convergence of the power sequence of a nearly monotone increasing fuzzy matrix abstract by introducing a new classification the essential role of the principal diagonal elements for the convergence of the power sequence of a fuzzy matrix a is exported at the level of a itself the established theorems cover those of monotone or nearly monotone increasing fuzzy matrices the convergence index of matrices of this type is always less than or equal to n the results can be considered to be a generalization of the results obtained by some authors on the one hand and on the other it is more important that the results have laid the foundation for studying the convergence and oscillation for power sequence of an arbitrary fuzzy matrix in general furthermore as a typical case which needs to be considered the necessary and sufficient conditions for an increasing fuzzy matrix a to have the property a n 1 a n a n 1 were established and the typical form was represented

guided image completion by confidence propagation this paper presents a new guided image completion method which fills any missing values by considering information from a guidance image we develop a confidence propagation scheme that allows the filling process to be carried out simultaneously without the need of deciding the filling order we conduct experiments in several applications where the problem can be formulated into a guided image completion problem such as interactive segmentation and colorization the experimental results show that our method provides good results and succeeds in situations where conventional methods fail in addition as all building blocks are parallel processes our method is much suitable for hardware acceleration highlightswe proposed an image completion method based on a new formulation filling process was carried out simultaneously without deciding the filling order good results were obtained in a variety of applications

an upper bound on indices of finite fuzzy relations abstract let r be an arbitrary n n fuzzy matrix which represents a finite fuzzy relation d and k be the period and the index of r respectively in this paper we present some further results about d and k and point out that k n 1 n where n is the least common multiple of 1 2 n

simultaneous structure and texture image inpainting an algorithm for the simultaneous filling in of texture and structure in regions of missing image information is presented in this paper the basic idea is to first decompose the image into the sum of two functions with different basic characteristics and then reconstruct each one of these functions separately with structure and texture filling in algorithms the first function used in the decomposition is of bounded variation representing the underlying image structure while the second function captures the texture and possible noise the region of missing information in the bounded variation image is reconstructed using image inpainting algorithms while the same region in the texture image is filled in with texture synthesis techniques the original image is then reconstructed adding back these two sub images the novel contribution of this paper is then in the combination of these three previously developed components image decomposition with inpainting and texture synthesis which permits the simultaneous use of filling in algorithms that are suited for different image characteristics examples on real images show the advantages of this proposed approach

invertible incline matrices and cramer s rule over inclines inclines are the additively idempotent semirings in which the products are less than or equal to factors thus inclines generalize boolean algebra fuzzy algebra and distributive lattice and the boolean matrices the fuzzy matrices and the lattice matrices are the prototypical examples of the incline matrices i e the matrices over inclines in this paper the complete description of the invertible incline matrices is given some necessary and sufficient conditions for an incline matrix to be invertible are studied cramer s rule over inclines is presented and the group of invertible incline matrices is investigated the main results in the present paper generalize and develop the corresponding results in the literatures for the boolean matrices the fuzzy matrices and the lattice matrices

the periodicity of square fuzzy matrices based on minimal strong components in this paper the notion of minimal strong component of a fuzzy matrix is proposed by using this concept the periodicity of the power sequence of a fuzzy matrix is described on the basis of the relation of periodicity between a fuzzy matrix and its cut matrices further the greatest value max li n li of periodicity of all n n fuzzy matrices is obtained

new extremal characterizations of generalized inverses of linear operators abstract in 1956 r penrose studied best approximate solutions of the matrix equation ax b he proved that a b where a is the moore penrose inverse is the unique matrix of minimal frobenius norm among all matrices which minimize the frobenius norm of ax b in particular a is the unique best approximate solution of ax i the vector version of penrose s result that is the fact that the vector a b is the best approximate solution in the euclidean norm of the vector equation ax b has long been generalized to infinite dimensional hilbert spaces in this paper an infinite dimensional version of penrose s full result is given we show that a straightforward generalization is not possible and provide new extremal characterizations in terms of the hermitian order of a and of the classes of generalized inverses associated with minimal norm solutions of consistent operator equations or with least squares solutions for a certain class of operators we can phrase our characterizations in terms of a whole class of norms including the hilbert schmidt and the trace norms thus providing new extremal characterizations even in the matrix case we treat both operators with closed range and with not necessarily closed range finally we characterize a as the unique inner inverse of minimal hilbert schmidt norm if a 2

