image reconstruction from zero crossings this study is concerned with the information in zero crossings zc of images logan s conditions specifying when a one dimensional signal may be recovered within a multiplicative constant from its zc are extended for various cases of two dimensional signals an algorithm is implemented in reconstruction of context free band pass images it is also successfully applied in reconstruction of contextual images by first dissecting the image into appropriate bandpass band limited two dimensional signals in almost all cases of spectrum confined to less than an octave in one dimension the reconstruction algorithm converges whereas it does not converge for any signal exceeding one octave in bandwidth this paper substantiates the proposition that images are well represented by the partial information confined to zc

discrete time wavelet extrema representation design and consistent reconstruction the paper studies wavelet transform extrema and zero crossings representations within the framework of convex representations in spl lscr z wavelet zero crossings representation of two dimensional signals is introduced as a convex multiscale edge representation as well one appealing property of convex representations is that the reconstruction problem can be solved at least theoretically using the method of alternating projections onto convex sets it turns out that in the case of the wavelet extrema and wavelet zero crossings representations this method yields simple and practical reconstruction algorithms nonsubsampled filter banks that implement the wavelet transform for the two representations are also studied in the paper relevant classes of nonsubsampled perfect reconstruction fir filter banks are characterized this characterization gives a broad class of wavelets for the representations which are derived from those of the filter banks which satisfy a regularity condition

wavelet domain blur invariants for image analysis radiometric degradation is a common problem in the image acquisition part of many applications there is much research carried out in an effort to deblur such images however it has been proven that it is not always necessary to go through a burdensome process of deblurring to tackle this problem different blur invariant descriptors have been proposed so far which are either in the spatial domain or based on the properties available in the fourier domain in this paper wavelet domain blur invariants are proposed for the first time for discrete 2 d signals these descriptors which are invariant to centrally symmetric blurs inherit the advantages that this domain provides it is also proven that the spatial domain blur invariants are a special version of the proposed invariants the performance of these invariants will be demonstrated through experiments

zero crossings of a wavelet transform the completeness stability and application to pattern recognition of a multiscale representation based on zero crossings is discussed an alternative projection algorithm is described that reconstructs a signal from a zero crossing representation which is stabilized by keeping the value of the wavelet transform integral between each pair of consecutive zero crossings the reconstruction algorithm has a fast convergence and each iteration requires o n log sup 2 n computation for a signal of n samples the zero crossings of a wavelet transform define a representation which is particularly well adapted for solving pattern recognition problems as an example the implementation and results of a coarse to fine stereo matching algorithm are described

hybrid image matching combining hausdorff distance with normalized gradient matching image matching has been a central problem in computer vision and image processing for decades most of the previous approaches to image matching can be categorized into the intensity based and edge based comparison hausdorff distance has been widely used for comparing point sets or edge maps since it does not require point correspondences in this paper we propose a new image similarity measure combining the hausdorff distance with a normalized gradient consistency score for image matching the normalized gradient consistency score is designed to compare the normalized image gradient fields between two images to alleviate the illumination variation problem in image matching by combining the edge based and intensity based information for image matching we are able to achieve robust image matching under different lighting conditions we show the superior robustness property of the proposed image matching technique through experiments on face recognition under different lighting conditions

on tetravalent symmetric dihedrants let be a tetravalent x arc transitive cayley graph of dihedral group for x aut let xv be the stabilizer of x on vv has been determined when it is 2 arc transitive or one regular this paper studies the case where is one transitive but not one regular and gives it an exactly characterization as an application of this result we give a compete classification of such graphs when xv 24 by production a compete classification is given for the stabilizers of tetravalent symmetric cayley graphs whenever its order is less than 25

signal representation in the combined phase spatial space reconstruction and criteria for uniqueness motivated by the major roles of the spectral phase in signal structure and by previous results on the importance of localized representation in images we develop conditions for unique representation of a signal by a combination of its spectral fourier phase and spatial samples methods for signal reconstruction from various combinations of spatial and phase information are introduced it is concluded that most of the previous results in the area of phase only representation and reconstruction are special cases of the general approach presented here

