method has significant applications in quantitative analysis of ligament healing and in comparison of treatment methods for ligament injuries

stereo correspondence by surface reconstruction an algorithm that solves the computational stereo correspondence and the surface reconstruction is presented the algorithm integrates the reconstruction process in the correspondence analysis by means of multipass attribute matching and disparity refinement in the matching process the requirement of attribute similarity is relaxed with the pass number while the requirement for agreement between the predicted and the measured disparity is tightened disparity discontinuities and occluded areas are detected by analyzing the partial derivatives of the reconstructed disparity surface results on synthetic and on real stereo image pairs are reported

estimation of optical flow based on higher order spatiotemporal derivatives in interlaced and non interlaced image sequences abstract this contribution 1 investigates local differential techniques for estimating optical flow and its derivatives based on the brightness change constraint by using the tensor calculus representation we build the taylor expansion of the gray value derivatives as well as of the optical flow in a spatiotemporal neighborhood such a formulation provides a unifying framework for all existing local differential approaches and allows to derive new systems of equations for the estimation of the optical flow and of its derivatives we also tested various optical flow estimation approaches on real image sequences recorded by a calibrated camera which was fixed on the arm of a robot by moving the arm of the robot along a precisely defined trajectory we can determine the true displacement rate of scene surface elements projected into the image plane and compare it quantitatively with the results of different optical flow estimators since the optical flow estimators are based on gray value derivatives of up to fourth order we were forced to develop modified gaussian derivative filters to obtain acceptable estimates for the derivatives further we show quantitatively that these filters contribute to a much more robust optical flow estimation in addition successive lines of tv cameras have an offset in time due to the interlace technique we demonstrate the adaptation of filter kernels for estimating higher order spatiotemporal derivatives in interlaced image sequences

q deformed necklace rings and q mobius function abstract we introduce a q deformation of the classical mobius function and investigate its properties in connection with q deformed truncated necklace rings also we study the strictly natural isomorphism of q deformed necklace rings

an edge detection technique using the facet model and parameterized relaxation labeling we present a method for detecting and labeling the edge structures in digital gray scale images in two distinct stages first a variant of the cubic facet model is applied to detect the location orientation and curvature of the putative edge points next a relaxation labeling network is used to reinforce meaningful edge structures and suppress noisy edges each node label of this network is a 3d vector parameterizing the orientation and curvature information of the corresponding edge point a hysteresis step in the relaxation process maximizes connected contours for certain types of images prefiltering by adaptive smoothing improves robustness against noise and spatial blurring

fast geometric approximation techniques and geometric embedding problems abstract given an undirected n vertex graph g and a set of n points in r d we wish to embed the vertices of g onto the points so as to minimize the total embedded edge length important special cases of this geometric embedding problem as those in which g is a binary tree a cycle or a star we give fast approximation algorithms for embedding these graphs on the line and in the plane in several metrics our principal techniques are a notion of approximate geometric sorting that can be computed in linear time and fast approximation schemes for the minimum spanning tree problem in the plane we expect that these approximation techniques can be applied to many geometric problems besides the embedding problem we give the example of approximating the convex hull of a set of points in the plane

fibonacci heaps and their uses in improved network optimization algorithms in this paper we develop a new data structure for implementing heaps priority queues our structure fibonacci heaps abbreviated f heaps extends the binomial queues proposed by vuillemin and studied further by brown f heaps support arbitrary deletion from an n item heap in o log n amortized time and all other standard heap operations in o 1 amortized time using f heaps we are able to obtain improved running times for several network optimization algorithms in particular we obtain the following worst case bounds where n is the number of vertices and m the number of edges in the problem graph o n log n m for the single source shortest path problem with nonnegative edge lengths improved from o m log m n 2 n o n 2 log n nm for the all pairs shortest path problem improved from o nm log m n 2 n o n 2 log n nm for the assignment problem weighted bipartite matching improved from o nm log m n 2 n o m m n for the minimum spanning tree problem improved from o m log log m n 2 n where m n min i u log i n m n note that m n log n if m n of these results the improved bound for minimum spanning trees is the most striking although all the results give asymptotic improvements for graphs of appropriate densities

