region merging techniques using information theory statistical measures the purpose of the current work is to propose under a statistical framework a family of unsupervised region merging techniques providing a set of the most relevant region based explanations of an image at different levels of analysis these techniques are characterized by general and nonparametric region models with neither color nor texture homogeneity assumptions and a set of innovative merging criteria based on information theory statistical measures the scale consistency of the partitions is assured through i a size regularization term into the merging criteria and a classical merging order or ii using a novel scale based merging order to avoid the region size homogeneity imposed by the use of a size regularization term moreover a partition significance index is defined to automatically determine the subset of most representative partitions from the created hierarchy most significant automatically extracted partitions show the ability to represent the semantic content of the image from a human point of view finally a complete and exhaustive evaluation of the proposed techniques is performed using not only different databases for the two main addressed problems object oriented segmentation of generic images and texture image segmentation but also specific evaluation features in each case under and oversegmentation error and a large set of region based pixel based and error consistency indicators respectively results are promising outperforming in most indicators both object oriented and texture state of the art segmentation techniques

analysis of complex and chaotic patterns near a codimension 2 turing hopf point in a reaction diffusion model we study a reaction diffusion system of activator inhibitor type and characterize the resulting complex and chaotic spatio temporal patterns by their lyapunov spectrum and by a karhunen loeve decomposition into empirical orthogonal eigenmodes different periodic patterns corresponding to localized hopf and turing modes and mixed modes including subharmonic spatio temporal spiking are found near a codimension 2 bifurcation point the asymptotic patterns are preceded by transient spatio temporal chaos before the system abruptly locks into a periodic state in space and time the karhunen loeve decomposition is shown to be a powerful tool for extracting detailed quantitative information of complex space time data

spatiotemporal chaos stimulated by transverse hopf instabilities in an optical bilayer system we study two dimensional spatiotemporal dynamics in an optical system of two identical nonlinear films irradiated from both sides by equal plane waves and show that a wide variety of chaotic behaviors can be obtained near the subcritical pitchfork bifurcation point the regimes arising in the vicinity of asymmetrical steady state depend on stability of the symmetrical steady state at the same driving field on interactions of hopf and turing instabilities occurring at the asymmetrical branch of solutions and on a transverse wave number of the hopf instability band center the wave number is controlled by a phase shift of the field passed between two films and the relative order of the turing and hopf bifurcations is controlled by a diffusion of charge carrier in a semiconductor media chaotic oscillating patterns are formed mainly by transverse hopf modes rising due to a time delay in the system

on an old article of tzitzeica and the inverse scattering method tzitzeica s class of surfaces in r3 is considered in connection with the inverse scattering method for the associated equation uxy eu e 2u the backlund transformation for this equation is derived from tzitzeica s darboux transformation for it

spatiotemporal patterns and localized structures in nonlinear optics we show that in a degenerate optical parametric oscillator with saturable losses for the frequency down converted field the steady state can be destabilized via either a hopf or a turing instability the relative order between the two bifurcations is controlled by the linear loss of the saturable absorber if the turing bifurcation is subcritical and the hopf bifurcation occurs in the hysteresis domain involving the homogeneous and inhomogeneous states steady localized structures are generated below the hopf bifurcation and time periodic localized structures are generated above the hopf bifurcation

spatiotemporal dynamics near a codimension two point spatiotemporal dynamics resulting from the interaction of two instabilities breaking respectively spatial and temporal symmetries are studied in the framework of the amplitude equation formalism the corresponding bifurcation scenarios feature steady hopf bistability with corresponding localized structures but also different types of mixed states some of these mixed modes result from self induced subharmonic instabilities of the pure steady and hopf modes the bifurcation schemes are then used to organize the results of numerical simulations of a one dimensional reaction diffusion model these dynamics are relevant to experimental chemical systems featuring a codimension two turing hopf point but also to any experimental setup where homogeneous temporal oscillations and spatial patterns are obtained for nearby values of parameters s1063 651x 96 03707 5

