aggregating local image descriptors into compact codes this paper addresses the problem of large scale image search three constraints have to be taken into account search accuracy efficiency and memory usage we first present and evaluate different ways of aggregating local image descriptors into a vector and show that the fisher kernel achieves better performance than the reference bag of visual words approach for any given vector dimension we then jointly optimize dimensionality reduction and indexing in order to obtain a precise vector comparison as well as a compact representation the evaluation shows that the image representation can be reduced to a few dozen bytes while preserving high accuracy searching a 100 million image data set takes about 250 ms on one processor core

a class of convex fuzzy mappings based on the concept of ordering defined by goetschel and voxman fuzzy sets and systems 18 1996 31 in this paper we present the concepts of epigraph and convexity of the fuzzy mappings and describe characteristics of the convex fuzzy mappings and quasi convex fuzzy mappings then we discuss the properties of convex fuzzy optimizations

preinvexity and φ 1 convexity of fuzzy mappings through a linear ordering the preinvexity prequasiinvexity 1 convexity and 1 quasiconvexity of fuzzy mappings are defined based on a linear ordering on the set of fuzzy numbers characterizations for these fuzzy mappings are obtained the local global minimum properties of real valued preinvex functions and 1 convex functions are extended to preinvex fuzzy mappings and 1 convex fuzzy mappings respectively it is also proved that every strict local minimizer of a prequasiinvex fuzzy mapping is a strict global minimizer and that every strict local minimizer of a 1 quasiconvex fuzzy mapping is a strict global minimizer

convex fuzzy mapping and operations of convex fuzzy mappings convex and concave fuzzy mappings are considered in this paper based on the seminal work of nanda and kar on the definition of convex fuzzy mapping the operations of convex fuzzy mapping are established some of the important concepts such as positively homogeneous infimal convolution right scalar multiplication and convex hull are introduced and the corresponding theorems are demonstrated by using the parametric representation of fuzzy numbers

spacetime texture representation and recognition based on a spatiotemporal orientation analysis this paper is concerned with the representation and recognition of the observed dynamics i e excluding purely spatial appearance cues of spacetime texture based on a spatiotemporal orientation analysis the term spacetime texture is taken to refer to patterns in visual spacetime x y t that primarily are characterized by the aggregate dynamic properties of elements or local measurements accumulated over a region of spatiotemporal support rather than in terms of the dynamics of individual constituents examples include image sequences of natural processes that exhibit stochastic dynamics e g fire water and windblown vegetation as well as images of simpler dynamics when analyzed in terms of aggregate region properties e g uniform motion of elements in imagery such as pedestrians and vehicular traffic spacetime texture representation and recognition is important as it provides an early means of capturing the structure of an ensuing image stream in a meaningful fashion toward such ends a novel approach to spacetime texture representation and an associated recognition method are described based on distributions histograms of spacetime orientation structure empirical evaluation on both standard and original image data sets shows the promise of the approach including significant improvement over alternative state of the art approaches in recognizing the same pattern from different viewpoints

small deformations superposed on large deformations of an elastic plastic material abstract in the context of a purely mechanical rate type theory of plasticity and utilizing a strain space formulation an infinitesimal theory is developed for motions superposed on any given motion of an elastic plastic material the given motion may involve all forms of elastic plastic deformation including both loading and unloading and in addition the loading conditions are allowed to change due to the superposed motion the infinitesimal theory is properly invariant under arbitrary finite superposed rigid motions

invex and generalized convex fuzzy mappings in this paper we introduce the concepts of pseudo convexity invexity and pseudo invexity for fuzzy mappings of one variable based on the notion of differentiability proposed by goetschel and voxman 4 and investigate the relationship between convex fuzzy mappings preinvex fuzzy mappings and these classes of fuzzy mappings we shall prove that pseudo convex fuzzy mappings and invex fuzzy mappings are pseudo invex and that a differentiable convex resp preinvex fuzzy mapping is pseudo convex resp invex in addition sufficient optimality conditions are obtained for pseudo convex invex and pseudo invex fuzzy mappings