reduced solutions of douglas equations and angles between subspaces in this paper we study some particular solutions of douglas type equations by means of generalized inverses and angles we apply this result to characterize positive solutions and some special projections which are symmetrizable for a semidefinited positive bounded linear operator

contour detection and hierarchical image segmentation this paper investigates two fundamental problems in computer vision contour detection and image segmentation we present state of the art algorithms for both of these tasks our contour detector combines multiple local cues into a globalization framework based on spectral clustering our segmentation algorithm consists of generic machinery for transforming the output of any contour detector into a hierarchical region tree in this manner we reduce the problem of image segmentation to that of contour detection extensive experimental evaluation demonstrates that both our contour detection and segmentation methods significantly outperform competing algorithms the automatically generated hierarchical segmentations can be interactively refined by user specified annotations computation at multiple image resolutions provides a means of coupling our system to recognition applications

the period of powers of a fuzzy matrix abstract a fuzzy matrix plays an important role in system models based on a fuzzy relation and the performance of such a system depends on forming powers of a fuzzy matrix the powers of a general fuzzy matrix either converge or oscillate with a finite period many properties about convergence have been investigated for example sufficient conditions for convergence are shown moreover a lot of properties about convergence of powers of a transitive fuzzy matrix have been considered however few investigations about the period have been made in this paper we consider the period of the powers of a general fuzzy matrix by a graph theoretical viewpoint and show conditions for convergence under the max min composition

indices and periods of incline matrices abstract inclines are the additively idempotent semirings in which products are less than or equal to factors thus inclines generalize boolean algebra fuzzy algebra and distributive lattice and the boolean matrices the fuzzy matrices and the lattice matrices are the prototypical examples of the incline matrices i e the matrices over inclines this paper studies the power sequence of incline matrices in detail a necessary and sufficient condition for the incline matrix to have index is given and the indices of some incline matrices with indices are estimated it is proved that the period of n n incline matrix with index is a divisor of n and that the set of periods of n n incline matrices with indices is not bounded from above in the sense of a power of n for all n an equivalent condition and some sufficient conditions for the incline matrix to converge in finite steps are established the stability of the orbits of an incline matrix is considered and a theorem in fuzzy sets and systems 81 1996 227 is pointed out being false the results in the present paper include some previous results in the literatures which were obtained for the boolean matrices the fuzzy matrices and the lattice matrices among their special cases

on the sequence of consecutive powers of a fuzzy matrix with max archimedean t norms in the literature the limiting behavior of powers of a fuzzy matrix has been studied with max product composition pang and guu proposed a simple and effective characterization for the limiting behavior with the notion of asymptotic period in this paper we shall extend pang and guu s work to the realm with the max archimedean t norm composition to which the max product belongs moreover some sufficient conditions for the powers to converge in finitely many steps will be established

on the oscillating power sequence of a fuzzy matrix abstract the properties of an oscillating power sequence of an n n fuzzy matrix have been studied the necessary and sufficient conditions have been established for a power sequence to be oscillatory furthermore the oscillation index was detailed to some degree especially for some typical boolean matrices it is also shown that the period index set of the power sequences of fuzzy matrices of order n is not bounded from above by a power of n for all integers n

