hole filling in 3d volumetric objects the construction of hole filling or hole segmentation method for 3d volumetric images is a new challenging issue in computer science it needs a geometrical approach since from a topological point of view 3d holes tunnels are not well delimited subsets of three dimensional space in this paper the authors propose an original efficient flexible algorithm of hole filling for volumetric objects the algorithm has been tested on artificial objects and very complicated crack propagation tomography images the qualitative results quantitative results and features of proposed approach are presented in the paper according to our knowledge it is the first algorithm of hole filling for volumetric objects

three dimensional euclidean distance transformation and its application to shortest path planning in this paper we present a novel method to obtain the three dimensional euclidean distance transformation edt in two scans of the image the shortest path can be extracted based on the distance maps using the minimum value tracing the edt is obtained correctly and efficiently in a constant time for arbitrary types of images including the existence of obstacles by adopting the new dynamically rotational mathematical morphology we not only guarantee the collision free in the shortest path but also reduce the time complexity dramatically

new algorithms for euclidean distance transformation of an n dimensional digitized picture with applications abstract in this paper we propose a new method to obtain the euclidean distance transformation and the voronoi diagram based on the exact euclidean metric for an n dimensional picture we present four algorithms to perform the transformation which are constructed by the serial composition of n dimensional filters when performed by a general purpose computer they are faster than the method by h yamada for a two dimensional picture those algorithms require only one n dimensional array for storing input output pictures and a single one dimensional array for a work area if an input picture needs not be preserved

a linear time algorithm for computing exact euclidean distance transforms of binary images in arbitrary dimensions a sequential algorithm is presented for computing the exact euclidean distance transform dt of a k dimensional binary image in time linear in the total number of voxels n the algorithm which is based on dimensionality reduction and partial voronoi diagram construction can be used for computing the dt for a wide class of distance functions including the l sub p and chamfer metrics at each dimension level the dt is computed by constructing the intersection of the voronoi diagram whose sites are the feature voxels with each row of the image this construction is performed efficiently by using the dt in the next lower dimension the correctness and linear time complexity are demonstrated analytically and verified experimentally the algorithm may be of practical value since it is relatively simple and easy to implement and it is relatively fast not only does it run in o n time but the time constant is small a simple modification of the algorithm computes the weighted euclidean dt which is useful for images with anisotropic voxel dimensions a parallel version of the algorithm runs in o n p time with p processors

color texture analysis based on fractal descriptors color texture classification is an important step in image segmentation and recognition the color information is especially important in textures of natural scenes such as leaves surfaces terrains models etc in this paper we propose a novel approach based on the fractal dimension for color texture analysis the proposed approach investigates the complexity in r g and b color channels to characterize a texture sample we also propose to study all channels in combination taking into consideration the correlations between them both these approaches use the volumetric version of the bouligand minkowski fractal dimension method the results show a advantage of the proposed method over other color texture analysis methods

solvability of mixed type operator equations in this paper we prove the existence of monotonic solution of the mixed type operator equations we discuss also the existence of solutions of nonlinear integral equations of fractional orders the technique rely on the concept of measure of noncompactness and its associated darbo fixed point theorem

binary picture thinning by an iterative parallel two subcycle operation abstract a thinning algorithm for digital binary pictures is presented the algorithm repeats the removal of the deletable border points in parallel and the extraction of the final points it is implemented as an iterative parallel two subcycle operation consequently the number of iterations required is about equal to the maximum width of the input figures the algorithm erases the end points while the iteration number is smaller than a given threshold utilization of the final point condition makes the algorithm faster and the flexible deletion of end points produces a line pattern of good quality even for noisy figures

a commutative algebra on degenerate cp1 and macdonald polynomials we introduce a unital associative algebra a associated with degenerate cp1 we show that a is a commutative algebra and whose poincare series is given by the number of partitions thereby we can regard a as a smooth degeneration limit of the elliptic algebra introduced by feigin and odesskii int math res notices 11 531 1997 then we study the commutative family of the macdonald difference operators acting on the space of symmetric functions a canonical basis is proposed for this family by using a and the heisenberg representation of the commutative family studied by shiraishi commun math phys 263 439 2006 it is found that the ding iohara algebra lett math phys 41 183 1997 provides us with an algebraic framework for the free field construction an elliptic deformation of our construction is discussed showing connections with the drinfeld quasi hopf twisting leningrad math j 1 1419 1990 in the sence of babelon bernard billey phys lett b 375 89 1996 the ruijsenaar

efficient euclidean distance transform algorithm of binary images in arbitrary dimensions in this paper we propose an efficient algorithm i e pbedt for short to compute the exact euclidean distance transform edt of a binary image in arbitrary dimensions the pbedt is based on independent scan and implemented in a recursive way i e the edt of a d dimensional image is able to be computed from the edts of its d 1 dimensional sub images in each recursion all of the rows in the current dimensional direction are processed one by one the points in the current processing row and their closest feature points in d 1 dimensional sub images can be shown in a euclidean plane by using the geometric properties of the perpendicular bisector the closest feature points of d 1 dimensional sub images are easily verified so as to lead to the edt of a d dimensional image after eliminating the invalid points the time complexity of the pbedt algorithm is linear in the amount of both image points and dimensions with a small coefficient compared with the state of the art edt algorithms the pbedt algorithm is much faster and more stable in most cases