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

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

hyperspectral super resolution of locally low rank images from complementary multisource data remote sensing hyperspectral images hsis are quite often low rank in the sense that the data belong to a low dimensional subspace manifold this has been recently exploited for the fusion of low spatial resolution hsi with high spatial resolution multispectral images in order to obtain super resolution hsi most approaches adopt an unmixing or a matrix factorization perspective the derived methods have led to state of the art results when the spectral information lies in a low dimensional subspace manifold however if the subspace manifold dimensionality spanned by the complete data set is large i e larger than the number of multispectral bands the performance of these methods mainly decreases because the underlying sparse regression problem is severely ill posed in this paper we propose a local approach to cope with this difficulty fundamentally we exploit the fact that real world hsis are locally low rank that is pixels acquired from a given spatial neighborhood span a very low dimensional subspace manifold i e lower or equal than the number of multispectral bands thus we propose to partition the image into patches and solve the data fusion problem independently for each patch this way in each patch the subspace manifold dimensionality is low enough such that the problem is not ill posed anymore we propose two alternative approaches to define the hyperspectral super resolution through local dictionary learning using endmember induction algorithms we also explore two alternatives to define the local regions using sliding windows and binary partition trees the effectiveness of the proposed approaches is illustrated with synthetic and semi real data

stochastic relaxation on partitions with connected components and its application to image segmentation we present a new method of segmentation in which images are segmented in partitions with connected components we give computationally inexpensive algorithms for probability simulation and simulated annealing on the space of partitions with connected components of a general graph in particular hastings algorithms 1970 and generalized metropolis algorithms are defined to avoid heavy computation to achieve segmentation we propose a hierarchical approach which at each step minimizes a cost function on the space of partitions with connected components of a graph the algorithm is applied to segment gray level color and textured images

the spatio temporal structure of spiral defect chaos abstract we present a study of the recently discovered spatially extended chaotic state known as spiral defect chaos which occurs in low prandtl number large aspect ratio rayleigh benard convection we employ the modulus squared of the space time fourier transform of time series of two dimensional shadowgraph images to construct the structure factor s k this analysis is used to characterize the average spatial and temporal scales of the chaotic state we find that the correlation length and time can be described by power law dependences on the reduced rayleigh number these power laws have as yet no theoretical explanation

fusion of supervised and unsupervised learning for improved classification of hyperspectral images in this paper we introduce a novel framework for improved classification of hyperspectral images based on the combination of supervised and unsupervised learning paradigms in particular we propose to fuse the capabilities of the support vector machine classifier and the fuzzy c means clustering algorithm while the former is used to generate a spectral based classification map the latter is adopted to provide an ensemble of clustering maps to reduce the computation complexity the most representative spectral channels identified by the markov fisher selector algorithm are used during the clustering process then these maps are successively labeled via a pairwise relabeling procedure with respect to the pixel based classification map using voting rules to generate the final classification result we propose to aggregate the obtained set of spectro spatial maps through different fusion methods based on voting rules and markov random field theory experimental results obtained on two hyperspectral images acquired by the reflective optics system imaging spectrometer and the airborne visible infrared imaging spectrometer respectively confirm the promising capabilities of the proposed framework

hyperspectral image representation and processing with binary partition trees the optimal exploitation of the information provided by hyperspectral images requires the development of advanced image processing tools this paper proposes the construction and the processing of a new region based hierarchical hyperspectral image representation relying on the binary partition tree bpt this hierarchical region based representation can be interpreted as a set of hierarchical regions stored in a tree structure hence the bpt succeeds in presenting 1 the decomposition of the image in terms of coherent regions and 2 the inclusion relations of the regions in the scene based on region merging techniques the bpt construction is investigated by studying the hyperspectral region models and the associated similarity metrics once the bpt is constructed the fixed tree structure allows implementing efficient and advanced application dependent techniques on it the application dependent processing of bpt is generally implemented through a specific pruning of the tree in this paper a pruning strategy is proposed and discussed in a classification context experimental results on various hyperspectral data sets demonstrate the interest and the good performances of the bpt representation