subpixel edge location in binary images using dithering this paper concerns the problem of obtaining subpixel estimates of the locations of straight edges in binary digital images using dithering by adding uniformly distributed independent random noise it is shown that estimation bias may be removed and that the estimation variance is inversely proportional to the length of the line segment the sensitivity to incorrect dither amplitude is calculated and implementation is discussed

approximation schemes for np hard geometric optimization problems a survey traveling salesman steiner tree and many other famous geometric optimization problems are np hard since we do not expect to design efficient algorithms that solve these problems optimally researchers have tried to design approximation algorithms which can compute a provably near optimal solution in polynomial time we survey such algorithms in particular a new technique developed over the past few years that allows us to design approximation schemes for many of these problems for any fixed constant c 0 the algorithm can compute a solution whose cost is at most 1 c times the optimum the running time is polynomial for every fixed c 0 and in many cases is even nearly linear we describe how these schemes are designed and survey the status of a large number of problems

object grammars and bijections a new systematic approach for the specification of bijections between sets of combinatorial objects is presented it is based on the notion of object grammars object grammars give recursive descriptions of objects and generalize context free grammars the study of a particular substitution in these object grammars confirms once more the key role of dyck words in the domain of enumerative and bijective combinatorics

on optimal linear arrangements of trees abstract in this paper we investigate the problem of finding a labeling of the vertices of an undirected tree with distinct integers such that the sum of weights of all edges is minimized the weight of an edge is the absolute value of the difference between the labelings of its end points we give an o n algorithm where is approximately log 3 log2 1 6 for solving this problem

a polynomial algorithm for the min cut linear arrangement of trees an algorithm is presented that finds a min cut linear arrangement of a tree in o n log n time an extension of the algorithm determines the number of pebbles needed to play the black and white pebble game on a tree

optimally isotropic laplacian operator laplacian operators used in the literature for digital image processing are not rotationally invariant we examine the anisotropy of 3 spl times 3 laplacian operators for images quantized in square pixels and find the operator which has the minimum overall anisotropy

decomposable functors and the exponential principle abstract we develop a combinatorial theory for the operation of forming the logarithm of generating functions associated with covariant functors on the category of finite sets and bijective maps this leads to a rather general and flexible exponential principle for labeled combinatorial structures we also introduce the concept of a topos like category which turns out to be a convenient framework for the discussion of a wide range of applications a few of which are studied in detail

the q t gaussian process the q t fock space fq t h introduced in this paper is a deformation of the q fock space of bozejko and speicher the corresponding creation and annihilation operators now satisfy the commutation relation aq t f aq t g qaq t g aq t f f g htn turn mathjax off a defining relation of the chakrabarti jagannathan deformed quantum oscillator algebra the moments of the deformed gaussian element sq t h aq t h aq t h are encoded by the joint statistics of crossings and nestings in pair partitions the q 0 t specialization yields a natural single parameter deformation of the full boltzmann fock space of free probability with the corresponding semicircular measure variously encoded via the rogers ramanujan continued fraction the t airy function the t catalan numbers of carlitz riordan and the first order statistics of the reduced wigner process

tracking a smooth fault line in a response surface we suggest a sequential or tracking algorithm for estimating a smooth fault line in a response surface the method starts with an approximation to a point on the line and from there the line is tracked as it meanders through the plane the technique differs from recent approaches in that it does not require a large part of the plane to be searched for evidence of a fault line this offers potential computational savings and produces a method that is invariant under rotations of coordinate axes except insofar as a rotation might affect the estimated starting point and the relative orientation of the grid on which calculations are done that feature is important if design points are not located on a regular grid we investigate properties of the method under very general conditions on the design allowing poisson cluster processes jiggled grid processes and deterministic regular lattices uniform rates of convergence are derived in all these settings for the case of noisy data and shown to be within logarithmic factors of optimal pointwise convergence rates in the no noise setting