comparing images using the hausdorff distance the hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another efficient algorithms for computing the hausdorff distance between all possible relative positions of a binary image and a model are presented the focus is primarily on the case in which the model is only allowed to translate with respect to the image the techniques are extended to rigid motion the hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived the method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods it is shown that the method extends naturally to the problem of comparing a portion of a model against an image

shape similarity matching for query by example this paper describes a unified approach for two dimensional 2 d shape matching and similarity ranking of objects by means of a modal representation in particular we propose a new shape similarity metric in the eigenshape space for object image retrieval from a visual database via query by example this differs from prior work which performed point correspondence determination and similarity ranking of shapes in separate steps the proposed method employs selected boundary and or contour points of an object as a coarse to fine shape representation and does not require extraction of connected boundaries or silhouettes it is rotation translation and scale invariant and can handle mild deformations of objects e g due to partial occlusions or pose variations results comparing the unified method with an earlier two step approach using b spline based modal matching and hausdorff distance ranking are presented on retail and museum catalog style still image databases

analytical footprints compact representation of elementary singularities in wavelet bases we introduce a family of elementary singularities that are point holder regular these singularities are self similar and are the green functions of fractional derivative operators i e by suitable fractional differentiation one retrieves a dirac function at the exact location of the singularity we propose to use fractional operator like wavelets that act as a multiscale version of the derivative in order to characterize and localize singularities in the wavelet domain we show that the characteristic signature when the wavelet interacts with an elementary singularity has an asymptotic closed form expression termed the analytical footprint practically this means that the dictionary of wavelet footprints is embodied in a single analytical form we show that the wavelet coefficients of the nonredundant decomposition can be fitted in a multiscale fashion to retrieve the parameters of the underlying singularity we propose an algorithm based on stepwise parametric fitting and the feasibility of the approach to recover singular signal representations

reconstructions from zero crossings in scale space in computer vision the one parameter family of images obtained from the laplacian of a gaussian filtered version of the image parameterized by the width of the gaussian has proved to be a useful data structure for the extraction of feature data in particular the zero crossings of this so called scale space data are associated with edges and have been proposed by d marr 1982 and others as the basis of a representation of the image data the question arises as to whether the representation is complete and stable the authors survey some of the studies and results related to these questions as well as several studies that attempt reconstructions based on this or related representations they formulate a novel method for reconstruction from zero crossings in scale space that is based on minimizing equation error and they present results showing that the reconstruction is possible but can be unstable they further show that the method applies when gradient data along the zero crossings are included in the representation and they demonstrate empirically that the reconstruction is then stable

a multiscale edge detection algorithm based on wavelet domain vector hidden markov tree model abstract the wavelet analysis is an efficient tool for the detection of image edges based on the wavelet analysis we present an unsupervised learning algorithm to detect image edges in this paper a wavelet domain vector hidden markov tree wd vhmt is employed in our algorithm to model the statistical properties of multiscale and multidirectional subband wavelet coefficients of an image with this model each wavelet coefficient is viewed as an observation of its hidden state and the hidden state indicates if the wavelet coefficient belongs to an edge the wd vhmt model can be learned by an expectation maximization algorithm after the model is learned we employ an extended viterbi algorithm to uncover the hidden state sequences according to the maximum a posterior estimation the experiment results of the edge detection for several images are provided to evaluate our algorithm

modal matching for correspondence and recognition modal matching is a new method for establishing correspondences and computing canonical descriptions the method is based on the idea of describing objects in terms of generalized symmetries as defined by each object s eigenmodes the resulting modal description is used for object recognition and categorization where shape similarities are expressed as the amounts of modal deformation energy needed to align the two objects in general modes provide a global to local ordering of shape deformation and thus allow for selecting which types of deformations are used in object alignment and comparison in contrast to previous techniques which required correspondence to be computed with an initial or prototype shape modal matching utilizes a new type of finite element formulation that allows for an object s eigenmodes to be computed directly from available image information this improved formulation provides greater generality and accuracy and is applicable to data of any dimensionality correspondence results with 2d contour and point feature data are shown and recognition experiments with 2d images of hand tools and airplanes are described