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

backlund transformation of partial differential equations from the painleve gambier classification ii tzitzeica equation from the existing methods of singularity analysis only we derive the two equations which define the backlund transformation of the tzitzeica equation this is achieved by defining a truncation in the spirit of the approach of weiss et al so as to preserve the lorentz invariance of the tzitzeica equation if one assumes a third order scattering problem this truncation admits a unique solution thus leading to a matrix lax pair and a darboux transformation in order to obtain the backlund transformation bt which is the main new result of this paper one represents the lax pair by an equivalent two component riccati pseudopotential this yields two different bts the first one is a bt for the hirota satsuma equation while the second one is a bt for the tzitzeica equation one of the two equations defining the bt is the fifth ordinary differential equation of gambier

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

the sparse matrix transform for covariance estimation and analysis of high dimensional signals covariance estimation for high dimensional signals is a classically difficult problem in statistical signal analysis and machine learning in this paper we propose a maximum likelihood ml approach to covariance estimation which employs a novel non linear sparsity constraint more specifically the covariance is constrained to have an eigen decomposition which can be represented as a sparse matrix transform smt the smt is formed by a product of pairwise coordinate rotations known as givens rotations using this framework the covariance can be efficiently estimated using greedy optimization of the log likelihood function and the number of givens rotations can be efficiently computed using a cross validation procedure the resulting estimator is generally positive definite and well conditioned even when the sample size is limited experiments on a combination of simulated data standard hyperspectral data and face image sets show that the smt based covariance estimates are consistently more accurate than both traditional shrinkage estimates and recently proposed graphical lasso estimates for a variety of different classes and sample sizes an important property of the new covariance estimate is that it naturally yields a fast implementation of the estimated eigen transformation using the smt representation in fact the smt can be viewed as a generalization of the classical fast fourier transform fft in that it uses butterflies to represent an orthonormal transform however unlike the fft the smt can be used for fast eigen signal analysis of general non stationary signals

power watershed a unifying graph based optimization framework in this work we extend a common framework for graph based image segmentation that includes the graph cuts random walker and shortest path optimization algorithms viewing an image as a weighted graph these algorithms can be expressed by means of a common energy function with differing choices of a parameter q acting as an exponent on the differences between neighboring nodes introducing a new parameter p that fixes a power for the edge weights allows us to also include the optimal spanning forest algorithm for watershed in this same framework we then propose a new family of segmentation algorithms that fixes p to produce an optimal spanning forest but varies the power q beyond the usual watershed algorithm which we term the power watershed in particular when q 2 the power watershed leads to a multilabel scale and contrast invariant unique global optimum obtained in practice in quasi linear time placing the watershed algorithm in this energy minimization framework also opens new possibilities for using unary terms in traditional watershed segmentation and using watershed to optimize more general models of use in applications beyond image segmentation

hyperspectral image segmentation using a new spectral unmixing based binary partition tree representation the binary partition tree bpt is a hierarchical region based representation of an image in a tree structure the bpt allows users to explore the image at different segmentation scales often the tree is pruned to get a more compact representation and so the remaining nodes conform an optimal partition for some given task here we propose a novel bpt construction approach and pruning strategy for hyperspectral images based on spectral unmixing concepts linear spectral unmixing consists of finding the spectral signatures of the materials present in the image endmembers and their fractional abundances within each pixel the proposed methodology exploits the local unmixing of the regions to find the partition achieving a global minimum reconstruction error results are presented on real hyperspectral data sets with different contexts and resolutions

antiextensive connected operators for image and sequence processing this paper deals with a class of morphological operators called connected operators these operators filter the signal by merging its flat zones as a result they do not create any new contours and are very attractive for filtering tasks where the contour information has to be preserved this paper shows that connected operators work implicitly on a structured representation of the image made of flat zones the max tree is proposed as a suitable and efficient structure to deal with the processing steps involved in antiextensive connected operators a formal definition of the various processing steps involved in the operator is proposed and as a result several lines of generalization are developed first the notion of connectivity and its definition are analyzed several modifications of the traditional approach are presented they lead to connected operators that are able to deal with texture they also allow the definition of connected operators with less leakage than the classical ones second a set of simplification criteria are proposed and discussed they lead to simplicity entropy and motion oriented operators the problem of using a nonincreasing criterion is analyzed its solution is formulated as an optimization problem that can be very efficiently solved by a viterbi 1979 algorithm finally several implementation issues are discussed showing that these operators can be very efficiently implemented