some properties of weakly convex fuzzy mappings in this paper we introduce the concepts of weakly convex fuzzy sets weakly convex fuzzy mappings and weakly quasi convex fuzzy mappings and then give characterization theorems for these fuzzy sets and fuzzy mappings

on properties of convex fuzzy mappings the objective of this paper is to obtain some important properties about convex fuzzy mappings based on a linear ordering of fuzzy numbers proposed by goetschel and voxman firstly a new kind of fuzzy mapping termed semistrictly convex fuzzy mapping is defined through this linear ordering note that semistrict convexity does not imply convexity and the interrelationships among convex strictly convex and semistrictly convex mappings are established under certain conditions furthermore this paper obtains several characterizations for the above three classes of fuzzy mappings under the conditions of upper or lower semicontinuity finally some further characteristic properties for semistrictly convex fuzzy mappings are derived

convexity of n dimensional fuzzy number valued functions and its applications the aim of this study is to generalize convexity from vector valued maps to n dimensional fuzzy number valued functions and to investigate some relations among the convexity and generalized convexity of n dimensional fuzzy number valued functions which are based on a new ordering of n dimensional fuzzy numbers proposed in this study furthermore some criteria are obtained for the convexity and generalized convexity under the conditions of lower and upper semicontinuity respectively finally we study the local global minimum properties of the convex fuzzy number valued functions

on characterizations of preinvex fuzzy mappings several characterizations about preinvex fuzzy mapping are obtained in this paper firstly an equivalent condition of preinvex fuzzy mapping is established under certain conditions furthermore the necessary and sufficient conditions for differentiable and twice differentiable preinvex fuzzy mapping are provided by using the given equivalent condition of preinvex fuzzy mapping finally a new proof of some known important conclusions is offered these results generalize and improve some known results

slow feature analysis unsupervised learning of invariances invariant features of temporally varying signals are useful for analysis and classification slow feature analysis sfa is a new method for learning invariant or slowly varying features from a vectorial input signal it is based on a nonlinear expansion of the input signal and application of principal component analysis to this expanded signal and its time derivative it is guaranteed to find the optimal solution within a family of functions directly and can learn to extract a large number of decorrelated features which are ordered by their degree of invariance sfa can be applied hierarchically to process high dimensional input signals and extract complex features sfa is applied first to complex cell tuning properties based on simple cell output including disparity and motion then more complicated input output functions are learned by repeated application of sfa finally a hierarchical network of sfa modules is presented as a simple model of the visual system the same unstructured network can learn translation size rotation contrast or to a lesser degree illumination invariance for one dimensional objects depending on only the training stimulus surprisingly only a few training objects suffice to achieve good generalization to new objects the generated representation is suitable for object recognition performance degrades if the network is trained to learn multiple invariances simultaneously

pseudolinear fuzzy mappings two classes of fuzzy mappings called pseudolinear and pseudolinear fuzzy mappings are introduced by relaxing the definitions of pseudo convex and pseudo invex fuzzy mappings first some characterizations of pseudolinear and pseudolinear fuzzy mappings are obtained then characterizations of the solution sets of pseudolinear and pseudolinear fuzzy programs are derived

the design and use of steerable filters the authors present an efficient architecture to synthesize filters of arbitrary orientations from linear combinations of basis filters allowing one to adaptively steer a filter to any orientation and to determine analytically the filter output as a function of orientation steerable filters may be designed in quadrature pairs to allow adaptive control over phase as well as orientation the authors show how to design and steer the filters and present examples of their use in the analysis of orientation and phase angularly adaptive filtering edge detection and shape from shading one can also build a self similar steerable pyramid representation the same concepts can be generalized to the design of 3 d steerable filters

nonconvex fuzzy mappings and the fuzzy pre variational inequality in this paper we introduce the concepts of fuzzy pseudoconvex fuzzy invex fuzzy pseudoinvex and fuzzy preinvex mapping from r n to the set of fuzzy numbers and put forward the concepts of fuzzy extended directional differential subgradient and subdifferential some properties are obtained for fuzzy pseudoconvex fuzzy invex fuzzy pseudoinvex and fuzzy preinvex mapping relations are discussed between the fuzzy pre variational inequality and the fuzzy vector optimization problem

