fuzzy measures on metric spaces abstract the aim of the present paper is to study the regularity and tightness properties of fuzzy measures on metric spaces among other results we shall give lusin s theorem and egoroff s theorem we shall also prove the singleton characterization of atom of fuzzy measure and an algorithm to evaluate the fuzzy integrals of non negative measurable functions over an atom and a union of finite disjoint atoms

convergences and topology via sequences of multifunctions in this paper we define different types of convergences for sequences of multifunctions and establish relationships among them using the convergence in fuzzy measure we obtain a topological structure on a space of multifunctions

generalized icm for image segmentation based on tsallis statistics abstract in this paper the iterated conditional modes optimization method of a markov random field technique for image segmentation is generalized based on tsallis statistics it is observed that for some q entropic index values the new algorithm performs better segmentation than the classical one the proposed algorithm also does not have a local minimum problem and reaches a global minimum energy point although the number of iterations remains the same as icm based on the findings of the new algorithm it can be expressed that the new technique can be used for the image segmentation processes in which the objects are gaussian or nearly gaussian distributed

image coding by adaptive tree structured segmentation a new algorithmic approach to segmentation based image coding is proposed a good compromise is achieved between segmentation by quadtree based decomposition and by free region growing in terms of time complexity and scene adaptability encoding is to recursively partition an image into convex n gons 3

adaptive image segmentation by combining photometric invariant region and edge information an adaptive image segmentation scheme is proposed employing the delaunay triangulation for image splitting the tessellation grid of the delaunay triangulation is adapted to the semantics of the image data by combining region and edge information to achieve robustness against imaging conditions e g shading shadows illumination and highlights photometric invariant similarity measures and edge computation are proposed experimental results on synthetic and real images show that the segmentation method is robust to edge orientation partially weak object boundaries and noisy but homogeneous regions furthermore the method is robust to a large degree to varying imaging conditions

a fuzzy gould type integral in this paper we introduce and study a set valued gould type integral of a real function with respect to a fuzzy multimeasure taking values in the family of all nonempty closed subsets of a banach space x some classical properties of the integral are obtained only using the hypothesis of monotonicity for the set valued fuzzy measure

a note on convergence properties of interval valued capacity functionals and choquet integrals based on the classical theory of random sets feng and nguyen 2007 5 studied the convergence of capacity functionals of random sets in terms of choquet integrals in this paper we consider an interval valued capacity functional which is motivated by the goal to generalize a capacity functional and the choquet integral with respect to an interval valued capacity in particular we discuss some convergence theorems for interval valued capacity functionals and interval valued probability measures in the hausdorff metric and choquet weak sense

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

regularity and stopping theorem for fuzzy martingales with continuous parameters the notion of graph convergence for fuzzy valued stochastic processes is introduced regularity for fuzzy super martingales with continuous parameters in the sense of gr km convergence is discussed finally we establish doob s stopping theorem for continuous parameter super sub martingales whose cut sets may be unbounded

a region based segmentation method for multichannel image data abstract segmentation has become a widely used tool in modern image analysis typical methods are highly nonlinear and often ad hoc and none so far have proved accessible to detailed statistical analysis even by asymptotic approximations can such methods be any good this article describes a segmentation procedure for multichannel image data and attempts to develop an understanding of its statistical performance characteristics in terms of nonparametric regression the procedure is based on a recursive merging algorithm defined via a nested sequence of discretizations of the image domain a cross validation rule with a near neighbor block replacement strategy is proposed for selecting the final segmentation model idealized numerical simulation experiments are used to evaluate the rate of convergence of the mean square error of estimation and also to study the efficiency of the cross validation technique interestingly the results show that the rate of convergence tends to decrease as the degree of smo

an inequality related to minkowski type for sugeno integrals an inequality related to minkowski type for the sugeno integral on abstract spaces is studied in a rather general form some previous results on chebyshev type inequality obtained by the authors are generalized several examples are given to illustrate the validity of this inequality the conditions such that this inequality becomes an equality are also discussed finally conclusions and some problems for further investigations are included

continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems we consider a dynamic system containing uncertain elements only the set of possible values of these uncertainties is known based on this information a class of state feedback controls is proposed in order to guarantee uniform ultimate boundedness of every system response within an arbitrarily small neighborhood of the zero state these feedback controls are continuous functions of the state

figure ground separation by cue integration this letter presents an improved cue integration approach to reliably separate coherent moving objects from their background scene in video sequences the proposed method uses a probabilistic framework to unify bottom up and top down cues in a parallel democratic fashion the algorithm makes use of a modified bayes rule where each pixel s posterior probabilities of figure or ground layer assignment are derived from likelihood models of three bottom up cues and a prior model provided by a top down cue each cue is treated as independent evidence for figure ground separation they compete with and complement each other dynamically by adjusting relative weights from frame to frame according to cue quality measured against the overall integration at the same time the likelihood or prior models of individual cues adapt toward the integrated result these mechanisms enable the system to organize under the influence of visual scene structure without manual intervention a novel contribution here is the incorporation of a top down cue it improves the system s robustness and accuracy and helps handle difficult and ambiguous situations such as abrupt lighting changes or occlusion among multiple objects results on various video sequences are demonstrated and discussed video demos are available at http organic usc edu 8376 tangx neco index html

generalized hough transform using regions with homogeneous color a novel generalized hough transform algorithm which makes use of the color similarity between homogeneous segments as the voting criterion is proposed in this paper the input of the algorithm is some regions with homogeneous color these regions are obtained by first pre segmenting the image using the morphological watershed algorithm and then refining the resultant outputs by a region merging algorithm region pairs belonging to the object are selected to generate entries of the reference table for the hough transform every r table entry stores a relative color between the selected region pairs this is done in order to compute the color similarity and in turn generate votes during the voting process and some relevant information to recover the transformation parameters of the object based on the experimental results our algorithm is robust to change of illumination occlusion and distortion of the segmentation output it recognizes objects which were translated rotated scaled and even located in a complex environment

regularity and lusin s theorem for riesz space valued fuzzy measures a smoothness condition the multiple egoroff property is introduced and imposed on a riesz space to show that every weakly null additive riesz space valued fuzzy borel measure on any metric space is regular it is also proved that lusin s theorem remains valid for such riesz space valued non additive measures

regularity and autocontinuity of set multifunctions in this paper we study different types of regularity for monotone uniformly autocontinuous set multifunctions defined on a ring of subsets of a locally compact hausdorff space t and taking values in the family of closed nonvoid sets of a real normed space x

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

fuzzy regular measures on topological spaces in this paper the concepts of the inner regularity outer regularity and regularity of a fuzzy measure are introduced on a topological space their properties are studied in detail egoroff theorem and lusin theorem are proved finally the conditions for a fuzzy measure to be tight and perfect are given respectively

robust control of robots by the computed torque law abstract for the trajectory following problem of a robot manipulator the standard computed torque control law is shown to be robust with respect to unknown dynamics by judiciously choosing the feedback gains and the estimates of the nonlinear dynamics the choices for the constant gains depend only on the coefficients of a polynomial bound of the unknown dynamics the asymptotic stability of the position and velocity tracking errors is also investigated

on the regularities of fuzzy set multifunctions with applications in variation extensions and fuzzy set valued integrability problems in this paper we continue our studies 6 7 concerning regularity in this sense we obtain extension results by preserving regularity and we establish basic properties and continuity properties for the variation of fuzzy set multifunctions this enables us to get relationships among different types of regularity and also to point out regularity properties of the fuzzy set valued integral 20