weighted least squares solutions of the equation axb c 0 abstract let h be a hilbert space l h the algebra of bounded linear operators on h and w l h a positive operator such that w 1 2 is in the p schatten class for some 1 p given a b l h with closed range and c l h we study the following weighted approximation problem analyze the existence of 0 1 m i n x l h a x b c p w where x p w w 1 2 x p we also study the related operator approximation problem analyze the existence of 0 2 m i n x l h a x b c w a x b c where the order is the one induced in l h by the cone of positive operators in this paper we prove that the existence of the minimum of 0 2 is equivalent to the existence of a solution of the normal equation a w a x b c 0 we also give sufficient conditions for the existence of the minimum of 0 1 and we characterize the operators where the minimum is attained

image inpainting by patch propagation using patch sparsity this paper introduces a novel examplar based inpainting algorithm through investigating the sparsity of natural image patches two novel concepts of sparsity at the patch level are proposed for modeling the patch priority and patch representation which are two crucial steps for patch propagation in the examplar based inpainting approach first patch structure sparsity is designed to measure the confidence of a patch located at the image structure e g the edge or corner by the sparseness of its nonzero similarities to the neighboring patches the patch with larger structure sparsity will be assigned higher priority for further inpainting second it is assumed that the patch to be filled can be represented by the sparse linear combination of candidate patches under the local patch consistency constraint in a framework of sparse representation compared with the traditional examplar based inpainting approach structure sparsity enables better discrimination of structure and texture and the patch sparse representation forces the newly inpainted regions to be sharp and consistent with the surrounding textures experiments on synthetic and natural images show the advantages of the proposed approach

fast image and video colorization using chrominance blending colorization the task of coloring a grayscale image or video involves assigning from the single dimension of intensity or luminance a quantity that varies in three dimensions such as red green and blue channels mapping between intensity and color is therefore not unique and colorization is ambiguous in nature and requires some amount of human interaction or external information a computationally simple yet effective approach of colorization is presented in this paper the method is fast and it can be conveniently used on the fly permitting the user to interactively get the desired results promptly after providing a reduced set of chrominance scribbles based on the concepts of luminance weighted chrominance blending and fast intrinsic distance computations high quality colorization results for still images and video are obtained at a fraction of the complexity and computational cost of previously reported techniques possible extensions of the algorithm introduced here included the capability of changing the colors of an existing color image or video as well as changing the underlying luminance and many other special effects demonstrated here

an application of incline matrices in dynamic analysis of generalized fuzzy bidirectional associative memories this paper studies an application of the incline matrix theory in the dynamic analysis of incline valued fuzzy bidirectional associative memories l fbams for short it is proved that the strong convergence and the strong stability of an l fbam are equivalent to the existence of indices and the convergence in finite steps of the product matrices of connection incline matrices of the l fbam respectively it is shown that the convergence index the period of limit cycles the stable states and equilibria of a strongly convergent l fbam are expressed by the indices the periods and the standard eigenvectors of the product matrices of connection incline matrices of the l fbam respectively

standard eigenvectors of incline matrices abstract inclines are the additively idempotent semirings in which products are less than or equal to either factor thus inclines generalize boolean algebra fuzzy algebra and distributive lattice this paper studies the standard eigenvectors of incline matrices i e matrices over inclines in detail as the main results for an incline matrix with index and for a lattice matrix the structures of all the standard eigenvectors are given and the greatest standard eigenvector is determined also it is proved that for an incline matrix with index the set of all the standard eigenvectors of it coincides with the set of all the standard eigenvectors of its transitive closure the power convergence of an incline matrix with index is characterized in terms of the sets of standard eigenvectors the results in the present paper include some previous results for the boolean matrices the fuzzy matrices and the lattice matrices among their special cases

on nilpotent incline matrices inclines are additively idempotent semirings in which products are less than or equal to either factor thus they generalize boolean algebra fuzzy algebra and distributive lattice this paper studies the nilpotent incline matrices in detail it is proved that an incline matrix is nilpotent if and only if it has index and the zero vector is its unique standard eigenvector the nilpotent matrices over an incline without nilpotent elements are characterized in terms of principal minors main diagonals nilpotent indices and adjoint matrices also some properties of the reduction of nilpotent matrices over an additively residuated incline without nilpotent elements are established the results obtained here generalize the corresponding ones on fuzzy matrices and lattice matrices shown in the references