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

delta ramp encoder for amplitude sampling and its interpretation as time encoding the theoretical basis for conventional acquisition of bandlimited signals typically relies on uniform time sampling and assumes infinite precision amplitude values in this paper we explore signal representation and recovery based on uniform amplitude sampling with assumed infinite precision timing information the approach is based on the delta ramp encoder which consists of applying a one level level crossing detector to the result of adding an appropriate sawtooth like waveform to the input signal the output samples are the time instants of these level crossings thus representing a time encoded version of the input signal for theoretical purposes this system can be equivalently analyzed by reversibly transforming through ramp addition a nonmonotonic input signal into a monotonic one which is then uniformly sampled in amplitude the monotonic function is then represented by the times at which the signal crosses a predefined and equally spaced set of amplitude values we refer to this technique as amplitude sampling the time sequence generated can be interpreted alternatively as nonuniform time sampling of the original source signal we derive duality and frequency domain properties for the functions involved in the transformation iterative algorithms are proposed and implemented for recovery of the original source signal as indicated in the simulations the proposed iterative amplitude sampling algorithm achieves a faster convergence rate than frame based reconstruction for nonuniform sampling the performance can also be improved by appropriate choice of the parameters while maintaining the same sampling density

note on the complexity of deciding the rainbow vertex connectedness for bipartite graphs a path in an edge colored graph is said to be a rainbow path if no two edges on the path share the same color an edge colored graph is strongly rainbow connected if there exists a rainbow geodesic path between every pair of vertices the strong rainbow connection number of g denoted by scr g respectively rc g is the smallest number of colors that are needed in order to make g strongly rainbow connected a vertex colored graph g is rainbow vertex connected if any pair of vertices in g are connected by a path whose internal vertices have distinct colors the rainbow vertex connection number of a connected graph g denoted by rvc g is the smallest number of colors that are needed in order to make g rainbow vertex connected though for a general graph g it is np complete to decide whether rc g 2 or rvc g 2 in this paper we show that the problem becomes easy when g is a bipartite graph whereas deciding whether rc g 3 or rvc g 3 is still np complete even when g is a bipartite graph moreover it is known that deciding whether a given edge vertex colored with an unbound number of colors graph is rainbow vertex connected is np complete we will prove that it is still np complete even when the edge vertex colored graph is bipartite we also show that a few np hard problems on rainbow connection are indeed np complete

reconstruction of nonperiodic two dimensional signals from zero crossings in this correspondence we present new results on the reconstruction of two dimensional signals from zero crossing or threshold crossing information specifically we develop new theoretical results which state conditions under which two dimensional bandlimited signals are uniquely specified to within a scale factor with this information unlike previous results in this area our new results do not constrain the signals to be periodic or bandpass

deformable prototypes for encoding shape categories in image databases abstract we describe a method for shape based image database search that uses deformable prototypes to represent categories rather than directly comparing a candidate shape with all shape entries in the database shapes are compared in terms of the types of nonrigid deformations differences that relate them to a small subset of representative prototypes to solve the shape correspondence and alignment problem we employ the technique of em modal matching an information preserving shape decomposition for matching describing and comparing shapes despite sensor variations and nonrigid deformations in modal matching shape is decomposed into an ordered basis of orthogonal principal components we demonstrate the utility of this approach for shape comparison in 2 d image databases

on quasi isometry of threshold based sampling the problem of isometry for threshold based sampling such as integrate and fire or send on delta is addressed while for uniform sampling the parseval theorem provides isometry and makes the euclidean metric canonical there is no analogy for threshold based sampling the relaxation of the isometric postulate to quasi isometry however allows the discovery of the underlying metric structure of threshold based sampling this paper characterizes this metric structure making hermann weyl s discrepancy measure canonical for threshold based sampling the usefulness of the approach is demonstrated by means of a novel adaptive threshold based sampling scheme which applied on electrocardiography signals allows a substantial reduction of the number of samples while maintaining nearly the same snr after reconstruction