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

map multi angled parallelism for feature extraction from topographical maps abstract map multi angled parallelism is proposed as a unification of conventional erosion dilation operations for binary images and higher order feature representation where each pixel is composed of multiple directional elements a twisting operation is also proposed which is able to have any direction of propagation and any directional width using 8 neighbor operations the map concept can be effectively and precisely achieved using the twisting operation by combining map with vibrational operations such as erosion dilation and dilation erosion a set of map operations to extract linear features is defined these map operations have been applied successfully to the extraction of straight lines sets of points buildings hatched areas roads and character regions of topographical maps such features are difficult to extract using conventional parallel operations

from local maxima to connected skeletons in picture processing it is often convenient to deal with a stick like version skeleton of binary digital images although skeleton connectedness is not necessary for storage and retrieval purposes this property is desirable when a structural description of images is of interest in this paper a parallel procedure is described which applied to a connected image originates a connected skeleton made by the union of simple digital arcs the procedure involves a step by step propagation of the background over the image at every step contour elements either belonging to the significant convex regions of the current image or being local maxima of the original image are selected as skeleton elements since the final set so obtained is not ensured to be connected the configurations in correspondence of which disconnections appear are investigated and the procedures to avoid this shortcoming are given the presence of the whole set of local maxima among the skeleton elements ensures the possibility of recovering the original image by means of a reverse distance transform the details of the program implementing the proposed algorithm on a parallel processor are finally included

on the superposition operator and integrable solutions of some functional equations on etudie les equations x t f t x t et x t f t x t dans l espace l 1 a b equipe de la topologie de la convergence faible on montre que ces equations ont des solutions integrables qui sont additionnellement des fonctions monotones p p

monotonic solutions of a convolution functional integral equation in this paper we show that a very general convolution functional integral equation has at least one monotonic solution in the space of lebesgue integrable functions on an unbounded interval a suitable combination of the technique associated with measures of noncompactness in both the weak and the strong sense and the darbo fixed point is the main tool in our analysis

recursive binary dilation and erosion using digital line structuring elements in arbitrary orientations performing morphological operations such as dilation and erosion of binary images using very long line structuring elements is computationally expensive when performed brute force following definitions we present two pass algorithms that run at constant time for obtaining binary dilations and erosions with all possible length line structuring elements simultaneously the algorithms run at constant time for any orientation of the line structuring element another contribution of this paper is the use of the concept of orientation error between a continuous line and its discrete counterpart the orientation error is used in determining the minimum length of the basic digital line structuring element used in obtaining what we call dilation and erosion transforms the transforms are then thresholded by the length of the desired structuring element to obtain the dilation and erosion results the algorithms require only one maximum operation for erosion transform and only one minimum operation for dilation transform and one thresholding step and one translation step per result pixel we tested the algorithms on sun sparc station 10 on a set of 240 spl times 250 salt and pepper noise images with probability of a pixel being a 1 pixel set to 0 25 for orientations of the normals of the structuring elements in the range spl pi 2 3 spl pi 2 and lengths in pixels in the range 5 145 we achieved a speed up of about 50 and for special orientations spl theta spl isin spl pi 2 3 spl pi 4 spl pi 5 spl pi 4 3 spl pi 2 a speed up of about 100 when the structuring elements had lengths of 145 pixels over the brute force methods in these experiments we compared the results of our dilation algorithm with those of the algorithm discussed by soille et al see ieee trans pattern anal machine intell vol 18 p 562 67 1996 and showed that for binary dilation and erosion since it is just the dilation of the background with the reflected structuring element our algorithm performed better and achieved a speed up of about four when dilation or erosion transform alone is obtained

monotonic solutions of urysohn integralequation on unbounded interval abstract in this paper we investigate a nonlinear urysohn integral equation on unboundedinterval we show that under some assumptions that the equation has monotonic solutions belonging to the space of functions being lebesgue integrable on unbounded interval the main tool used in our study is the technique associated with measures of weak noncompactness and measures of noncompactness in strong sense

a thinning algorithm based on prominence detection abstract binary pictures are taken into account and an algorithm which transforms a digital figure into a set of 8 simple digital arcs and curves by employing local sequential operations il illustrated the adopted procedure considers the removal of suitable contour elements of the given figure and it is repeated on every current set of 1 elements as long as the final thinned figure is obtained the notion of local elongation is employed to find at every step of the process those contour regions which can be regarded as significant protrusions then such regions are detected before applying the removal operations contributing hence to the isotropic behavior of the proposed thinning transformation further refinements of the algorithm are also discussed

integrable solutions of a generalized mixed type functional integral equation in this work we prove the existence of integrable solutions for the following generalized mixed type nonlinear functional integral equation x t g t t x t f t 0 t k t s u t s q x s d s t 0 our result is established by means of a krasnosel skii type fixed point theorem proved by taoudi 2009 in the last section we give an example to illustrate our result

