training free generic object detection using locally adaptive regression kernels we present a generic detection localization algorithm capable of searching for a visual object of interest without training the proposed method operates using a single example of an object of interest to find similar matches does not require prior knowledge learning about objects being sought and does not require any preprocessing step or segmentation of a target image our method is based on the computation of local regression kernels as descriptors from a query which measure the likeness of a pixel to its surroundings salient features are extracted from said descriptors and compared against analogous features from the target image this comparison is done using a matrix generalization of the cosine similarity measure we illustrate optimality properties of the algorithm using a naive bayes framework the algorithm yields a scalar resemblance map indicating the likelihood of similarity between the query and all patches in the target image by employing nonparametric significance tests and nonmaxima suppression we detect the presence and location of objects similar to the given query the approach is extended to account for large variations in scale and rotation high performance is demonstrated on several challenging data sets indicating successful detection of objects in diverse contexts and under different imaging conditions

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

structure sensitive saliency detection via multilevel rank analysis in intrinsic feature space this paper advocates a novel multiscale structure sensitive saliency detection method which can distinguish multilevel reliable saliency from various natural pictures in a robust and versatile way one key challenge for saliency detection is to guarantee the entire salient object being characterized differently from nonsalient background to tackle this our strategy is to design a structure aware descriptor based on the intrinsic biharmonic distance metric one benefit of introducing this descriptor is its ability to simultaneously integrate local and global structure information which is extremely valuable for separating the salient object from nonsalient background in a multiscale sense upon devising such powerful shape descriptor the remaining challenge is to capture the saliency to make sure that salient subparts actually stand out among all possible candidates toward this goal we conduct multilevel low rank and sparse analysis in the intrinsic feature space spanned by the shape descriptors defined on over segmented super pixels since the low rank property emphasizes much more on stronger similarities among super pixels we naturally obtain a scale space along the rank dimension in this way multiscale saliency can be obtained by simply computing differences among the low rank components across the rank scale we conduct extensive experiments on some public benchmarks and make comprehensive quantitative evaluation between our method and existing state of the art techniques all the results demonstrate the superiority of our method in accuracy reliability robustness and versatility

modulating shape features by color attention for object recognition bag of words based image representation is a successful approach for object recognition generally the subsequent stages of the process feature detection feature description vocabulary construction and image representation are performed independent of the intentioned object classes to be detected in such a framework it was found that the combination of different image cues such as shape and color often obtains below expected results this paper presents a novel method for recognizing object categories when using multiple cues by separately processing the shape and color cues and combining them by modulating the shape features by category specific color attention color is used to compute bottom up and top down attention maps subsequently these color attention maps are used to modulate the weights of the shape features in regions with higher attention shape features are given more weight than in regions with low attention we compare our approach with existing methods that combine color and shape cues on five data sets containing varied importance of both cues namely soccer color predominance flower color and shape parity pascal voc 2007 and 2009 shape predominance and caltech 101 color co interference the experiments clearly demonstrate that in all five data sets our proposed framework significantly outperforms existing methods for combining color and shape information

natural image statistics and low complexity feature selection low complexity feature selection is analyzed in the context of visual recognition it is hypothesized that high order dependences of bandpass features contain little information for discrimination of natural images this hypothesis is characterized formally by the introduction of the concepts of conjunctive interference and decomposability order of a feature set necessary and sufficient conditions for the feasibility of low complexity feature selection are then derived in terms of these concepts it is shown that the intrinsic complexity of feature selection is determined by the decomposability order of the feature set and not its dimension feature selection algorithms are then derived for all levels of complexity and are shown to be approximated by existing information theoretic methods which they consistently outperform the new algorithms are also used to objectively test the hypothesis of low decomposability order through comparison of classification performance it is shown that for image classification the gain of modeling feature dependencies has strongly diminishing returns best results are obtained under the assumption of decomposability order 1 this suggests a generic law for bandpass features extracted from natural images that the effect on the dependence of any two features of observing any other feature is constant across image classes

scaling theorems for zero crossings we characterize some properties of the zero crossings of the laplacian of signals in particular images filtered with linear filters as a function of the scale of the filter extending recent work by witkin 16 we prove that in any dimension the only filter that does not create generic zero crossings as the scale increases is the gaussian this result can be generalized to apply to level crossings of any linear differential operator it applies in particular to ridges and ravines in the image intensity in the case of the second derivative along the gradient there is no filter that avoids creation of zero crossings unless the filtering is performed after the derivative is applied