maximum order index of matrices over commutative inclines an answer to an open problem abstract this paper proves that the maximum order index of n n matrices over an arbitrary commutative incline equals n 1 2 1 this is an answer to an open problem compute the maximum order index of a member of m n l proposed by cao kim and roush in a monograph incline algebra and applications 1984 where m n l is the set of all n n matrices over an incline l

periodicity of powers of fuzzy matrices finite fuzzy relations for an arbitrary n n fuzzy matrix r we define its period of oscillation d and index k we present some properties of d and k and show that d n where n is the least common multiple of 1 2 n then we obtain an algorithm to find d and k the results are useful for examining periodicity of powers of finite fuzzy relations and they also hold for a boolean matrix

depth video enhancement based on weighted mode filtering this paper presents a novel approach for depth video enhancement given a high resolution color video and its corresponding low quality depth video we improve the quality of the depth video by increasing its resolution and suppressing noise for that a weighted mode filtering method is proposed based on a joint histogram when the histogram is generated the weight based on color similarity between reference and neighboring pixels on the color image is computed and then used for counting each bin on the joint histogram of the depth map a final solution is determined by seeking a global mode on the histogram we show that the proposed method provides the optimal solution with respect to l1 norm minimization for temporally consistent estimate on depth video we extend this method into temporally neighboring frames simple optical flow estimation and patch similarity measure are used for obtaining the high quality depth video in an efficient manner experimental results show that the proposed method has outstanding performance and is very efficient compared with existing methods we also show that the temporally consistent enhancement of depth video addresses a flickering problem and improves the accuracy of depth video

note on convergence of powers of a fuzzy matrix we show by example that a theorem in thomason j math anal appl 57 1977 476 also recently quoted in imai et al fuzzy sets and systems 109 2000 405 about the convergence of fuzzy matrices is false

efficient algorithms for globally optimal trajectories we present serial and parallel algorithms for solving a system of equations that arises from the discretization of the hamilton jacobi equation associated to a trajectory optimization problem of the following type a vehicle starts at a prespecified point x sub o and follows a unit speed trajectory x t inside a region in spl rscr sup m until an unspecified time t that the region is exited a trajectory minimizing a cost function of the form spl int sub 0 sup t r x t dt q x t is sought the discretized hamilton jacobi equation corresponding to this problem is usually solved using iterative methods nevertheless assuming that the function r is positive we are able to exploit the problem structure and develop one pass algorithms for the discretized problem the first algorithm resembles dijkstra s shortest path algorithm and runs in time o n log n where n is the number of grid points the second algorithm uses a somewhat different discretization and borrows some ideas from a variation of dial s shortest path algorithm 1969 that we develop here it runs in time o n which is the best possible under some fairly mild assumptions finally we show that the latter algorithm can be efficiently parallelized for two dimensional problems and with p processors its running time becomes o n p provided that p o spl radic n log n

weighted procrustes problems abstract let h be a hilbert space l h the algebra of bounded linear operators on h and w l h a positive operator such that w 1 2 is in the p schatten class for some 1 p given a l h with closed range and b l h we study the following weighted approximation problem analyze the existence of m i n x l h a x b p w where x p w w 1 2 x p in this paper we prove that the existence of this minimum is equivalent to a compatibility condition between r b and r a involving the weight w and we characterize the operators which minimize this problem as w inverses of a in r b

on the powers of matrices in bottleneck fuzzy algebra abstract powers of square matrices under the operations max and min are studied we show that the powers of a given matrix stabilize if and only if its orbits stabilize for each starting vector and prove a necessary and sufficient condition for this property using the associated graphs of the matrix applications of the obtained results to several special classes of matrices including circulants are given