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

morphological representation of discrete and binary images a general theory for the morphological representation of discrete and binary images is presented the basis of this theory relies on the generation of a set of nonoverlapping segments of an image via repeated erosions and set transformations which in turn produces a decomposition that guarantees exact reconstruction the relationship between the proposed representation and some existing shape analysis tools e g discrete size transform pattern spectrum skeletons is investigated thus introducing the representation as the basis of a unified theory for geometrical image analysis particular cases of the general representation scheme are shown to yield a number of useful image decompositions which are directly related to various forms of morphological skeletons the relationship between the representation and the various forms of morphological skeletons is studied as a result of this study a unified theory is developed for the mathematical description of the morphological skeleton decomposition of discrete and binary images

a list processing approach to compute voronoi diagrams and the euclidean distance transform we propose an efficient voronoi transform algorithm for constructing voronoi diagrams using segment lists of rows a significant feature of the algorithm is that it takes segments rather than pixels as the basic units to represent and propagate the nearest neighbor information the segment lists are dynamically updated as they are scanned a distance map can then be easily computed from the segment list representation of the voronoi diagram experimental results have demonstrated its high efficiency extension of the algorithm to higher dimensions is also discussed

on generalized distance transformation of digitized pictures in this paper we present a generalization of the distance transformation of a digitized picture in two different aspects first we define the generalized distance transformation of a binary picture gdtb a subclass of gdtb called a local minimum filter family of gdtb lmf gdtb characterized by a series of local minimum filters with varying neighborhoods is discussed in detail a skeleton is defined for lmf gdtb and it is proved that any binary picture can be reconstructed exactly from its skeleton with the distance value on it second the gray weighted distance transformation gwdt is extended to a generalized gwdt ggwdt by introducing an arbitrary initial picture after the fundamental equation of ggwdt and its solution are derived it is proved that an arbitrary gray picture is generated by iterative application of ggwdt from a uniquely determined elementary picture and a sequence of initial value pictures

on a perturbed functional integral equation of urysohn type abstract we study the existence of monotonic solutions for a perturbed functional integral equation of urysohn type in the space of lebesgue integrable functions on an unbounded interval the technique associated with measures of noncompactness in both the weak and the strong sense and the darbo fixed point are the main tool to prove our main result

a nonlinear operator functional equation of volterra type in this work we establish the existence of a solution of a nonlinear equation of volterra type in the class of monotonic functions on the interval r 0 our technique rely on the concept of measure of noncompactness and its associated darboux fixed point theorem

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

morphological filters part i their set theoretic analysis and relations to linear shift invariant filters this paper examines the set theoretic interpretation of morphological filters in the framework of mathematical morphology and introduces the representation of classical linear filters in terms of morphological correlations which involve supremum infimum operations and additions binary signals are classified as sets and multilevel signals as functions two set theoretic representations of signals are reviewed filters are classified as set processing sp or function processing fp conditions are provided for certain fp filters that pass binary signals to commute with signal thresholding because then they can be analyzed and implemented as sp filters the basic morphological operations of set erosion dilation opening and closing are related to minkowski set operations and are used to construct fp morphological filters emphasis is then given to analytically and geometrically quantifying the similarities and differences between morphological filtering of signals by sets and functions the latter case allows the definition of morphological convolutions and correlations toward this goal various properties of fp morphological filters are also examined linear shift invariant filters due to their translation invariance are uniquely characterized by their kernel which is a special collection of input signals increasing linear filters are represented as the supremum of erosions by their kernel functions if the filters are also discrete and have a finite extent impulse response they can be represented as the supremum of erosions only by their minimal with respect to a signal ordering kernel functions stable linear filters can be represented as the sum of at most two weighted suprema of erosions these results demonstrate the power of mathematical morphology as a unifying approach to both linear and nonlinear signal shaping strategies

integrable solutions of a nonlinear functional integral equation on an unbounded interval abstract in this paper we prove the existence of integrable solutions of a generalized functional integral equation which includes many key integral and functional equations that arise in nonlinear analysis and its applications this is achieved by means of an improvement of a krasnosel skii type fixed point theorem recently proved by k latrach and the author the result presented in this paper extends the corresponding result of j banas a chlebowicz on existence of integrable solutions of a functional integral equation under caratheodory condition nonlinear anal 2008 doi 10 1016 j na 2008 04 020 an example which shows the importance and the applicability of our result is also included

pattern spectrum and multiscale shape representation the results of a study on multiscale shape description smoothing and representation are reported multiscale nonlinear smoothing filters are first developed using morphological opening and closings g matheron 1975 used openings and closings to obtain probabilistic size distributions of euclidean space sets continuous binary images these distributions are used to develop a concept of pattern spectrum a shape size descriptor a pattern spectrum is introduced for continuous graytone images and arbitrary multilevel signals as well as for discrete images by developing a discrete size family of patterns large jumps in the pattern spectrum at a certain scale indicate the existence of major protruding or intruding substructures of the signal at the scale an entropy like shape size complexity measure is also developed based on the pattern spectrum for shape representation a reduced morphological skeleton transform is introduced for discrete binary and graytone images this transform is a sequence of skeleton components sparse images which represent the original shape at various scales it is shown that the partially reconstructed images from the inverse transform on subsequences of skeleton components are the openings of the image at a scale determined by the number of eliminated components in addition two way correspondences are established among the degree of shape smoothing via multiscale openings or closings the pattern spectrum zero values and the elimination or nonexistence of skeleton components at certain scales