ray saliency bottom up visual saliency for a rotating and zooming camera we extend the classical notion of computational visual saliency to multi image data collected using a stationary pan tilt zoom ptz camera by introducing the concept of consistency the requirement that the set of generated saliency maps should each assign the same saliency value to unique regions of the environment that appear in more than one image we show that processing each image independently will often fail to provide a consistent measure of saliency and that using an image mosaic to quantify saliency suffers from several drawbacks we then propose ray saliency and an immediate extension approximate ray saliency a mosaic free method for calculating a consistent measure of bottom up saliency experimental results demonstrating the effectiveness of the proposed approach are presented

groups of adjacent contour segments for object detection we present a family of scale invariant local shape features formed by chains of k connected roughly straight contour segments kas and their use for object class detection kas are able to cleanly encode pure fragments of an object boundary without including nearby clutter moreover they offer an attractive compromise between information content and repeatability and encompass a wide variety of local shape structures we also define a translation and scale invariant descriptor encoding the geometric configuration of the segments within a kas making kas easy to reuse in other frameworks for example as a replacement or addition to interest points ips software for detecting and describing kas is released at http lear inrialpes fr software we demonstrate the high performance of kas within a simple but powerful sliding window object detection scheme through extensive evaluations involving eight diverse object classes and more than 1 400 images we 1 study the evolution of performance as the degree of feature complexity k varies and determine the best degree 2 show that kas substantially outperform ips for detecting shape based classes and 3 compare our object detector to the recent state of the art system by dalal and triggs 2005

study of visual saliency detection via nonlocal anisotropic diffusion equation in this paper a nonlocal anisotropic diffusion equation is constructed to model the evolution of visual saliency a new multi directions discretization scheme is adopted to solve the equation visual attention diffusion is modeled as a series of diffusion progresses until achieving a stable status so two stages of diffusion are involved in the first stage image boundaries are used to guide the background iterative diffusion process and the initial saliency seeds are obtained by sorting in the second stage an optimization of saliency seeds is executed and the good saliency seeds are strengthened and updated during each iteration the final saliency map is obtained through iteratively diffusing saliency scores from the optimal saliency seeds i e the most representative salient elements extensive experimental results on two large benchmark databases demonstrate the effectiveness of the proposed method highlightswe propose a novel method for the visual saliency detection problem the proposed method is based on nonlocal anisotropic diffusion equation an iteration of diffusion is used to formulate the visual attention spreading the boundary prior is exploited to diffusion from boundary to the entire image the proposed method has a promising performance in terms of accuracy and speed

discriminative saliency propagation with sink points salient object detection is still very challenging especially in images with complex or cluttered background in this paper we present an efficient and discriminative framework to address it in specially a discriminative similarity metric is first proposed by measuring the chi square distance in a new constructed feature space then we apply it to calculate a background based coarse saliency map by introducing distribution prior to remove foreground noises in the image boundaries based on manifold ranking a robust saliency propagation mechanism is further developed to highlight salient object and simultaneously suppress background region by setting appropriate sink points finally several simple refinement techniques are utilized to generate pixel wise and smooth saliency maps extensive experimental results show the superior performance of the proposed method in terms of different evaluation metrics in addition the proposed framework can be also applied to the existing saliency propagation methods for significant performance boosting we also believe that it is a good choice for subsequent applications based on the achieved high performance and acceptable computational overhead a discriminative similarity metric is proposed to distinguish similar regions we propose an efficient distribution guided background based weak saliency method a discriminative propagation mechanism is developed to optimize coarse saliency maps several new refinements are utilized to enhance the visual quality of the output we make a good balance between saliency detection accuracy and computational cost