detection of a polymorphic mesoamerican symbol using a rule based approach this paper describes a technique to recognize a mesoamerican symbol whose shape is extremely variable we extract symbols from a drawing and we encode them as discrete curves we perform the recognition using a set of rules that define the correct symbol one of the rules is the presence of a single symmetry axis we describe a comparison metric between curves in order to search for symmetries the other rules used for the recognition concern the morphology of the symbol the proposed technique proves to be fast and efficient we present recognition results obtained on various pre hispanic images the rule based approach proposed and implemented here appears suitable to detect polymorphic signs a common feature of mesoamerican symbols to the best of our knowledge this is the first study of pattern recognition into the field of mesoamerican iconography

optimal filter banks for signal reconstruction from noisy subband components conventional design techniques for analysis and synthesis filters in subband processing applications guarantee perfect reconstruction of the original signal from its subband components the resulting filters however lose their optimality when additive noise due for example to signal quantization disturbs the subband sequences we propose filter design techniques that minimize the reconstruction mean squared error mse taking into account the second order statistics of signals and noise in the case of either stochastic or deterministic signals a novel recursive pseudo adaptive algorithm is proposed for efficient design of these filters analysis and derivations are extended to 2 d signals and filters using powerful kronecker product notation a prototype application of the proposed ideas in subband coding is presented simulations illustrate the superior performance of the proposed filter banks versus conventional perfect reconstruction filters in the presence of additive subband noise

invariant matching and identification of curves using b splines curve representation there have been many techniques for curve shape representation and analysis ranging from fourier descriptors to moments to implicit polynomials to differential geometry features to time series models to b splines etc the b splines stand as one of the most efficient curve surface representations and possess very attractive properties such as spatial uniqueness boundedness and continuity local shape controllability and invariance to affine transformations these properties made them very attractive for curve representation and consequently they have been extensively used in computer aided design and computer graphics very little work however has been devoted to them for recognition purposes one possible reason might be due to the fact that the b spline curve is not uniquely described by a single set of parameters control points which made the curve matching recognition process difficult when comparing the respective parameters of the curves to be matched this paper is an attempt to find matching solutions despite this limitation and as such it deals the problem of using b splines for shape recognition and identification from curves with an emphasis on the following applications affine invariant matching and classification of 2 d curves with applications in identification of aircraft types based on image silhouettes and writer identification based on handwritten text

denoising by singularity detection a new algorithm for noise reduction using the wavelet transform is proposed similar to mallat s 1992 wavelet transform modulus maxima denoising approach we estimate the regularity of a signal from the evolution of its wavelet transform coefficients across scales however we do not perform maxima detection and processing therefore complicated reconstruction is avoided instead the local regularities of a signal are estimated by computing the sum of the modulus of its wavelet coefficients inside the corresponding cone of influence and the coefficients that correspond to the regular part of the signal for reconstruction are selected the algorithm gives an improved denoising result as compared with the previous approaches in terms of mean squared error and visual quality the new denoising algorithm is also invariant to translation it does not introduce spurious oscillations and requires very little a priori information of the signal or noise besides we extend the method to two dimensions to estimate the regularity of an image by computing the sum of the modulus of its wavelet coefficients inside the so called directional cone of influence the denoising technique is applied to tomographic image reconstruction where the improved performance of the new approach can clearly be observed

improved transient signal detection using a wavepacket based detector with an extended translation invariant wavelet transform this paper presents the theory of m band extended translation invariant eti wavelet transforms the eti generalizes the translation invariant wavelet transform of weiss 1933 it is shown that iteration of the eti in a tree structure provides a signal decomposition into an orthonormal wavepacket basis other properties such as translation invariance and invertibility of the transform are proven the theory is then applied to transient signal detection through development of a family of translation invariant wavepacket based detectors this family of detectors provides improved the performance over previously defined wavepacket based detectors a performance analysis is conducted roc curves generated by monte carlo simulation are presented indicating the detector performance the detector performance is demonstrated to be independent of the signal translation

