optimal feedback control for semilinear fractional evolution equations in banach spaces abstract in this paper we study optimal feedback controls of a system governed by semilinear fractional evolution equations via a compact semigroup in banach spaces by using the cesari property the fillippove theorem and extending the earlier work on fractional evolution equations we prove the existence of feasible pairs an existence result of optimal control pairs for the lagrange problem is presented

approximate controllability of partial neutral functional differential systems of fractional order with state dependent delay we prove the approximate controllability of control systems governed by a class of partial neutral functional differential systems of fractional order with state dependent delay in an abstract space sufficient conditions for approximate controllability of the control systems are established provided the approximate controllability of the corresponding linear control systems the results are obtained by using the krasnoselskii schaefer type fixed point theorem with the fractional power of operators an example is provided to illustrate the main results

flat zones filtering connected operators and filters by reconstruction this correspondence deals with the notion of connected operators starting from the definition for operator acting on sets it is shown how to extend it to operators acting on function typically a connected operator acting on a function is a transformation that enlarges the partition of the space created by the flat zones of the functions it is shown that from any connected operator acting on sets one can construct a connected operator for functions however it is not the unique way of generating connected operators for functions moreover the concept of pyramid is introduced in a formal way it is shown that if a pyramid is based on connected operators the flat zones of the functions increase with the level of the pyramid in other words the flat zones are nested filters by reconstruction are defined and their main properties are presented finally some examples of application of connected operators and use of flat zones are described

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

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

approximation of solutions to fractional integral equation in this paper we shall study a fractional integral equation in an arbitrary banach space x we used the analytic semigroups theory of linear operators and the fixed point method to establish the existence and uniqueness of solutions of the given problem we also prove the existence of global solution the existence and convergence of the faedo galerkin solution to the given problem is also proved in a separable hilbert space with some additional assumptions on the operator a finally we give an example to illustrate the applications of the abstract results

existence of mild solutions for fractional neutral evolution equations abstract in this paper by using the fractional power of operators and some fixed point theorems we discuss a class of fractional neutral evolution equations with nonlocal conditions and obtain various criteria on the existence and uniqueness of mild solutions in the end we give an example to illustrate the applications of the abstract results

on some fractional evolution equations abstract in this paper the solutions of some evolution equations with fractional orders in a banach space are considered conditions are given which ensure the existence of a resolvent operator for an evolution equation in a banach space

on the initial value problem of fractional evolution equations with noncompact semigroup in this paper we study the initial value problem of fractional semilinear evolution equations with noncompact semigroup in banach spaces the existence of saturated mild solutions and global mild solutions is obtained under weaker conditions particularly we find that the results obtained are also valid for the initial value problem of fractional ordinary differential equations in banach spaces the theorems proved in this paper improve and extend some related conclusions on this topic an example is given to illustrate that our results are valuable

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

cart and best ortho basis a connection we study what we call dyadic cart a method of nonparametric regression which constructs a recursive partition by optimizing a complexity penalized sum of squares where the optimization is over all recursive partitions arising from midpoint splits we show that the method is adaptive to unknown degrees of anisotropic smoothness specifically consider the anisotropic smoothness classes of nikol skii consisting of bivariate functions f xl x2 whose finite difference of distance h in direction i is bounded in lp norm by ch8i i 1 2 we show that dyadic cart with an appropriate complexity penalty parameter a u2 const log n is within logarithmic terms of minimax over every anisotropic smoothness class 0 c x 0 81 82 1 the proof shows that dyadic cart is identical to a certain adaptive best ortho basis algorithm based on the library of all anisotropic haar bases then it applies empirical basis selection ideas of donoho and johnstone the basis empirically selected by dyadic cart is shown to be nearly as good as a basis ideally adapted to the underlying f the risk of estimation in an ideally adapted anisotropic haar basis is shown to be comparable to the minimax risk over anisotropic smoothness classes underlying the success of this argument is harmonic analysis of anisotropic smoothness classes we show that for each anisotropic smoothness class there is an anisotropic haar basis which is a best orthogonal basis for representing that smoothness class the basis is optimal not just within the library of anisotropic haar bases but among all orthogonal bases of l2 0 1 2