on invertible matrices over antirings abstract an antiring is a semiring which is zerosumfree i e a b 0 implies a b 0 for any a b in this semiring in this paper the complete description of the invertible matrices over a commutative antiring is given and some necessary and sufficient conditions for a matrix over a commutative antiring to be invertible are obtained also cramer s rule over commutative antirings is presented the main results in this paper generalize and develop the corresponding results for the boolean matrices the fuzzy matrices the lattice matrices and the incline matrices

on the asymptotic period of powers of a fuzzy matrix in our prior study we have examined in depth the notion of an asymptotic period of the power sequence of an nxn fuzzy matrix with max archimedean t norms and established a characterization for the power sequence of an nxn fuzzy matrix with an asymptotic period using analytical decomposition methods in this paper by using graph theoretical tools we further give an alternative proof for this characterization with the notion of an asymptotic period using graph theoretical tools we additionally show a new characterization for the limit behaviour and then derive some results for the power sequence of an nxn fuzzy matrix with an asymptotic period

graph cuts and efficient n d image segmentation combinatorial graph cut algorithms have been successfully applied to a wide range of problems in vision and graphics this paper focusses on possibly the simplest application of graph cuts segmentation of objects in image data despite its simplicity this application epitomizes the best features of combinatorial graph cuts methods in vision global optima practical efficiency numerical robustness ability to fuse a wide range of visual cues and constraints unrestricted topological properties of segments and applicability to n d problems graph cuts based approaches to object extraction have also been shown to have interesting connections with earlier segmentation methods such as snakes geodesic active contours and level sets the segmentation energies optimized by graph cuts combine boundary regularization with region based properties in the same fashion as mumford shah style functionals we present motivation and detailed technical description of the basic combinatorial optimization framework for image segmentation via s t graph cuts after the general concept of using binary graph cut algorithms for object segmentation was first proposed and tested in boykov and jolly 2001 this idea was widely studied in computer vision and graphics communities we provide links to a large number of known extensions based on iterative parameter re estimation and learning multi scale or hierarchical approaches narrow bands and other techniques for demanding photo video and medical applications

powers of matrices over distributive lattices a review in this paper we review the results on powers of matrices over a distributive lattice we stress the significance of the graph theoretical approach and show how several previous results for matrices of special types can be obtained in a unified way

on generalized fuzzy matrices with periods in this paper generalized fuzzy matrices are considered as matrices over a special type of semiring which is called path algebra some properties and characterizations for generalized fuzzy matrices with periods are established and an expression for the transitive closure of a generalized fuzzy matrix with a period as a sum of its powers is shown reduction of generalized fuzzy matrices is defined and some properties for reduction of generalized fuzzy matrices with periods are obtained also the structure of all standard eigenvectors for a generalized fuzzy matrix with a period is determined

on the powers of matrices over a distributive lattice abstract in this paper the index and the period for a lattice matrix are estimated some necessary and sufficent conditions for the convergence of the powers of a lattice matrix are obtained also some equivalent conditions for a nilpotent lattice matrix are discussed

the semigroup of incline hall matrices this paper investigates the semigroup of incline hall matrices an incline hall matrix means an incline matrix which is greater than or equal to an incline invertible matrix it is proved that any incline hall matrix has index some necessary and sufficient conditions for an incline hall matrix to be regular in the semigroup of incline hall matrices are given and green s relations on the such semigroup are described also the sandwich semigroup of incline hall matrices is considered the main results in the present paper generalize some previous results on boolean matrices fuzzy matrices and lattice matrices

convergence eigen fuzzy sets and stability analysis of relational matrices abstract if stable control applications are formulated with a max product composition then instability in the relational matrix under any conditions is undesirable this paper reviews the stability analysis of relational matrices combined with the max min composition 19 and then presents an analysis of the stability of relational matrices combined with the max product composition this analysis includes results defining the convergence properties of the relational matrix determination of the eigen fuzzy sets of the stable matrices and algorithmic solutions for several important cases a method is also presented to stabilize unstable relational matrices for some control applications