evaluation of hierarchical watersheds this paper aims to understand the practical features of hierarchies of morphological segmentations namely the quasi flat zones hierarchy and watershed hierarchies and to evaluate their potential in the context of natural image analysis we propose a novel evaluation framework for the hierarchies of partitions designed to capture various aspects of those representations precision of their regions and contours possibility to extract high quality horizontal cuts and optimal non horizontal cuts for image segmentation and the ease of finding a set of regions representing a semantic object this framework is used to assess and to optimize hierarchies with respect to the possible pre and post processing steps we show that used in conjunction with a state of the art contour detector watershed hierarchies are competitive with the complex state of the art methods for hierarchy construction in particular the proposed framework allows us to identify a watershed hierarchy based on a novel extinction value the number of parent nodes that outperforms the other hierarchies of morphological segmentations this coupled with the fact that watershed hierarchies satisfy clear global optimality properties and can be efficiently computed on large data make them valuable candidates for various computer vision tasks

spectral spatial classification of hyperspectral data based on a stochastic minimum spanning forest approach in this paper a new method for supervised hyperspectral data classification is proposed in particular the notion of stochastic minimum spanning forest msf is introduced for a given hyperspectral image a pixelwise classification is first performed from this classification map m marker maps are generated by randomly selecting pixels and labeling them as markers for the construction of msfs the next step consists in building an msf from each of the m marker maps finally all the m realizations are aggregated with a maximum vote decision rule in order to build the final classification map the proposed method is tested on three different data sets of hyperspectral airborne images with different resolutions and contexts the influences of the number of markers and of the number of realizations m on the results are investigated in experiments the performance of the proposed method is compared to several classification techniques both pixelwise and spectral spatial using standard quantitative criteria and visual qualitative evaluation

an endmember based distance for content based hyperspectral image retrieval we propose a specific content based image retrieval cbir system for hyperspectral images exploiting its rich spectral information the cbir image features are the endmember signatures obtained from the image data by endmember induction algorithms eias endmembers correspond to the elementary materials in the scene so that the pixel spectra can be decomposed into a linear combination of endmember signatures eia search for points in the high dimensional space of pixel spectra defining a convex polytope often a simplex covering the image data this paper introduces a dissimilarity measure between hyperspectral images computed over the image induced endmembers proving that it complies with the axioms of a distance we provide a comparative discussion of dissimilarity functions and quantitative evaluation of their relative performances on a large collection of synthetic hyperspectral images and on a dataset extracted from a real hyperspectral image alternative dissimilarity functions considered are the hausdorff distance and robust variations of it we assess the cbir performance sensitivity to changes in the distance between endmembers the eia employed and some other conditions the proposed hyperspectral image distance improves over the alternative dissimilarities in all quantitative performance measures the visual results of the cbir on the real image data demonstrate its usefulness for practical applications

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

learning conditional random fields for classification of hyperspectral images hyperspectral images exhibit strong dependencies across spatial and spectral neighbors which have been proved to be very useful for hyperspectral image classification state of the art hyperspectral image classification algorithms use the dependencies in a heuristic way or in probabilistic frameworks but impose unreasonable assumptions on observed data in this paper we formulate a conditional random field crf to replace such heuristics and unreasonable assumptions for the classification of hyperspectral images moreover because of avoiding explicit modeling of the observed data the proposed method can incorporate the classification of hyperspectral images with different statistics characteristics into a unified probabilistic framework since the usual classification task for hyperspectral images needs the proposed crf to be trained on local samples available global training methods cannot be directly used under piecewise training framework this paper develops an efficient local method to train the crf it is efficiently implemented through separated trainings of simple classifiers defined by corresponding potentials however the independent classifier trainings may lead to over counting problems during inference so we further propose a strategy to combine the independently trained models to obtain final crf model experiments on real world hyperspectral data show that our algorithm is competitive with the most recent results in hyperspectral image classification