decision theoretic saliency computational principles biological plausibility and implications for neurophysiology and psychophysics a decision theoretic formulation of visual saliency first proposed for top down processing object recognition gao vasconcelos 2005a is extended to the problem of bottom up saliency under this formulation optimality is defined in the minimum probability of error sense under a constraint of computational parsimony the saliency of the visual features at a given location of the visual field is defined as the power of those features to discriminate between the stimulus at the location and a null hypothesis for bottom up saliency this is the set of visual features that surround the location under consideration discrimination is defined in an information theoretic sense and the optimal saliency detector derived for a class of stimuli that complies with known statistical properties of natural images it is shown that under the assumption that saliency is driven by linear filtering the optimal detector consists of what is usually referred to as the standard architecture of v1 a cascade of linear filtering divisive normalization rectification and spatial pooling the optimal detector is also shown to replicate the fundamental properties of the psychophysics of saliency stimulus pop out saliency asymmetries for stimulus presence versus absence disregard of feature conjunctions and weber s law finally it is shown that the optimal saliency architecture can be applied to the solution of generic inference problems in particular for the class of stimuli studied it performs the three fundamental operations of statistical inference assessment of probabilities implementation of bayes decision rule and feature selection

scale affine invariant interest point detectors in this paper we propose a novel approach for detecting interest points invariant to scale and affine transformations our scale and affine invariant detectors are based on the following recent results 1 interest points extracted with the harris detector can be adapted to affine transformations and give repeatable results geometrically stable 2 the characteristic scale of a local structure is indicated by a local extremum over scale of normalized derivatives the laplacian 3 the affine shape of a point neighborhood is estimated based on the second moment matrix our scale invariant detector computes a multi scale representation for the harris interest point detector and then selects points at which a local measure the laplacian is maximal over scales this provides a set of distinctive points which are invariant to scale rotation and translation as well as robust to illumination changes and limited changes of viewpoint the characteristic scale determines a scale invariant region for each point we extend the scale invariant detector to affine invariance by estimating the affine shape of a point neighborhood an iterative algorithm modifies location scale and neighborhood of each point and converges to affine invariant points this method can deal with significant affine transformations including large scale changes the characteristic scale and the affine shape of neighborhood determine an affine invariant region for each point we present a comparative evaluation of different detectors and show that our approach provides better results than existing methods the performance of our detector is also confirmed by excellent matching resultss the image is described by a set of scale affine invariant descriptors computed on the regions associated with our points

on the accuracy of the simple peak hour approximation for markovian queues we empirically explore the accuracy of the simple stationary peak hour approximation spha for estimating peak hour performance in multiserver queuing systems with exponential service times and periodic sinusoidal poisson arrival processes we show that the spha is very good for a range of parameter values corresponding to a reasonably broad spectrum of real systems however we do find and document that there are many situations in which this approximation will be very inaccurate we postulate and then support empirically a set of hypotheses that link the accuracy of the spha and the related point wise stationary approximation psa to key parameter values and model characteristics we also present results on the time dependent behavior of these systems as a function of key parameters finally we present results which indicate that our findings developed for models with sinusoidal input streams may apply to a much broader range of markovian models with more general cyclic inputs

resolution of singularities and modular galois theory i shall sketch a brief history of the desingularization problem from riemann thru zariski to hironaka including the part i played in it and the work on galois theory which this led me to and how that caused me to search out many group theory gurus i shall also formulate several conjectures and suggest numerous thesis problems

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

wavelet based texture retrieval using generalized gaussian density and kullback leibler distance we present a statistical view of the texture retrieval problem by combining the two related tasks namely feature extraction fe and similarity measurement sm into a joint modeling and classification scheme we show that using a consistent estimator of texture model parameters for the fe step followed by computing the kullback leibler distance kld between estimated models for the sm step is asymptotically optimal in term of retrieval error probability the statistical scheme leads to a new wavelet based texture retrieval method that is based on the accurate modeling of the marginal distribution of wavelet coefficients using generalized gaussian density ggd and on the existence a closed form for the kld between ggds the proposed method provides greater accuracy and flexibility in capturing texture information while its simplified form has a close resemblance with the existing methods which uses energy distribution in the frequency domain to identify textures experimental results on a database of 640 texture images indicate that the new method significantly improves retrieval rates e g from 65 to 77 compared with traditional approaches while it retains comparable levels of computational complexity