using canny s criteria to derive a recursively implemented optimal edge detector a highly efficient recursive algorithm for edge detection is presented using canny s design 1 we show that a solution to his precise formulation of detection and localization for an infinite extent filter leads to an optimal operator in one dimension which can be efficiently implemented by two recursive filters moving in opposite directions in addition to the noise truncature immunity which results the recursive nature of the filtering operations leads with sequential machines to a substantial saving in computational effort five multiplications and five additions for one pixel independent of the size of the neighborhood the extension to the two dimensional case is considered and the resulting filtering structures are implemented as two dimensional recursive filters hence the filter size can be varied by simply changing the value of one parameter without affecting the time execution of the algorithm performance measures of this new edge detector are given and compared to canny s filters various experimental results are shown

scale space using mathematical morphology in this paper we prove that the scale space of a one dimensional gray scale signal based on morphological filterings satisfies causality no new feature points are created as scale gets larger for this we refine the standard definition of zero crossing so as to allow signals with certain singularity and use them to define feature points this new definition of zero crossing agrees with the standard one in the case of functions with second order derivative in particular the scale space based on the gaussian kernel g does not need this concept because a filtered signal g f is always infinitely differentiable using this generalized concept of zero crossing we show that a morphological filtering based on opening and hence also closing by duality satisfies causality we note that some previous works have mistakes which are corrected in this paper our causality results do not apply to more general two dimensional gray scale images causality results on alternating sequential filter obtained as byproduct are also included

a multiscale algorithm for image segmentation by variational method most segmentation algorithms are composed of several procedures split and merge small region elimination boundary smoothing each depending on several parameters the introduction of an energy to minimize leads to a drastic reduction of these parameters the authors prove that the most simple segmentation tool the region merging algorithm made according to the simplest energy is enough to compute a local energy minimum belonging to a compact class and to achieve the job of most of the tools mentioned above the authors explain why merging in a variational framework leads to a fast multiscale multichannel algorithm with a pyramidal structure the obtained algorithm is o n ln n where n is the number of pixels of the picture this fast algorithm is applied to make grey level and texture segmentation and experimental results are shown

affine invariant segmentation by variational method affine invariance viewed as a simplified projective invariance is an essential requirement for analysis of natural scenes we propose an affine invariant analogue of mumford and shah energy functional to segment images and we discuss it we present a simple multiscale algorithm to minimize it based on region growing methods and we display our first numerical experiments

binary partition tree as an efficient representation for image processing segmentation and information retrieval this paper discusses the interest of binary partition trees as a region oriented image representation binary partition trees concentrate in a compact and structured representation a set of meaningful regions that can be extracted from an image they offer a multiscale representation of the image and define a translation invariant 2 connectivity rule among regions as shown in this paper this representation can be used for a large number of processing goals such as filtering segmentation information retrieval and visual browsing furthermore the processing of the tree representation leads to very efficient algorithms finally for some applications it may be interesting to compute the binary partition tree once and to store it for subsequent use for various applications in this context the paper shows that the amount of bits necessary to encode a binary partition tree remains moderate

hierarchical image analysis using irregular tessellations a novel multiresolution image analysis technique based on hierarchies of irregular tessellations generated in parallel by independent stochastic processes is presented like traditional image pyramids these hierarchies are constructed in a number of steps on the order of log image size steps however the structure of a hierarchy is adapted to the image content and artifacts of rigid resolution reduction are avoided two applications of these techniques are presented connected component analysis of labeled images and segmentation of gray level images in labeled images every connected component is reduced to a separate root with the adjacency relations among the components also extracted in gray level images the output is a segmentation of the image into a small number of classes as well as the adjacency graph of the classes

scale sets image analysis this paper introduces a multi scale theory of piecewise image modelling called the scale sets theory and which can be regarded as a region oriented scale space theory the first part of the paper studies the general structure of a geometrically unbiased region oriented multi scale image description and introduces the scale sets representation a representation which allows to handle such a description exactly the second part of the paper deals with the way scale sets image analyses can be built according to an energy minimization principle we consider a rather general formulation of the partitioning problem which involves minimizing a two term based energy of the form c d where d is a goodness of fit term and c is a regularization term we describe the way such energies arise from basic principles of approximate modelling and we relate them to operational rate distorsion problems involved in lossy compression problems we then show that an important subset of these energies constitutes a class of multi scale energies in that the minimal cut of a hierarchy gets coarser and coarser as parameter increases this allows us to devise a fast dynamic programming procedure to find the complete scale sets representation of this family of minimal cuts considering then the construction of the hierarchy from which the minimal cuts are extracted we end up with an exact and parameter free algorithm to build scale sets image descriptions whose sections constitute a monotone sequence of upward global minima of a multi scale energy which is called the scale climbing algorithm this algorithm can be viewed as a continuation method along the scale dimension or as a minimum pursuit along the operational rate distorsion curve furthermore the solution verifies a linear scale invariance property which allows to completely postpone the tuning of the scale parameter to a subsequent stage for computational reasons the scale climbing algorithm is approximated by a pair wise region merging scheme however the principal properties of the solutions are kept some results obtained with mumford shah s piece wise constant model and a variant are provided and different applications of the proposed multi scale analyses are finally sketched