universal description of laser dynamics near threshold abstract complex order parameter descriptions of large aspect ratio single longitudinal mode two level lasers with flat end reflectors valid near onset of lasing and for small detunings of the laser from the peak gain are given in terms of a complex swift hohenberg equation for class a and c lasers and by a complex swift hohenberg equation coupled to a mean flow for the case of a class b laser the latter coupled system is a physically consistent generalized rate equation model for wide aperture stiff laser systems these universal order parameter equations provide a connection between spatially homogeneous oscillating states of the complex ginzburg landau equation description of the laser system valid for finite negative detunings and traveling wave states described by coupled newell whitehead segel equations valid for finite positive detunings one of the main conclusions of the present paper is that the usual eckhaus instability boundary associated with a long wavelength phase instability and which delineates the region of the stable traveling wave solutions for class a and c lasers no longer defines the stability boundary for the mathematically stiff class b laser instead a short wavelength phase instability appears causing the stability domain to shrink as a function of increasing stiffness of the system this prediction is consistent with the strong spatiotemporal filamentation instabilities experimentally observed in a borad area semiconductor laser a class b system

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

forced patterns near a turing hopf bifurcation we study time periodic forcing of spatially extended patterns near a turing hopf bifurcation point a symmetry based normal form analysis yields several predictions including that i weak forcing near the intrinsic hopf frequency enhances or suppresses the turing amplitude by an amount that scales quadratically with the forcing strength and ii the strongest effect is seen for forcing that is detuned from the hopf frequency to apply our results to specific models we perform a perturbation analysis on general two component reaction diffusion systems which reveals whether the forcing suppresses or enhances the spatial pattern for the suppressing case our results are consistent with features of previous experiments on the chlorine dioxide iodine malonic acid chemical reaction however we also find examples of the enhancing case which has not yet been observed in experiment numerical simulations verify the predicted dependence on the forcing parameters

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

directed connected operators asymmetric hierarchies for image filtering and segmentation connected operators provide well established solutions for digital image processing typically in conjunction with hierarchical schemes in graph based frameworks such operators basically rely on symmetric adjacency relations between pixels in this article we introduce a notion of directed connected operators for hierarchical image processing by also considering non symmetric adjacency relations the induced image representation models are no longer partition hierarchies i e trees but directed acyclic graphs that generalize standard morphological tree structures such as component trees binary partition trees or hierarchical watersheds we describe how to efficiently build and handle these richer data structures and we illustrate the versatility of the proposed framework in image filtering and image segmentation

regularized tree partitioning and its application to unsupervised image segmentation in this paper we propose regularized tree partitioning approaches we study normalized cut ncut and average cut acut criteria over a tree forming two approaches 1 normalized tree partitioning ntp and 2 average tree partitioning atp we give the properties that result in an efficient algorithm for ntp and atp in addition we present the relations between the solutions of ntp and atp over the maximum weight spanning tree of a graph and ncut and acut over this graph to demonstrate the effectiveness of the proposed approaches we show its application to image segmentation over the berkeley image segmentation data set and present qualitative and quantitative comparisons with state of the art methods

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

fast vector quantization algorithms based on nearest partition set search a fast search method for vector quantization is proposed in this paper it makes use of the fact that in the generalized lloyd algorithm gla a vector in a training sequence is either placed in the same minimum distance partition mdp as in the previous iteration or in a partition within a very small subset of partitions the proposed method searches for the mdp for a training vector only in this subset of partitions plus the single previous mdp as the size of this subset is much smaller than the total number of codevectors the search process is speeded up significantly the creation of the subset is essential as it has a direct effect on the improvement in computation time of the proposed method the schemes that create the subset efficiently have been proposed the proposed method generates a codebook identical to that generated using the gla it is simple and requires only minor modification of the gla and a modest amount of additional memory the experimental results show that the computation time of codebook training was improved by factors from 6 6 to 50 7 and from 5 8 to 70 4 for two test data sets when codebooks of sizes from n 16 to 2048 were trained the proposed method was also combined with an earlier published method to further improve the computation time

on the cauchy problem for the integrable system of lie minimal surfaces in this paper we apply the cartan kahler theory of exterior differential systems to solve the cauchy problem for the integrable system of lie minimal surfaces and discuss the underlying geometry one purpose for this work is to show how methods and language from the theory of exterior differential systems may prove to be useful in the study of real analytic initial value problems especially for gaining insight into the geometric aspects of the initial conditions and the solutions