discriminant saliency the detection of suspicious coincidences and applications to visual recognition a discriminant formulation of top down visual saliency intrinsically connected to the recognition problem is proposed the new formulation is shown to be closely related to a number of classical principles for the organization of perceptual systems including infomax inference by detection of suspicious coincidences classification with minimal uncertainty and classification with minimum probability of error the implementation of these principles with computational parsimony by exploitation of the statistics of natural images is investigated it is shown that barlow s principle of inference by the detection of suspicious coincidences enables computationally efficient saliency measures which are nearly optimal for classification this principle is adopted for the solution of the two fundamental problems in discriminant saliency feature selection and saliency detection the resulting saliency detector is shown to have a number of interesting properties and act effectively as a focus of attention mechanism for the selection of interest points according to their relevance for visual recognition experimental evidence shows that the selected points have good performance with respect to 1 the ability to localize objects embedded in significant amounts of clutter 2 the ability to capture information relevant for image classification and 3 the richness of the set of visual attributes that can be considered salient

singularity theory and phantom edges in scale space the process of detecting edges in a one dimensional signal by finding the zeros of the second derivative of the signal can be interpreted as the process of detecting the critical points of a general class of contrast functions that are applied to the signal it is shown that the second derivative of the contrast function at the critical point is related to the classification of the associated edge as being phantom or authentic the contrast of authentic edges decreases with filter scale while the contrast of phantom edges are shown to increase with scale as the filter scale increases an authentic edge must either turn into a phantom edge or join with a phantom edge and vanish the points in the scale space at which these events occur are seen to be singular points of the contrast function using ideas from singularity or catastrophy theory the scale map contours near these singular points are found to be either vertical or parabolic

time dependent queues a single server queue is considered having exponentially distributed inter arrival and service times with slowly changing time dependent rates lambda varepsilon t and mu varepsilon t the parameter varepsilon is the ratio of an average inter arrival time to the time over which the rates change appreciably so it is small therefore an asymptotic solution valid for varepsilon small is constructed for the time dependent queue length probability distribution it consists of five typical parts corresponding to five typical time periods they are the initial period the period of light traffic when lambda mu 1 the saturation transition period when lambda mu increases through unity the oversaturation period when lambda mu starts out greater than unity and then decreases below unity and the transition period at the end of oversaturation when the queue returns to the light traffic condition by combining the solutions for these five intervals the solution fo

variational problems and partial differential equations on implicit surfaces a novel framework for solving variational problems and partial differential equations for scalar and vector valued data defined on surfaces is introduced in this paper the key idea is to implicitly represent the surface as the level set of a higher dimensional function and to solve the surface equations in a fixed cartesian coordinate system using this new embedding function the equations are then both intrinsic to the surface and defined in the embedding space this approach thereby eliminates the need for performing complicated and inaccurate computations on triangulated surfaces as is commonly done in the literature we describe the framework and present examples in computer graphics and image processing applications including texture synthesis flow field visualization and image and vector field intrinsic regularization for data defined on 3d surfaces

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

asymptotic analysis of the time dependent m m 1 queue using operator analytic techniques we develop a nonstationary markovian queueing theory starting with the mt mt 1 queue we employ an asymptotic approach quite different from the usual large time analysis instead we uniformly accelerate the queue length process that is we divide the arrival and service rate by a common parameter e then for a fixed time interval we consider the asymptotics for the distribution mean and variance of the queue length process as e goes to zero the effects of e can be quite different for the given time interval this gives us a dynamic asymptotic behavior for the queue length process we can formulate a time dependent traffic intensity parameter that determines when the process is asymptotically stable and when it is asymptotically unstable

performance bounds for nonhomogeneous queues this paper considers nonhomogeneous m t m t 1 queues which can model systems such as communications networks for such systems bounds on moment generating functions and on the tail distribution of the queue process are obtained these bounds are useful for characterizing the quality of service a system can provide to its users an approach utilizing the theory of differential equations is adapted the bounds given in this paper are tighter than those previously available in fact the bounds can be made arbitrarily tight given sufficient computational effort

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

the curvature primal sketch in this paper we introduce a novel representation of the significant changes in curvature along the bounding contour of planar shape we call the representation the curvature primal sketch because of the close analogy to the primal sketch representation advocated by marr for describing significant intensity changes we define a set of primitive parameterized curvature discontinuities and derive expressions for their convolutions with the first and second derivatives of a gaussian we describe an implemented algorithm that computes the curvature primal sketch by matching the multiscale convolutions of a shape and illustrate its performance on a set of tool shapes several applications of the representation are sketched