continuity and semicontinuity of fuzzy mappings we study two different concepts of semicontinuity of fuzzy mappings by establishing characterizations of these fuzzy mappings relationships between semicontinuity and continuity of fuzzy mappings are explored some basic properties of these semicontinuous and continuous fuzzy mappings are presented and proved

duality theory in fuzzy mathematical programming problems with fuzzy coefficients in this paper the notions of subgradient subdifferential and differential with respect to convex fuzzy mappings are investigated which provides the basis for the fuzzy extremum problem theory we consider the problems of minimizing or maximizing a convex fuzzy mapping over a convex set and develop the necessary and or sufficient optimality conditions furthermore the concept of saddle points and minimax theorems under fuzzy environment is discussed the results obtained are used to formulate the lagrangian dual of fuzzy programming under certain fuzzy convexity assumptions kkt conditions for fuzzy programming are derived and the perturbed convex fuzzy programming is considered finally these results are applied to fuzzy linear programming and fuzzy quadratic programming

metric spaces of fuzzy sets two classes of metrics are introduced for spaces of fuzzy sets their equivalence is discussed and basic properties established a characterisation of compact and locally compact subsets is given in terms of boundedness and p mean equileft continuity and the spaces shown to be locally compact complete and separable metric spaces

directional derivatives and subdifferential of convex fuzzy mappings and application in convex fuzzy programming abstract in this paper we put forward the concepts of directional derivative differential and subdifferential of fuzzy mappings from r n into e 1 and discuss the characterizations of directional derivative and differential by respectively using the directional derivative and differential of two crisp functions that are determined by the fuzzy mapping and we also consider the problem of existence of directional derivative for convex fuzzy mappings and discuss the relations among directional derivative differential and subdifferential of fuzzy mappings at last we give two results of application in convex fuzzy programming

on fuzzy metric spaces abstract in this paper we introduce the concept of a fuzzy metric space the distance between two points in a fuzzy metric space is a non negative upper semicontinuous normal and convex fuzzy number properties of fuzzy metric spaces are studied and some fixed point theorems are proved

convexity and local lipschitz continuity of fuzzy valued mappings abstract two concepts of a convexity and a local lipschitz continuity are introduced into the class of fuzzy valued mappings the convexity is defined through the fuzzy max order on the class of fuzzy numbers the local lipschitz continuity of the fuzzy valued mapping cannot be defined in the same manner as in the case of the real valued function since the space of values of the fuzzy valued mapping is not a linear space owing to this reason the local lipschitz continuity is defined in a new formula through the fuzzy max order a fundamental theorem concerning the local lipschitz continuity of the fuzzy valued convex mapping is given

preinvex fuzzy mappings abstract in this paper we introduce the concepts of preinvex fuzzy mappings quasi preinvex fuzzy mappings and invex sets by modifying the concepts proposed by noor we also give two characterization theorems for preinvex fuzzy mappings and present some new results for preinvex fuzzy mappings strictly preinvex fuzzy mappings and quasi preinvex fuzzy mappings

generalized convex fuzzy mappings and fuzzy variational like inequality in this paper we introduce the concepts of some generalized convex fuzzy mappings from r n to the set of fuzzy numbers under the condition of upper or lower semicontinuity a new criterion be obtained for the existence of a fuzzy preinvex mapping a fuzzy preinvex mapping can be achieved when the invex subset of r n satisfies certain conditions the relations between generalized convex fuzzy mappings are discussed and some properties are obtained that relate the concepts of fuzzy pseudoinvex and fuzzy prequasiinvex mapping fuzzy invex and fuzzy preinvex mapping fuzzy preinvex and fuzzy prequasiinvex mapping we also discuss the relationship between the fuzzy variational like inequality the fuzzy weak variational like inequality and fuzzy optimization problems and an application example of a fuzzy variational like inequality the fuzzy variational like inequality representation of a fuzzy transportation equilibrium problem

properties of b vex fuzzy mappings and applications to fuzzy optimization convexity plays a key role in operations research and fuzzy optimization theory the concept of b vex and logarithmic b vex for fuzzy mappings is introduced by relaxing the definition of convexity of a fuzzy mapping most of the basic properties of b vex fuzzy mapping are discussed and established for the nondifferentiable case necessary and sufficient conditions for b vex fuzzy mapping are presented several important results are given for nonlinear fuzzy optimization problems assuming that objective and constraint functions are b vex fuzzy mappings