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

connected filtering based on multivalued component trees in recent papers a new notion of component graph was introduced it extends the classical notion of component tree initially proposed in mathematical morphology to model the structure of gray level images component graphs can indeed model the structure of any gray level or multivalued images we now extend the anti extensive filtering scheme based on component trees to make it tractable in the framework of component graphs more precisely we provide solutions for building a component graph reducing it based on selection criteria and reconstructing a filtered image from a reduced component graph in this paper we first consider the cases where component graphs still have a tree structure they are then called multivalued component trees the relevance and usefulness of such multivalued component trees are illustrated by applicative examples on hierarchically classified remote sensing images

customizing kernel functions for svm based hyperspectral image classification previous research applying kernel methods such as support vector machines svms to hyperspectral image classification has achieved performance competitive with the best available algorithms however few efforts have been made to extend svms to cover the specific requirements of hyperspectral image classification for example by building tailor made kernels observation of real life spectral imagery from the aviris hyperspectral sensor shows that the useful information for classification is not equally distributed across bands which provides potential to enhance the svm s performance through exploring different kernel functions spectrally weighted kernels are therefore proposed and a set of particular weights is chosen by either optimizing an estimate of generalization error or evaluating each band s utility level to assess the effectiveness of the proposed method experiments are carried out on the publicly available 92av3c dataset collected from the 220 dimensional aviris hyperspectral sensor results indicate that the method is generally effective in improving performance spectral weighting based on learning weights by gradient descent is found to be slightly better than an alternative method based on estimating relevance between band information and ground truth

binary partition tree construction from multiple features for image segmentation in the context of digital image processing and analysis the binary partition tree bpt is a classical data structure for the hierarchical modelling of images at different scales bpts belong both to the families of graph based models and morphological hierarchies they constitute an efficient way to define sets of nested partitions of image support that further provide knowledge guided reduced research spaces for optimization based segmentation procedures basically a bpt is built in a mono feature way i e for one given image and one given metric by merging pairs of connected image regions that are similar in the induced feature space we propose in this work a generalization of the bpt construction framework allowing to embed multiple features the cornerstone of our approach relies on a collaborative strategy enabling to establish a consensus between different metrics thus allowing to obtain a unified hierarchical segmentation space in particular this provides alternatives to the complex issue of arbitrary metric construction from several possibly non comparable features to reach that goal we first revisit the bpt construction algorithm to describe it in a fully graph based formalism then we present the structural and algorithmic evolutions and impacts when embedding multiple features in bpt construction we also discuss different ways to tackle the induced memory and time complexity issues raised by this generalized framework final experiments illustrate how this multi feature framework can be used to build bpts from multiple metrics computed through the potentially multiple image content s in particular in the context of remote sensing

hyper complex four manifolds from the tzitzeica equation it is shown how solutions to the tzitzeica equation can be used to construct a family of pseudo hyper complex metrics in four dimensions

a novel technique for subpixel image classification based on support vector machine this paper presents a novel support vector machine classifier designed for subpixel image classification pixel spectral unmixing the proposed classifier generalizes the properties of svms to the identification and modeling of the abundances of classes in mixed pixels by using fuzzy logic this results in the definition of a fuzzy input fuzzy output support vector machine f2svm classifier that can 1 process fuzzy information given as input to the classification algorithm for modeling the subpixel information in the learning phase of the classifier and 2 provide a fuzzy modeling of the classification results allowing a relation many to one between classes and pixels the presented binary f2svm can address multicategory problems according to two strategies the fuzzy one against all foaa and the fuzzy one against one foao strategies these strategies generalize to the fuzzy case techniques based upon ensembles of binary classifiers used for addressing multicategory problems in crisp classification problems the effectiveness of the proposed f2svm classifier is tested on three problems related to image classification in presence of mixed pixels having different characteristics experimental results confirm the validity of the proposed subpixel classification method