crystallization of deformed virasoro algebra ding iohara miki algebra and 5d agt correspondence in this paper we consider the q 0 limit of the deformed virasoro algebra and that of the level 1 2 representation of the ding iohara miki algebra moreover 5d agt correspondence in this limit is discussed this specialization corresponds to the limit from macdonalds functions to hall littlewood functions using the theory of hall littlewood functions some problems are solved for example the simplest case of 5d agt conjectures is proven in this limit and we obtain a formula for the 4 point correlation function of a certain operator

distances defined by neighborhood sequences abstract this paper investigates general properties of distance functions defined over digitized space we assume that a distance between two points is defined as the length of a shortest path connecting them in the underlying graph which is defined by a given neighborhood sequence many typical distance functions can be described in this form but there are cases in which given neighborhood sequence do not define distance functions we first derive a necessary and sufficient condition for a neighborhood sequence to define a distance function we then discuss another important problem of estimating how tight such distances can approximate the euclid distance from the view point of relative error and absolute error

quantum 401 1401 1401 1algebras and macdonald polynomials we derive a quantum deformation of thew n algebra and its quantum miura transformation whose singular vectors realize the macdonald polynomials

instanton counting on blowup i 4 dimensional pure gauge theory we give a mathematically rigorous proof of nekrasov s conjecture the integration in the equivariant cohomology over the moduli spaces of instantons on 4 gives a deformation of the seiberg witten prepotential for n 2 susy yang mills theory through a study of moduli spaces on the blowup of 4 we derive a differential equation for the nekrasov s partition function it is a deformation of the equation for the seiberg witten prepotential found by losev et al and further studied by gorsky et al

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

boolean reconstructions of complex materials integral geometric approach we show that for the boolean model of random composite media one can from a single image of a system at any particle fraction define a set of parameters which allows one to accurately reconstruct the medium for all other phase fractions the morphological characterization is based on a family of measures known in integral geometry which provides powerful formulas for the boolean model the percolation thresholds of either phase are obtained with good accuracy from the reconstructions one can subsequently predict property curves for the material across all phase fractions from the single three dimensional image we illustrate this for transport and mechanical properties of complex boolean systems and for experimental sandstone samples

strongly normal sets of contractible tiles in n dimensions the second and third authors and others have studied collections of usually convex tiles a generalization of pixels or voxels in r 2 and r 3 that have a property called strong normality sn for any tile p only finitely many tiles intersect p and any nonempty intersection of those tiles also intersects p this paper extends basic results about strong normality to collections of contractible polyhedra in r n whose nonempty intersections are contractible we also give sufficient and trivially necessary conditions on a locally finite collection of contractible polyhedra in r 2 or r 3 for their nonempty intersections to be contractible

on the existence of solutions of functional integral equation of urysohn type in this paper we introduce a brief historical note about the study of the existence of solutions of functional integral equations hence we prove the existence of monotonic solutions of the functional integral equation of urysohn type the technique rely on the concept of measure of noncompactness and its associated darbo fixed point theorem

solvability of urysohn integral equation in this paper we present the existence theorem of integrable solutions of urysohn integral equation in the class of monotonic functions the proof of that theorem is based on the fixed point theorem associated with the notion of a measure of noncompactness

fast distance transformation on irregular two dimensional grids in this article we propose a new fast algorithm to compute the squared euclidean distance transform e 2dt on every two dimensional 2 d irregular isothetic grids regular square grids quadtree based grids etc our new fast algorithm is an extension of the e 2dt method proposed by breu et al 3 it is based on the implicit order of the cells in the grid and builds a partial voronoi diagram of the centers of background cells thanks to a data structure of lists we compare the execution time of our method with the ones of others approaches we developed in previous works in those experiments we consider various kinds of classical 2 d grids in imagery to show the interest of our methodology and to point out its robustness we also show that our method may be interesting regarding an application where we extract an adaptive medial axis construction based on a quadtree decomposition scheme

q vertex operator from 5d nekrasov function the five dimensional agt correspondence implies the connection between the q deformed virasoro block and the 5d nekrasov partition function in this paper we determine a q deformation of the four point block in the coulomb gas representation from the 5d nekrasov function and obtain an expression of the q deformed vertex operator if we use only one kind of the q vertex operators one of the insertion points of them must be modified in order to hold the 2d 5d correspondence