optimal approximations by piecewise smooth functions and associated variational problems abstract this reprint will introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision in computer vision a fundamental problem is to appropriately decompose the domain r of a function g x y of two variables this problem starts by describing the physical situation which produces images assume that a three dimensional world is observed by an eye or camera from some point p and that g1 rho represents the intensity of the light in this world approaching the point sub 1 from a direction rho if one has a lens at p focusing this light on a retina or a film in both cases a plane domain r in which we may introduce coordinates x y then let g x y be the strength of the light signal striking r at a point with coordinates x y g x y is essentially the same as sub 1 rho possibly after a simple transformation given by the geometry of the imaging syste the function g x y defined on the plane domain r will be called an image what sort of function is g the light reflected off the surfaces si of various solid objects o sub i visible from p will strike the domain r in various open subsets r sub i when one object o1 is partially in front of another object o2 as seen from p but some of object o2 appears as the background to the sides of o1 then the open sets r1 and r2 will have a common boundary the edge of object o1 in the image defined on r and one usually expects the image g x y to be discontinuous along this boundary jhd

constructing simple stable descriptions for image partitioning a new formulation of the image partitioning problem is presented construct a complete and stable description of an image in terms of a specified descriptive language that is simplest in the sense of being shortest we show that a descriptive language limited to a low order polynomial description of the intensity variation within each region and a chain code like description of the region boundaries yields intuitively satisfying partitions for a wide class of images the advantage of this formulation is that it can be extended to deal with subsequent steps of the image understanding problem or to deal with other attributes such as texture in a natural way by augmenting the descriptive language experiments performed on a variety of both real and synthetic images demonstrate the superior performance of this approach over partitioning techniques based on clustering vectors of local image attributes and standard edge detection techniques

semigroups and some nonlinear fractional differential equations equations of the formd au t dt a au t f t b 1 t u t b r t u t are considered where 0 0 is a family of linear closed operators defined on dense sets in e into e and f is a given abstract nonlinear function defined on 0 t xe r with values in e t 0 it is assumed that a generates an analytic semigroup under suitable conditions on the family of operators b i t i 1 r t 0 and on f we study the existence and uniqueness of the solution of the cauchy problem for the considered equation some properties concerning the stability of solutions are obtained we also give an application for nonlinear partial differential equations of fractional orders

on sequentially closed graph mappings in fuzzy neighborhood spaces abstract two notions of closed graph and strongly closed graph in fuzzy neighbourhood spaces have been introduced one in fuzzy sets and system 48 1992 377 382 and the other by the author we prove that those notions are equivalent we introduce the notion of sequential convergence in fuzzy neighbourhood space

existence of mild solutions for fractional integrodifferential equations of sobolev type with nonlocal conditions abstract this paper is concerned with the fractional integrodifferential equations of sobolev type with nonlocal condition in a separable banach space with the help of the theory of propagation family as well as the theory of the measures of noncompactness and the condensing maps we obtain the existence result of mild solutions for above equations two examples are given to illustrate the existence theorem

explicit solutions of jacobi and gauss differential equations by means of operators of fractional calculus judging by the remarkably large number of recent publications on fractional calculus and its applications in several widely diverse areas of mathematical physical and engineering sciences the current popularity and importance of the subject of fractional calculus cannot be overemphasized motivated by some of these potentially useful developments many authors have recently demonstrated the usefulness of fractional calculus in the derivation of explicit particular solutions of a number of linear ordinary and partial differential equations of the second and higher orders the main object of the present paper is to show how several interesting contributions on this subject involving a certain class of ordinary differential equations associated with for example the celebrated gauss and jacobi differential equations can be obtained in a unified manner by suitably applying some general theorems on explicit particular solutions of a family of linear ordinary fractional differintegral equations