some defects in finite difference edge finders this work illustrates and explains various artifacts in the output of five finite difference edge finders those of j f canny 1983 1986 r a boie et al 1986 and r a boie and i j cox 1987 and three variations on that of d marr and e c hildreth 1980 reimplemented with a common output format and method of noise suppression these artifacts include gaps in boundaries spurious boundaries and deformation of region shape

necklace rings and logarithmic functions in this paper we develop the theory of the necklace ring and the logarithmic function regarding the necklace ring we introduce the necklace ring functor nr from the category of special rings into the category of special rings and then study the associated adams operators as far as the logarithmic function is concerned we generalize the results in bryant s paper free lie algebras and formal power series j algebra 253 1 2002 167 188 to the case of graded lie super algebras with a group action by applying the euler poincare principle

a refined algorithm for multisensor image registration based on pixel migration multimodality image registration via pixel migration is a powerful approach however it suffers from a serious problem the global maximum on the sum of squared gradient magnitude ssg surface does not correspond to the correct solution of registration to solve the problem we partition the search space into feasible and infeasible regions the genetic algorithm global optimizer is used to obtain a good initial estimate of registration parameters and followed by a fast refining with powell s approach local optimizer the experimental results demonstrate that the use of this modified pixel migration algorithm on multisensor image registration is very effective

the position orientation masking approach to parametric search for template matching a new search method over x y spl theta called position orientation masking is introduced it is applied to vertices that are allowed to be separated into different bands of acuteness position orientation masking yields exactly one spl theta value for each x y that it considers to be the location of a possible occurrence of an object detailed matching of edge segments is performed at only these candidate x y spl theta to determine if objects actually do occur there template matching is accelerated dramatically since the candidates comprise only a small fraction of all x y spl theta position orientation masking eliminates the need for exhaustive search when deriving the candidate x y spl theta search is guided by correlations between template vertices and distance transforms of image vertices when a poor correlation is encountered at a particular position and orientation nearby positions at that orientation and nearby orientations at that position are masked out position and orientation traversal are by quadrant and binary decomposition

an application of burnside rings in elementary finite group theory abstract a canonical map from the burnside ring c of a finite cyclic group c into the burnside ring g of any finite group g of the same order is exhibited and it is shown that many results from elementary finite group theory in particular those claiming certain congruence relations are simple consequences of the existence of this map in addition it is shown that this map defines an isomorphism from c onto the subring 0 g of g consisting of those virtual g sets x which have the same number of invariants for every two subgroups u v of g of the same order if and only if g is nilpotent finally a rather natural extension to profinite groups is indicated

robust and fast computation of edge characteristics in image sequences in this paper we consider a non parametric analytical model of the intensity for a curved edge and derive the relations between the image data and some local characteristics of the edge in the discrete case in order to identify this model we also study how to develop high order non biased spatial derivative operators with subpixel accuracy in fact this discrete approach corresponds to the notion of spatio temporal surfaces in the continuous case and provides a way to obtain some of the spatio temporal parameters from an image sequence an implementation is proposed and experimental data are provided

aperiodic rings necklace rings and witt vectors in n metropolis and gian carlo rota witt vectors and the algebra of necklaces adv in math 50 1983 95 125 metropolis and rota show that the cyclotomic identity provides a linkage between the necklace ring and the ring of witt vectors in this paper we study this linkage let a be the class of rings a with the property that the additive group of a is torsion free we will prove that the ring of witt vectors over a for any a a is isomorphic to a suitably defined subring of the necklace ring of the rationalization a q of a alternatively to a subring of the aperiodic ring of a a major part of this paper is concerned with a development of the properties and relationships involving the aperiodic ring which parallels the treatment of the necklace ring given in n metropolis and gian carlo rota witt vectors and the algebra of necklaces adv in math 50 1983 95 125 in addition we translate the combinatorial proof of the cyclotomic identity given by metropolis and rota n metropolis and gian carlo rota the cyclotomic identity contemp math 34 1984 19 27 into the language of species in the sense of joyal thereby making clear the naturality of the identity