on existence of integrable solutions of a functional integral equation under caratheodory conditions abstract we study the solvability of a functional integral equation in the space of lebesgue integrable functions on an unbounded interval using the conjunction of the technique of measures of weak noncompactness with the classical schauder fixed point principle we show that the equation in question is solvable in the mentioned function space our existence result is obtained under the assumption that functions involved in the investigated functional integral equation satisfy caratheodory conditions moreover that result generalizes several ones obtained earlier in many research papers and monographs

a multiscanning approach based on morphological filtering it is argued that the mathematical morphology method seems to be more reasonable and powerful in studying certain multiscaling vision problems than the approach that uses derivatives of gaussian shaped filters of different sizes to show the validity of this method the authors concentrated on an application that involves forming scale space image of a 2 d shape using morphological opening filtering a proof is given to show that morphological opening filtering has a property of not introducing additional zero crossings as one moves to a coarser scale this is a different result from the conclusion by a l yuille and t a poggio ibid vol pami 8 jan 1986 that the gaussian filter is the only filter with this property in addition opening filtering is computationaly simpler than the gaussian filter

nonlinear alternatives of schauder and krasnosel skij types with applications to hammerstein integral equations in l1 spaces abstract this paper is devoted to establishing new variants of some nonlinear alternatives of leray schauder and krasnosel skij type involving the weak topology of banach spaces the de blasi measure of weak noncompactness is used an application to solving a nonlinear hammerstein integral equation in l 1 spaces is given our results complement recent ones in k latrach m a taoudi a zeghal some fixed point theorems of the schauder and the krasnosel skij type and application to nonlinear transport equations j differential equations 221 2006 256 2710 and k latrach m a taoudi existence results for a generalized nonlinear hammerstein equation on l 1 spaces nonlinear anal 66 2007 2325 2333

line based recognition using a multidimensional hausdorff distance a line feature based approach for model based recognition using a four dimensional hausdorff distance is proposed this approach reduces the problem of finding the rotation scaling and translation transformations between a model and an image to the problem of finding a single translation minimizing the hausdorff distance between two sets of points in a four dimensional space the implementation of the proposed algorithm can be naturally extended to higher dimensional spaces to efficiently find correspondences between n dimensional patterns the method performance and sensitivity to segmentation problems are quantitatively characterized using an experimental protocol with simulated data it is shown that the algorithm performs well is robust to occlusion and outliers and that it degrades nicely as the segmentation problems increase experiments with real images are also presented

enhancing fractal descriptors on images by combining boundary and interior of minkowski dilation abstract this work proposes to obtain novel fractal descriptors from gray level texture images by combining information from interior and boundary measures of the minkowski dilation applied to the texture surface at first the image is converted into a surface where the height of each point is the gray intensity of the respective pixel in that position in the image thus this surface is morphologically dilated by spheres the radius of such spheres is ranged within an interval and the volume and the external area of the dilated structure are computed for each radius the final descriptors are given by such measures concatenated and subject to a canonical transform to reduce the dimensionality the proposal is an enhancement to the classical bouligand minkowski fractal descriptors where only the volume interior information is considered as different structures may have the same volume but not the same area the proposal yields to more rich descriptors as confirmed by results on the classification of benchmark databases

yangian gelfand zetlin bases gl n jack polynomials and computation of dynamical correlation functions in the spin calogero sutherland model we consider the invariant calogero sutherland models with n 1 2 3 in the framework of symmetric polynomials

fast 2 d distance transformations the performance of a number of image processing methods depends on the output quality of a distance transformation dt process most of the fast dt methodologies are not accurate whereas other error free dt algorithms are not very fast in this paper a novel fast simple and error free dt algorithm is presented by recording the relative x and y coordinates of the examined image pixels an optimal algorithm can be developed to achieve the dt of an image correctly and efficiently in constant time without any iteration furthermore the proposed method is general since it can be used by any kind of distance function leading to accurate image dts

generalized macdonald functions on fock tensor spaces and duality formula for changing preferred direction an explicit formula is obtained for the generalized macdonald functions on the n fold fock tensor spaces calculating a certain matrix element of a composition of several screened vertex operators as an application we prove the factorization property of the arbitrary matrix elements of the multi valent intertwining operator or refined topological vertex operator associated with the ding iohara miki algebra dim algebra with respect to the generalized macdonald functions which was conjectured by awata feigin hoshino kanai yanagida and one of the authors our proof is based on the combinatorial and analytic properties of the asymptotic eigenfunctions of the ordinary macdonald operator of a type and the euler transformation formula for kajihara and noumi s multiple basic hypergeometric series that factorization formula provides us with a reasonable algebraic description of the 5d k theoretic alday gaiotto tachikawa agt correspondence and the interpretation of the invariance under the preferred direction from the point of view of the sl 2 mathbb z duality of the dim algebra

integral solution of a class of nonlinear integral equations this paper is concerned with the existence of integral solutions to a general nonlinear integral equationx t f 1 t x f 1 t f 2t 0 f 2 t k t s f 3 s x f 3 s ds t r with the help of krasnoselskii s fixed point theorem and the theory of measure of weak noncompactness we establish a new and general existence theorem for the nonlinear functional integral equation moreover an example which can not be treated by the related theorems in 5 20 22 is given to illustrate the new existence theorem