elementary fuzzy calculus abstract in 2 dubois and prade introduced the notion of fuzzy numbers and defined the basic operations of addition subtraction multiplication and division a slightly modified definition of fuzzy numbers was presented in 4 and in that paper a metric was defined for this family of fuzzy sets another less restrictive definition of fuzzy numbers can be found in 1 in the present paper we consider fuzzy numbers from a somewhat different perspective basically we shall view fuzzy numbers in a topological vector space setting using the customary vector space operations together with the metric given in 4 we will define differentiation and integration of fuzzy valued functions in ways that parallel closely the corresponding definitions for real differentiation and integration

general theory of small elastic deformations superposed on finite elastic deformations using tensor notations a general theory is developed for small elastic deformations of either a compressible or incompressible isotropic elastic body superposed on a known finite deformation without assuming special forms for the strain energy function the theory is specialized to the case when the finite deformation is pure homogeneous when two of the principal extension ratios are equal the changes in displacement and stress due to the small superposed deformation are expressed in terms of two potential functions in a manner which is analogous to that used in the infinitesimal deformation of hexagonally aeolotropic materials the potential functions are used to solve the problem of the infinitesimally small indentation by a spherical punch of the plane surface of a semi infinite body of incompressible isotropic elastic material which is first subjected to a finite pure homogeneous deformation symmetrical about the normal to the force free plane surface

convexity and semicontinuity of fuzzy mappings in this paper a criterion for the convex fuzzy mapping is obtained under the condition of upper and lower semicontinuity respectively an upper lower semicontinuous fuzzy mapping is proved which convexity is equivalent to weak convexity or b vexity satisfying a special condition

φ1 φ2 convex fuzzy mappings abstract the concepts of 1 2 convexity 1 b vexity and 1 convexity for fuzzy mappings are introduced through the so called fuzzy max order among fuzzy numbers we show that the class of 1 2 convex fuzzy mappings 1 b vex fuzzy mappings and 1 convex fuzzy mappings includes many well known classes of fuzzy mappings such as convex fuzzy mappings and preinvex fuzzy mappings as its subclasses we also give a characterization for 1 b vex fuzzy mappings by proposing the concept of 1 b vex sets in addition some basic properties of fuzzy mappings from the standpoint of convex analysis are discussed

physically nonlinear and related approximate theories of elasticity and their invariance properties the existing developments of physically nonlinear elasticity have several shortcomings with the aim of remedying these deficiencies a number of approximate theories of elasticity are discussed in the present paper and in particular a theory of physically nonlinear elasticity is systematically developed more specifically stress strain relations for anisotropic physically nonlinear materials are derived the method of casey naghdi 1 is then applied to obtain properly invariant results this method involves the use of auxiliary motions obtained by removing from any given motion the translation and rotation at any one particle called a pivot the auxiliary motions represent the original motions in the approximate theory the connection between the transformation of fields under a change of pivot and invariance requirements associated with the auxiliary motions is investigated

an invariant infinitesimal theory of motions superposed on a given motion abstract the development is applicable to any material but special attention is given to elastic solids included as a special case is an infinitesimal theory of elasticity with the following properties 1 it is properly invariant under arbitrary not necessarily infinitesimal superposed rigid body motions 2 it reduces by specialization to the theory of rigid bodies undergoing finite motion and 3 it can be brought into correspondence with the classical linear elasticity through a suitable reinterpretation of the symbols in the constitutive equation of the latter author

fuzzy preinvex functions in this paper we introduce the concept of fuzzy preinvex functions and invex sets these functions are more general than convex fuzzy functions and when differentiable are fuzzy invex some different types of fuzzy preinvexity functions are defined and their properties are studied it is proved that the minimum of the fuzzy preinvex functions on the invex sets can be characterized by variational like inequalities