complex wavelet bases steerability and the marr like pyramid our aim in this paper is to tighten the link between wavelets some classical image processing operators and david marr s theory of early vision the cornerstone of our approach is a new complex wavelet basis that behaves like a smoothed version of the gradient laplace operator starting from first principles we show that a single generator wavelet can be defined analytically and that it yields a semi orthogonal complex basis of l 2 r2 irrespective of the dilation matrix used we also provide an efficient fft based filterbank implementation we then propose a slightly redundant version of the transform that is nearly translation invariant and that is optimized for better steerability gaussian like smoothing kernel we call it the marr like wavelet pyramid because it essentially replicates the processing steps in marr s theory of early vision we use it to derive a primal wavelet sketch which is a compact description of the image by a multiscale subsampled edge map finally we provide an efficient iterative algorithm for the reconstruction of an image from its primal wavelet sketch

efficient design of orthonormal wavelet bases for signal representation the efficient representation of a signal as a linear combination of elementary atoms or building blocks is central to much signal processing theory and many applications wavelets provide a powerful flexible and efficiently implementable class of such atoms in this paper we develop an efficient method for selecting an orthonormal wavelet that is matched to a given signal in the sense that the squared error between the signal and some finite resolution wavelet representation of it is minimized since the squared error is not an explicit function of the design parameters some form of approximation of this objective is required if conventional optimization techniques are to be used previous approximations have resulted in nonconvex optimization problems which require delicate management of local minima in this paper we employ an approximation that results in a design problem that can be transformed into a convex optimization problem and efficiently solved constraints on the smoothness of the wavelet can be efficiently incorporated into the design we show that the error incurred in our approximation is bounded by a function that decays to zero as the number of vanishing moments of the wavelet grows in our examples we demonstrate that our method provides wavelet bases that yield substantially better performance than members of standard wavelet families and are competitive with those designed by more intricate nonconvex optimization methods

signal recovery from wavelet transform maxima the paper presents an iterative algorithm for signal recovery from discrete time wavelet transform maxima the signal recovery algorithm is developed by using the method of projections onto convex sets convergence of the algorithm is assured

higher order spectra hos invariants for shape recognition abstract this paper describes a shape feature based invariant object recognition method first a set of features invariant to rotation translation and scaling rts is generated using the radon transform and bispectral analysis in order to improve the noise resistance of the invariants the ensemble averaging technique is introduced into the estimation of bispectra the feature data are further reduced to a smaller set using thresholding and principal component analysis the resultant feature invariants are proved to be more reliable and discriminable in the classification stage than the original ones it is shown experimentally that the extracted higher order spectra hos invariants form compact and isolated clusters in the feature space and that a simple minimum distance classifier yields high classification accuracy with low snr inputs the comparison study with hu s moment invariants and fourier descriptors also shows that the performance of the proposed method is better than these two methods especially in the presence of background noise the hos invariants algorithm is also applied to shape similarity based image indexing a new similarity matching technique based on tanimoto measure is employed for fast image retrieval the retrieval accuracy is high as shown in the experimental results

efficient sampling of band limited signals from sine wave crossings this correspondence presents an efficient method for reconstructing a band limited signal in the discrete domain from its crossings with a sine wave the method makes it possible to design analog to discrete a d converters that only deliver the crossing timings which are then used to interpolate the input signal at arbitrary instants potentially it may allow for reductions in power consumption and complexity in these converters the reconstruction in the discrete domain is based on a recently proposed modification of the lagrange interpolator which is readily implementable with linear complexity and efficiently given that it reuses known schemes for variable fractional delay vfd filters as a spin off the method allows one to perform spectral analysis from sine wave crossings with the complexity of the fft finally the results in the correspondence are validated in several numerical examples

an effective and fast iris recognition system based on a combined multiscale feature extraction technique the randomness of iris pattern makes it one of the most reliable biometric traits on the other hand the complex iris image structure and the various sources of intra class variations result in the difficulty of iris representation although a number of iris recognition methods have been proposed it has been found that several accurate iris recognition algorithms use multiscale techniques which provide a well suited representation for iris recognition in this paper and after a thorough analysis and summarization a multiscale edge detection approach has been employed as a pre processing step to efficiently localize the iris followed by a new feature extraction technique which is based on a combination of some multiscale feature extraction techniques this combination uses special gabor filters and wavelet maxima components finally a promising feature vector representation using moment invariants is proposed this has resulted in a compact and efficient feature vector in addition a fast matching scheme based on exclusive or operation to compute bits similarity is proposed where the result experimentation was carryout out using casia database the experimental results have shown that the proposed system yields attractive performances and could be used for personal identification in an efficient and effective manner and comparable to the best iris recognition algorithm found in the current literature