a general scheme for constructing skeleton models abstract a general scheme which constructs connected skeleton models from digital images is presented the scheme comprises three stages 1 1 a distance transformation to obtain skeleton points 2 2 extraction of the connected skeleton and 3 3 construction of the model first distance transformations and thinning algorithms are discussed an isotropic thinning algorithm is then presented based on this algorithm an algorithm to extract the connected skeleton is described it is followed by the definition of a formal skeleton model and the model construction algorithm the relation between thinning operations and distance transforms is also discussed

optimal separable algorithms to compute the reverse euclidean distance transformation and discrete medial axis in arbitrary dimension in binary images the distance transformation dt and the geometrical skeleton extraction are classic tools for shape analysis in this paper we present time optimal algorithms to solve the reverse euclidean distance transformation and the reversible medial axis extraction problems for d dimensional images we also present a d dimensional medial axis filtering process that allows us to control the quality of the reconstructed shape

fast homotopy preserving skeletons using mathematical morphology two algorithms for skeletonization of 2 d binary images each of which explicitly separates the two major aspects of skeletonization are described the identification of points critical to shape representation and the identification of further points necessary to preserve homotopy sets of points critical to shape representation are found by eroding the original image i with a nested sequence of structuring elements e sub i by choosing appropriate e sub i and d a structuring element either algorithm is capable of producing a variety of skeletons corresponding to different distance functions a sufficient condition is given for the original image to be reconstructed from the skeleton in the case of the first algorithm there are few restrictions on the set of structuring elements it uses a simple search strategy to find points whose removal would alter homotopy the second faster algorithm has a more constructional approach to finding points necessary for preserving homotopy which limits it to a more restricted set of structuring elements than the first algorithm however it may still be used with a variety of distance functions

on a functional integral equation with deviating arguments we study the solvability of a functional integral equation with deviating arguments where our investigations take place in the space of lebesgue integrable functions on an unbounded interval in this space we show that our functional integral equation has at least one nonnegative and nonincreasing solution the proof of our main result is based on a suitable combination of the technique associated with measures of noncompactness in both the weak and the strong sense and the darbo fixed point in the end we conclude an example to illustrate our abstract results

shape based averaging a new method for averaging multidimensional images is presented which is based on signed euclidean distance maps computed for each of the pixel values we refer to the algorithm as shape based averaging sba because of its similarity to raya and udupa s shape based interpolation method the new method does not introduce pixel intensities that were not present in the input data which makes it suitable for averaging nonnumerical data such as label maps segmentations using segmented human brain magnetic resonance images sba is compared to label voting for the purpose of averaging image segmentations in a multiclassifier fashion sba on average performed as well as label voting in terms of recognition rates of the averaged segmentations sba produced more regular and contiguous structures with less fragmentation than did label voting sba also was more robust for small numbers of atlases and for low atlas resolutions in particular when combined with shape based interpolation we conclude that sba improves the contiguity and accuracy of averaged image segmentations

agt correspondence ding iohara algebra at roots of unity and lepowsky wilson construction it was recently conjectured that the agt correspondence between the instanton counting on and the two dimensional field theories with the conformal symmetry algebra can be considered as a root of unity limit of its k theoretic analogue from this point of view the algebra and a special basis in its representation are limits of the ding iohara algebra and the macdonald polynomials respectively in this paper we confirm this conjecture for the special case r 1 we uncover the implicit symmetry in this limit we also found that the vertex operators in the special basis have factorized aflt form

the affine yangian of gl1 revisited abstract the affine yangian of gl 1 has recently appeared simultaneously in the work of maulik okounkov 11 and schiffmann vasserot 20 in connection with the alday gaiotto tachikawa conjecture while the presentation from 11 is purely geometric the algebraic presentation in 20 is quite involved in this article we provide a simple loop realization of this algebra which can be viewed as an additivization of the quantum toroidal algebra of gl 1 in the same way as the yangian y h g is an additivization of the quantum loop algebra u q l g for a simple lie algebra g we also explain the similarity between the representation theories of the affine yangian and the quantum toroidal algebras of gl 1 by generalizing the main result of 10 to the current settings

vertex operators and hall littlewood symmetric functions abstract we consider vertex operators on space v with a parameter t their components form an associative algebra which is a generalization of the clifford algebra a distinguished orthogonal basis of v is proved to be the hall littlewood symmetric functions we show that kostka foulkes polynomials or certain kazhdan lusztig polynomials for the affine weyl group of type a are matrix coefficients on the space v we also obtain certain generating functions for the product of hall littlewood functions and the kostka foulkes polynomials

five dimensional su 2 agt conjecture and recursive formula of deformed gaiotto state this paper deals with the five dimensional pure su 2 alday gaiotto tachikawa agt conjecture proposed by awata and yamada j high energy phys 1001 125 2010 we give a conjecture on a recursive formula for the inner product of the deformed gaiotto state we also show that the k theoretic pure su 2 nekrasov partition function satisfies the same recursion relation therefore the five dimensional agt conjecture is reduced to our conjectural recursive formula