diophantine equations hilbert series and undecidable spaces summary in 1979 jan erik roos published a fascinating paper 22 making explicit connections between the poincare betti series of loop spaces or local rings and the hilbert series of finitely presented graded hopf algebras this paper develops a way to model diophantine equations within the category of graded hopf algebras combining this with roos work we obtain loop spaces and local rings whose series reflect the solution sets of arbitrary diophantine equations by matiyasevic s negative solution to hilbert s tenth problem 15 16 there is no algorithm for deciding in general whether or not a given diophantine equation has solutions for us one consequence is that no algorithm exists to decide whether a given finitely presented graded algebra is generic see 3 as to rings there is no finite procedure for evaluating whether an arbitrary ring s poincare series equals a given series even though by 10 the sequence of coefficients is recursive likewise given two finite simply connected cw complexes there is no guaranteed method to tell in general whether their loop spaces have the same rational homotopy type at the same time matiyasevic showed that there exist undecidable diophantine equations i e polynomial equations for which neither the existence nor the non existence of integer solutions may be proved in a given axiomatization of arithmetic we obtain undecidable local rings undecidable spaces and undecidable topological maps these concepts will be made precise in section 4 a few other consequences of the link between diophantine equations and hilbert series may be listed first a graded algebra resp loop space or local ring exists whose hilbert resp poincare series radius of convergence may be proved to be a transcendental number also the hilbert series can represent a transcendental function which solves no algebraic differential equation lastly we prove a stability theorem for diophantine solution sets of bounded complexity

multiple widths yield reliable finite differences computer vision a finite difference edge finder in which the finite difference is computed at a range of widths i e a range of distances between data points is introduced wide operators report low amplitude responses more reliably than narrow operators so if wide operators are used to fill gaps in narrow operator responses each operator can be restricted to report only statistically reliable responses without losing many real features this sharply reduces the noise in the final output theoretical bounds on spurious responses in the finite difference outputs given only weak assumptions about the signal and noise are presented the expected response of the edge finder to an ideal straight step edge is also analyzed these performance measures are compared with those of a standard algorithm based on gaussian smoothing and those of a second algorithm that also considers the spatial structure of noise the algorithms prove equally good at suppressing noise but are better able to detect faint or blurred features these predictions are confirmed by empirical tests on real images

the burnside ring of the infinite cyclic group and its relations to the necklace algebra λ rings and the universal ring of witt vectors abstract it is shown that well known product decompositions of formal power series arise from combinatorially defined canonical isomorphisms between the burnside ring of the infinite cyclic group on the one hand and grothendieck s ring of formal power series with constant term 1 as well as the universal ring of witt vectors on the other hand

generalized burnside grothendieck ring functor and aperiodic ring functor associated with profinite groups abstract for every profinite group g we construct two covariant functors g and ap g which are equivalent to the functor w g introduced in a dress c siebeneicher the burnside ring of profinite groups and the witt vectors construction adv math 70 1988 87 132 we call g the generalized burnside grothendieck ring functor and ap g the aperiodic ring functor associated with g in case g is abelian we also construct another functor ap g from the category of commutative rings with identity to itself as a generalization of the functor ap introduced in k varadarajan k wehrhahn aperiodic rings necklace rings and witt vectors adv math 81 1990 1 29 finally it is shown that there exist q analogues of these functors i e w g g ap g and ap g in case g is the profinite completion of the multiplicative infinite cyclic group c