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

wavelet transforms for detecting microcalcifications in mammograms clusters of fine granular microcalcifications in mammograms may be an early sign of disease individual grains are difficult to detect and segment due to size and shape variability and because the background mammogram texture is typically inhomogeneous the authors develop a 2 stage method based on wavelet transforms for detecting and segmenting calcifications the first stage is based on an undecimated wavelet transform which is simply the conventional filter bank implementation without downsampling so that the low low ll low high lh high low hl and high high hh sub bands remain at full size detection takes place in hh and the combination lh hl four octaves are computed with 2 inter octave voices for finer scale resolution by appropriate selection of the wavelet basis the detection of microcalcifications in the relevant size range can be nearly optimized in fact the filters which transform the input image into hh and lh hl are closely related to prewhitening matched filters for detecting gaussian objects idealized microcalcifications in 2 common forms of markov background noise the second stage is designed to overcome the limitations of the simplistic gaussian assumption and provides an accurate segmentation of calcification boundaries detected pixel sites in hh and lh hl are dilated then weighted before computing the inverse wavelet transform individual microcalcifications are greatly enhanced in the output image to the point where straightforward thresholding can be applied to segment them frog curves are computed from tests using a freely distributed database of digitized mammograms

image restoration by the method of convex projections part 1ߞtheory a projection operator onto a closed convex set in hilbert space is one of the few examples of a nonlinear map that can be defined in simple abstract terms moreover it minimizes distance and is nonexpansive and therefore shares two of the more important properties of ordinary linear orthogonal projections onto closed linear manifolds in this paper we exploit the properties of these operators to develop several iterative algorithms for image restoration from partial data which permit any number of nonlinear constraints of a certain type to be subsumed automatically their common conceptual basis is as follows every known property of an original image f is envisaged as restricting it to lie in a well defined closed convex set thus m such properties place f in the intersection e0 ei of the corresponding closed convex sets e1 e2 em given only the projection operators pi onto the individual ei s i 1 m we restore f by recursive means clearly in this approach the realization of the pi s in a hilbert space setting is one of the major synthesis problems section i describes the geometrical significance of the three main theorems in considerable detail and most of the underlying ideas are illustrated with the aid of simple diagrams section ii presents rules for the numerical implementation of 11 specific projection operators which are found to occur frequently in many signal processing applications and the appendix contains proofs of all the major results

shape discrimination using fourier descriptors description or discrimination of boundary curves shapes is an important problem in picture processing and pattern recognition fourier descriptors fd s have interesting properties in this respect first a critical review is given of two kinds of fd s some properties of the fd s are given and a distance measure is proposed in terms of fd s that measures the difference between two boundarv curves it is shown how fd s can be used for obtaining skeletons fobjects finally experimental results are given in character recognition and machine parts recognition

two different approaches for iris recognition using gabor filters and multiscale zero crossing representation abstract importance of biometric user identification is increasing everyday one of the most promising techniques is the one based on the human iris the authors in this work describe different approaches to develop this biometric technique based on the works carried out by daugman the authors have worked using gabor filters and hamming distance but in addition they have also worked in zero crossing representation of the dyadic wavelet transform applied to two different iris signatures one based on a single virtual circle of the iris the other one based on an annular region also other metrics have been applied to be compared with the results obtained with the hamming distance in this work euclidean distance and d z will be shown the last proposed approach is translation rotation and scale invariant results will show a classification success up to 99 6 achieving an equal error rate down to 0 12 and the possibility of having null false acceptance rates with very low false rejection rates

a new framework for reconstruction of images from boundaries the problem of reconstructing images from boundaries has been studied in the literature chiefly as one based on the information from zero crossings in contrast we formulate the problem within the framework of approximation theory and we propose a representation scheme involving i the points arbitrarily near the boundaries and ii the gradient information at these points we show that the representation scheme is complete and stable under reasonable conditions further we develop an efficient reconstruction mechanism using the concept of a regularized solution in which we penalize a candidate solution in proportion to its departure from a model which resembles the original in shape but is simple to construct finally we demonstrate the effectiveness of the cost functional with the help of experimental results using a representation in which the number of data points is much less than the number of pixels in the original image