existence results for a generalized nonlinear hammerstein equation on l1 spaces abstract in this paper we are concerned with existence results for a nonlinear hammerstein integral equation acting on l 1 vector valued functions making use of the de blasi measure of weak noncompactness we establish a variant of the topological fixed point theorem of krasnosel skii for the sum of two operators without requiring weak compactness or weak continuity assumptions such a result provides an adequate tool for deriving an existence theory for problem 1 1

set valued integral equations of fractional orders the topic of fractional calculus derivative and integral of arbitrary orders is enjoying growing interest not only among mathematicians but also among physicists and engineers see 6 16 18 20 23 25 the set valued integral equations integral inclusions arises in the study of control system see 21 22 26 in this paper we prove the existence of locally bounded variation solution of a volterra type set valued integral equation of arbitrary not necessarily integer order the proof will be based on the measure of weak noncompactness and the existence of caratheodory selectors as a consequence we study the initial value problem for some set valued differential and integro differential equations the corresponding single valued problems will be firstly considered

weighted distance transforms generalized to modules and their computation on point lattices this paper presents the generalization of weighted distances to modules and their computation through the chamfer algorithm on general point lattices the first part is dedicated to formalization of definitions and properties distance metric norm of weighted distances on modules it resumes tools found in literature to express the weighted distance of any point of a module and to compute optimal weights in the general case to get rotation invariant distances the second part of this paper proves that for any point lattice the sequential two scan chamfer algorithm produces correct distance maps finally the definitions and computation of weighted distances are applied to the face centered cubic fcc and body centered cubic bcc grids

on the solutions for a nonlinear boundary value problem modeling a proliferating cell population with inherited cycle length abstract this paper deals with existence results for a nonlinear boundary value problem derived from a model introduced by lebowitz and rubinow 1974 describing a proliferating cell population cells are distinguished by age a and cycle length l the cycle length is viewed as an inherited property determined at birth the boundary condition models the process of cell division of mother cells and the inheritance of cycle length by daughter cells in our framework daughter cells and mother cells are related by a general reproduction rule which covers all known biological ones in this work the cycle length l is allowed to be infinite that is l l 1 this hypothesis introduces some mathematical difficulties which are overcome by using domination arguments in the lattice sense and recent fixed point theorems involving continuous weakly compact operators on non reflexive banach spaces

extraction of the euclidean skeleton based on a connectivity criterion abstract the skeleton is essential for general shape representation the commonly required properties of a skeletonization algorithm are that the extracted skeleton should be accurate robust to noise position and rotation able to reconstruct the original object and able to produce a connected skeleton in order to preserve its topological and hierarchical properties however the use of a discrete image presents a lot of problems that may influence the extraction of the skeleton moreover most of the methods are memory intensive and computationally intensive and require a complex data structure in this paper we propose a fast efficient and accurate skeletonization method for the extraction of a well connected euclidean skeleton based on a signed sequential euclidean distance map a connectivity criterion is proposed which can be used to determine whether a given pixel is a skeleton point independently the criterion is based on a set of point pairs along the object boundary which are the nearest contour points to the pixel under consideration and its 8 neighbors our proposed method generates a connected euclidean skeleton with a single pixel width without requiring a linking algorithm or iteration process experiments show that the runtime of our algorithm is faster than the distance transformation and is linearly proportional to the number of pixels of an image

a width independent fast thinning algorithm the skeleton of a digital figure can often be regarded as a convenient alternative to the figure itself it is useful both to diminish drastically the amount of data to be handled and to simplify the computational procedures required for description and classification purposes thinning a digital figure down to its skeleton is a time consuming process when conventional sequential computers are employed the procedure we propose allows one to speed up the thinning transformation and to get a well shaped skeleton after cleaning of the input picture has been performed the pixels of the figure are labeled according to their distance from the background and a set whose pixels are symmetrically placed with respect to distinct contour parts of the figure is found this set is then given a linear structure by applying topology preserving removal operations finally a pruning step regarding branches not relevant in the framework of the problem domain completes the process the resulting skeleton is a labeled set of pixels which is shown to possess all the required properties particularly those concerning connectedness topology and shape moreover the original figure can almost completely be recovered by means of a reverse distance transformation only a fixed and small number of sequential passes through the picture is necessary to achieve the goal the computational effort is rather modest and the use of the proposed algorithm turns out to be more advantageous the greater the width of the figure to be thinned

using dominant points and variants for profile extraction from chromosomes abstract the most accurate methods for automatic analysis of chromosomes under a light microscope today extract numerical features from band pattern profiles along their longitudinal axes the construction of a reliable axis is a crucial step in this process we propose a new way based on the dominant points of the contour and cubic splines the dominant points serve as candidates for the tips of the chromosome ambiguities are dissolved by the recently developed method of variants for object identification a voronoi diagram decomposes the chromosome in slices for profile extraction the method improves the currently best classification results significantly yielding a test set error rate of 0 61