a segmentation based predictive multiresolution image coder recursive rectilinear tessellations like quadtree are widely used in image coding but a regular tessellation despite simple geometry may not suit image compression because it is too rigid to reflect the scene structure of an image the paper presents a new image pyramid formed by adaptive tree structured segmentation to be a framework of a predictive multiresolution image coder subjectively appealing compression results are obtained at different resolutions by scene adaptive tree structured segmentation and by exploiting the statistical dependency between the layers of the image pyramid the adaptive segmentation based image coder is constructed by recursive least squares piecewise functional approximation the seemingly expensive encoding process can be made efficient by an incremental least squares computation technique the decoding is simple and can be done in real time if assisted by existing hardware technology

a gaussian mixture based image segmentation algorithm this paper focuses on the formulation development and evaluation of an autonomous segmentation algorithm which can segment targets in a wide class of highly degraded images a segmentation algorithm based on a gaussian mixture model of a two class image is selected because it has the potential for effective segmentation provided that the histogram of the image approximates a gaussian mixture and the parameters of the model can be estimated accurately a selective sampling approach based on the laplacian of the image is developed to transform the histogram of any image into an approximation of a gaussian mixture and a new estimation method which uses information derived from the tails of the mixture density is formulated to estimate the model parameters the resulting selective sampling gaussian mixture parameter estimation segmentation algorithm is tested and evaluated on a set of real degraded target images and the results show that the algorithm is able to accurately segment diverse images

on set valued fuzzy measures so far there have been many discussions on sugeno s fuzzy measures and fuzzy integrals but most of them are concentrated on single valued functions motivated by aumann s set valued integral j math anal appl 12 1965 1 we have introduced the fuzzy integral of set valued functions fuzzy sets syst 56 1993 237 fuzzy sets syst 76 1995 365 fuzzy sets syst 78 1996 341 ph d dissertation harbin institute of technology 1998 it is a well behaved extension of fuzzy integrals of single valued functions it is well known that arstein s set valued measure trans am math soc 165 1972 103 is an important branch in set valued analysis set valued analysis birkhauser berlin 1990 or theory of correspondences theory of correspondences wiley new york 1984 compared to it the present paper will try to establish the basic idea of set valued fuzzy measures which are monotone set valued set functions it is also a natural generalization of single valued fuzzy measures as well as an extension of set valued measures in the case of one dimension these works include the concept of set valued fuzzy measures set valued fuzzy measures defined by set valued fuzzy integrals and set valued pseudo additive measures it can be viewed as a continuation of previous work fuzzy sets syst 56 1993 237 fuzzy sets syst 76 1995 365 fuzzy sets syst 78 1996 341

non atomicity and the darboux property for fuzzy and non fuzzy borel baire multivalued set functions in this paper we establish results concerning non atomicity and the darboux property for multisubmeasures fuzzy multivalued set functions defined on the baire respectively borel d ring b 0 respectively b of a locally compact hausdorff space

on set valued fuzzy integrals abstract in the paper we extend fuzzy integrals of point valued functions which were defined by ralescu and adams to set valued functions some properties similar to auman integrals are shown and these include convexity monotonicity fatou s lemma lebesgue convergence theorem etc

generalized fuzzy integrals of set valued functions in this paper based on wu s generalized fuzzy integrals of point valued function c wu et al fuzzy sets and systems 70 1995 75 a theory of generalized fuzzy integrals of fuzzy valued functions will be investigated it includes definitions properties and various kinds of convergence theorems these are extensions of results in c wu et al fuzzy sets and systems 70 1995 75 d zhang and z wang fuzzy sets and systems 54 1993 63

regularities of riesz space valued non additive measures with applications to convergence theorems for choquet integrals a deeper investigation of radonness and t smoothness properties of riesz space valued borel non additive measures is carried out to this end due to a lack of e argument in a riesz space the multiple egoroff property is introduced and enforced on the involved riesz space the established regularity properties of borel non additive measures are instrumental when formulating certain types of monotone convergence theorems for choquet integrals