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

support vector shape a classifier based shape representation we introduce a novel implicit representation for 2d and 3d shapes based on support vector machine svm theory each shape is represented by an analytic decision function obtained by training svm with a radial basis function rbf kernel so that the interior shape points are given higher values this empowers support vector shape svs with multifold advantages first the representation uses a sparse subset of feature points determined by the support vectors which significantly improves the discriminative power against noise fragmentation and other artifacts that often come with the data second the use of the rbf kernel provides scale rotation and translation invariant features and allows any shape to be represented accurately regardless of its complexity finally the decision function can be used to select reliable feature points these features are described using gradients computed from highly consistent decision functions instead from conventional edges our experiments demonstrate promising results

object based image similarity computation using inductive learning of contour segment relations describes an efficient and effective image similarity calculation method for object based image comparison at the level of object classes it uses probabilistic prediction voting based on the predicted class distribution of each segment of the contour of an object in an image to determine the class of the object the c4 5 inductive learning algorithm is used to predict the class distribution of object contour segments this method is invariant to rotation scaling and translation of objects experimental results show that the method is effective and efficient it can be used for object based image retrieval

a new framework for complex wavelet transforms although the discrete wavelet transform dwt is a powerful tool for signal and image processing it has three serious disadvantages shift sensitivity poor directionality and lack of phase information to overcome these disadvantages we introduce two stage mapping based complex wavelet transforms that consist of a mapping onto a complex function space followed by a dwt of the complex mapping unlike other popular transforms that also mitigate dwt shortcomings the decoupled implementation of our transforms has two important advantages first the controllable redundancy of the mapping stage offers a balance between degree of shift sensitivity and transform redundancy this allows us to create a directional non redundant complex wavelet transform with potential benefits for image coding systems to the best of our knowledge no other complex wavelet transform is simultaneously directional and non redundant the second advantage of our approach is the flexibility to use any dwt in the transform implementation as an example we can exploit this flexibility to create the complex double density dwt cddwt a shift insensitive directional complex wavelet transform with a low redundancy of 3 sup m 1 2 sup m 1 in m dimensions to the best of our knowledge no other transform achieves all these properties at a lower redundancy

note on two generalizations of the randic index for a given graph g the well known randic index of g introduced by milan randic in 1975 is defined as r g u v e g d u d v 1 2 where the sum is taken over all edges uv and du denotes the degrees of u bollobas and erdos generalized this index by replacing 1 2 with any real number which is called the general randic index dvo ak et al introduced a modified version of randic index r g u v e g max d u d v 1 based on this recently knor et al introduced two generalizations r g u v e g min d u d v and r g u v e g max d u d v for any real number clearly the former is a lower bound for the general randic index and the latter is its upper bound knor et al studied extremal values of r g and r g and concluded some open problems in this paper we consider the open problems and give some comments and results some results for chemical trees are obtained

reconstruction of finite signal derivatives from multiscale extrema representations application to transient estimation and signal approximation in this correspondence we propose a novel approach to the reconstruction of finite signal derivatives from the extrema of a multiscale representation first introduced by berkner we show that this reconstruction procedure naturally leads to the definition of a signal characteristic scale we also focus on signal approximation from the multiscale extrema representation of one of its derivatives numerical applications involve the use of the signal characteristic scale for transient estimation and also the study of the new signal approximation method we propose

properties of the multiscale maxima and zero crossings representations the analysis of a discrete multiscale edge representation is considered a general signal description called an inherently bounded adaptive quasi linear representation aqlr motivated by two important examples namely the wavelet maxima representation and the wavelet zero crossings representation is introduced this paper mainly addresses the questions of uniqueness and stability it is shown that the dyadic wavelet maxima zero crossings representation is in general nonunique nevertheless using the idea of the inherently bounded aqlr two stability results are proven for a general perturbation a global bibo stability is shown for a special case where perturbations are limited to the continuous part of the representation a lipschitz condition is satisfied

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