convergence analysis of solution sets for fuzzy optimization problems abstract in this paper we first consider fuzzy optimization problem in short fop and sequences of fuzzy optimization problems in short fop n then we establish the concept of d convergence of a sequence of fuzzy mappings and its characterizations finally the painleve kuratowski lower convergence and the painleve kuratowski convergence of approximate solution sets for these problems are proposed using d convergence of a sequence of fuzzy mappings some examples are provided to illustrate the essentialness of the imposed assumptions

generalization of preinvex and b vex fuzzy mappings a class of fuzzy mappings called b preinvex and strictly b preinvex fuzzy mappings is introduced by relaxing the definition of preinvexity of a fuzzy mapping similarly based on a notion of differentiability of fuzzy mappings different from the usual one the class of pseudo b vex b invex and pseudo b invex fuzzy mappings is defined as a generalization of pseudo convex invex and pseudo invex fuzzy mappings we prove that a strictly b vex or b preinvex fuzzy mapping has at most one global minimum point and that the class of b vex fuzzy mappings forms a subset of the class of quasi convex fuzzy mappings b vex resp b preinvex fuzzy mappings satisfy most of the basic properties of convex resp preinvex fuzzy mappings in addition characterizations and sufficient optimality conditions are obtained for b vex and b preinvex fuzzy mappings

modeling the shape of the scene a holistic representation of the spatial envelope in this paper we propose a computational model of the recognition of real world scenes that bypasses the segmentation and the processing of individual objects or regions the procedure is based on a very low dimensional representation of the scene that we term the spatial envelope we propose a set of perceptual dimensions naturalness openness roughness expansion ruggedness that represent the dominant spatial structure of a scene then we show that these dimensions may be reliably estimated using spectral and coarsely localized information the model generates a multidimensional space in which scenes sharing membership in semantic categories e g streets highways coasts are projected closed together the performance of the spatial envelope model shows that specific information about object shape or identity is not a requirement for scene categorization and that modeling a holistic representation of the scene informs about its probable semantic category

fuzzy φ convexity and fuzzy decision making the notion of convexity and its various generalization is important for quantitative and qualitative studies in operations research or applied mathematics it has also been considered by many authors in fuzzy set theory in this paper we study the concept of f convex and f quasiconvex fuzzy sets which was proposed bychen et al 1 and develop some useful extrema properties of these fuzzy sets we prove that any local maximizer of a f convex fuzzy set is also a global maximizer and that any strict local maximizer of a f quasiconvex fuzzy set is also a global maximizer we also study the class of strictly f convex respectively strictly f quasiconvex fuzzy sets that is more restricted than the class of f convex respectively f quasiconvex fuzzy sets we prove for both families of strictly f convex and strictly f quasiconvex fuzzy sets that every local maximizer is also the unique global maximizer in addition some applications to fuzzy decision making are discussed

dynamic scene recognition with complementary spatiotemporal features this paper presents dynamically pooled complementary features dpcf a unified approach to dynamic scene recognition that analyzes a short video clip in terms of its spatial temporal and color properties the complementarity of these properties is preserved through all main steps of processing including primitive feature extraction coding and pooling in the feature extraction step spatial orientations capture static appearance spatiotemporal oriented energies capture image dynamics and color statistics capture chromatic information subsequently primitive features are encoded into a mid level representation that has been learned for the task of dynamic scene recognition finally a novel dynamic spacetime pyramid is introduced this dynamic pooling approach can handle both global as well as local motion by adapting to the temporal structure as guided by pooling energies the resulting system provides online recognition of dynamic scenes that is thoroughly evaluated on the two current benchmark datasets and yields best results to date on both datasets in depth analysis reveals the benefits of explicitly modeling feature complementarity in combination with the dynamic spacetime pyramid indicating that this unified approach should be well suited to many areas of video analysis

concavoconvex fuzzy set abstract the concept of a concavoconvex fuzzy set in euclidean space is reported the idea is conceived by combining the concepts of convex and concave fuzzy sets together useful properties of the concavoconvex fuzzy set are established the union intersection of two concavoconvex fuzzy sets is either concavoconvex or concave convex depending on the type of their characteristic function

convex fuzzy mappings abstract in this note the concept of convexity and logarithmic convexity for fuzzy mappings are introduced and some applications to optimization are discussed