fixed point theorems for nonexpansive maps in banach spaces abstract in this work we present some new versions of fixed point theorems for nonexpansive maps and 1 set contractions defined on closed convex not necessarily bounded subsets of banach spaces our proofs rely on a compactness result for an approximate fixed point set the kuratowski measure of noncompactness is used throughout to illustrate the results obtained some applications to banach algebras and hammerstein integral equations are provided

an algebraic approach for morphological operations on 2d and 3d images abstract this paper describes an algebraic approach to morphological operations on 2d and 3d images for 2d images a matching algorithm based on mathematical morphology is given for 3d images represented by voxels algorithms are developed for the shape decomposition and thinning the possible advantages of the algebraic approach are indicated by showing that a considerable speedup takes place for large sized templates if the fast fourier transform fft is used to compute the convolutions

recursive erosion dilation opening and closing transforms a new group of recursive morphological transforms on the discrete space z sup 2 are discussed the set of transforms include the recursive erosion transform ret the recursive dilation transform rdt the recursive opening transform rot and the recursive closing transform rct the transforms are able to compute in constant time per pixel erosions dilations openings and closings with all sized structuring elements simultaneously they offer a solution to some vision tasks that need to perform a morphological operation but where the size of the structuring element has to be determined after a morphological examination of the content of the image the computational complexities of the transforms show that the recursive erosion and dilation transform can be done in n 2 operations per pixel where n is the number of pixels in the base structuring element the recursive opening and closing transform can be done in 14n operations per pixel based on experimental results

a q γ analog of the w1 algebra a q analog of the w1 algebra is introduced irreducible quasifinite highest weight modules of this algebra and r matrices acting on a tensor product of these modules are investigated a connection with the q deformed virasoro and wn algebras is also discussed

some sequential algorithms for a generalized distance transformation based on minkowski operations a generalized distance transformation gdt of binary images and the related medial axis transformation mat are discussed these transformations are defined in a discrete space of arbitrary dimension and arbitrary grids the gdt is based on successive morphological operations using alternatively n arbitrary structuring elements n is called the period of the gdt the gdt differs from the classical distance transformations based on a point to point distance however the well known chessboard city block and hexagonal distance transformations are special cases of the one period gdt whereas the octagonal distance transformation is a special case of the two period gdt in this paper both one and two period gdts are discussed different sequential algorithms are proposed for computing such gdts these algorithms need a maximum of two scannings of the image the computation of the mat is also discussed

new fusion operations for digitized binary images and their applications this paper proposes a new class of fusion operations which are useful for binary image processing to begin with an algorithm for the classical fusion operations is presented they are sequentially composed of two basic operations that is expansion and contraction the strategy of the proposed algorithm is as follows the first operation is performed with the distance transformation and the second operation utilizes the distance information obtained in the first operation next a topological contraction and a topological expansion are defined the topological contraction preserves the euler number of an input image except that some simply connected components of 1 pixels are erased the topological expansion preserves the euler number of an input image except that some simply connected holes are filled then several new fusion operations are obtained by combining the classical contraction and the topological expansion or the classical expansion and the topological contraction sequentially the algorithms for them use the same strategy as the proposed algorithm for the classical fusion operations finally experimental results show that the new fusion operations and their combinations are effectively used in the binary image processing such as shape smoothing merging and separating connected components and structure analysis

optimal morphological pattern restoration from noisy binary images a theoretical analysis of morphological filters for the optimal restoration of noisy binary images is presented the problem is formulated in a general form and an optimal solution is obtained by using fundamental tools from mathematical morphology and decision theory consideration is given to the set difference distance function as a measure of comparison between images this function is used to introduce the mean difference function as a quantitative measure of the degree of geometrical and topological distortion introduced by morphological filtering it is proved that the class of alternating sequential filters is a set of parametric smoothing morphological filters that best preserve the crucial structure of input images in the least mean difference sense

existence of solutions of functional integral equations of convolution type using a new construction of a measure of noncompactness on l p r let l p r denote the space of lebesgue integrable functions on r with the standard norm x p 0 x t p d t 1 p first we define a new measure of noncompactness on the spaces l p r 1 p in addition we study the existence of entire solutions for a class of nonlinear functional integral equations of convolution type using darbo s fixed point theorem which is associated with the new measure of noncompactness we provide some examples to demonstrate that our results are applicable whereas the previous results are not

three dimensional structural texture modeling and segmentation the structural approach one of the various modeling techniques in texture analysis perceives texture as a region composed of detectable primitive elements tokens in this paper we extend this concept to three dimensional 3d image and develop a segmentation scheme based on clustering of 3d texture tokens 3d structural texture is composed of texture tokens which are modeled as tiny objects embedded inside image sequence texture tokens located spatially close to one another and having similar shape are grouped into homogenous texture volume some of the texture tokens may be in contact with one another to form clump like structures our approach first disconnects these clumps by a 3d clump decomposition process a 3d irregular pyramid construction process is then carried out on these isolated 3d tokens the process inputs a delaunay graph with each vertex representing the shape feature vector of a texture token and each edge representing the neighborhood relationship of two texture tokens through stepwise grouping of similar shape tokens a segmentation of the texture volume is obtained