visual saliency based on scale space analysis in the frequency domain we address the issue of visual saliency from three perspectives first we consider saliency detection as a frequency domain analysis problem second we achieve this by employing the concept of nonsaliency third we simultaneously consider the detection of salient regions of different size the paper proposes a new bottom up paradigm for detecting visual saliency characterized by a scale space analysis of the amplitude spectrum of natural images we show that the convolution of the image amplitude spectrum with a low pass gaussian kernel of an appropriate scale is equivalent to an image saliency detector the saliency map is obtained by reconstructing the 2d signal using the original phase and the amplitude spectrum filtered at a scale selected by minimizing saliency map entropy a hypercomplex fourier transform performs the analysis in the frequency domain using available databases we demonstrate experimentally that the proposed model can predict human fixation data we also introduce a new image database and use it to show that the saliency detector can highlight both small and large salient regions as well as inhibit repeated distractors in cluttered images in addition we show that it is able to predict salient regions on which people focus their attention

interpreting line drawings of curved objects in this thesis we study the problem of interpreting line drawings of scenes composed or opaque regular solid objects bounded by piecewise smooth surfaces with no markings or texture on them it is assumed that the line drawing has been formed by orthographic projection of such a scene under general viewpoint that the line drawing is error free and that there are no lines due to shadows or specularities our definition implicitly excludes laminae wires and the apices of cones a major component of the interpretation of line drawings is line labelling by line labelling we mean a classification of each image curve as corresponding to either a depth or orientation discontinuity in the scene and b further subclassification of each kind of discontinuity for a depth discontinuity we determine whether it is a limb a locus of points on the surface where the line of sight is tangent to the surface or an occluding edge a tangent plane discontinuity of the surface for an orientation discontinuity we determine whether it corresponds to a convex or concave edge this thesis presents the first mathematically rigorous scheme for labelling line drawings of the class of scenes described by analysing the projection of the neighborhoods of different kinds of points on a piecewise smooth surface we are able to catalog all local labelling possibilities for the different types of junctions in a line drawing an algorithm is developed which utilizes this catalog to determine all legal labellings of the line drawing a local minimum complexity rule at each vertex select those labellings which correspond to the minimum number of faces meeting at the vertex is used in order to prune highly counter intuitive interpretations the labelling scheme was implemented and tested on a number of line drawings the labellings obtained are few and by and large in accordance with human interpretations

image compression via joint statistical characterization in the wavelet domain we develop a probability model for natural images based on empirical observation of their statistics in the wavelet transform domain pairs of wavelet coefficients corresponding to basis functions at adjacent spatial locations orientations and scales are found to be non gaussian in both their marginal and joint statistical properties specifically their marginals are heavy tailed and although they are typically decorrelated their magnitudes are highly correlated we propose a markov model that explains these dependencies using a linear predictor for magnitude coupled with both multiplicative and additive uncertainties and show that it accounts for the statistics of a wide variety of images including photographic images graphical images and medical images in order to directly demonstrate the power of the model we construct an image coder called epwic embedded predictive wavelet image coder in which subband coefficients are encoded one bitplane at a time using a nonadaptive arithmetic encoder that utilizes conditional probabilities calculated from the model bitplanes are ordered using a greedy algorithm that considers the mse reduction per encoded bit the decoder uses the statistical model to predict coefficient values based on the bits it has received despite the simplicity of the model the rate distortion performance of the coder is roughly comparable to the best image coders in the literature

focus of attention from local color symmetries in this paper a continuous valued measure for local color symmetry is introduced the new algorithm is an extension of the successful gray value based symmetry map proposed by reisfeld et al the use of color facilitates the detection of focus points fps on objects that are difficult to detect using gray value contrast only the detection of fps is aimed at guiding the attention of an object recognition system therefore fps have to fulfill three major requirements stability distinctiveness and usability the proposed algorithm is evaluated for these criteria and compared with the gray value based symmetry measure and two other methods from the literature stability is tested against noise object rotation and variations of lighting as a measure for the distinctiveness of fps the principal components of fp centered windows are compared with those of windows at randomly chosen points on a large database of natural images finally usability is evaluated in the context of an object recognition task

strong approximations for time dependent queues a time dependent mt mt 1 queue alternates through periods of under over and critical loading we derive period dependent pathwise asymptotic expansions for its queue length within the framework of strong approximations our main results include time dependent fluid approximations supported by a functional strong law of large numbers and diffusion approximations supported by a functional central limit theorem this complements and extends previous work on asymptotic expansions of the queue length transition probabilities

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed