invariant character recognition with zernike and orthogonal fourier mellin moments abstract in this paper we consider the use of orthogonal moments for invariant classification of alphanumeric characters of different size in addition to the zernike and pseudo zernike moments zms and pzms which have been previously proposed for invariant character recognition a new method of combining orthogonal fourier mellin moments ofmms with centroid bounding circle scaling is introduced which is shown to be useful in characterizing images with large variability through extensive experimentation using zms and ofmms as features different scaling methodologies and classifiers it is shown that ofmms give the best overall performance in terms of both image reconstruction and classification accuracy

efficient parallel algorithms for the computation of two dimensional image moments abstract moments constitute an important set of parameters for image analysis the low order moments contain significant information about a simple object they have been used in finding the location and orientation of an object moment invariants have been used as features for pattern recognition to compute moments of a two dimensional image a large number of multiplications and additions are required in a direct approach multiplications which are the most time consuming operations in simple processors can be completely avoided in the proposed algorithms for low order moments in this paper parallel algorithms are proposed for efficient implementation in processor arrays the basic idea is to decompose a 2 d moment into many vertical moments and a horizontal moment and to use the data parallelism for the vertical moments and the task parallelism for the horizontal moment

the hough transform versus the upwrite this paper compares the hough transform and the upwrite for the detection of lines circles and ellipses both ideal and noisy images are tested the upwrite is found to be more robust for images containing perturbation noise for ideal images and images with speckle noise the results are found to depend on the complexity of the object being detected with more complex objects favoring the upwrite

a moment based unified approach to image feature detection in this paper a novel model based approach is proposed for generating a set of image feature maps or primal sketches for each type of feature a piecewise smooth parametric model is developed to characterize the local intensity function in an image projections of the intensity profile onto a set of orthogonal zernike moment generating polynomials are used to estimate model parameters and in turn generate the desired feature map a small set of moment based detectors is identified that can extract various kinds of primal sketches from intensity as well as range images one main advantage of using parametric model based techniques is that it is possible to extract complete information i e model parameters about the underlying image feature which is desirable in many high level vision tasks experimental results are included to demonstrate the effectiveness of proposed feature detectors

image quality assessment by discrete orthogonal moments this paper proposes a novel full reference quality assessment qa metric that automatically assesses the quality of an image in the discrete orthogonal moments domain this metric is constructed by representing the spatial information of an image using low order moments the computation up to fourth order moments is performed on each individual 8x8 non overlapping block for both the test and reference images then the computed moments of both the test and reference images are combined in order to determine the moment correlation index of each block in each order the number of moment correlation indices used in this study is nine next the mean of each moment correlation index is computed and thereafter the single quality interpretation of the test image with respect to its reference is determined by taking the mean value of the computed means of all the moment correlation indices the proposed objective metrics based on two discrete orthogonal moments tchebichef and krawtchouk moments are developed and their performances are evaluated by comparing them with subjective ratings on several publicly available databases the proposed discrete orthogonal moments based metric performs competitively well with the state of the art models in terms of quality prediction while outperforms them in terms of computational speed

the revised fundamental theorem of moment invariants a revised fundamental theorem of moment invariants for pattern recognition which corrects the fundamental theorem proposed by m k hu 1962 is presented the correction affects neither similitude scale nor rotation invariants derived using the original theorem but it does affect features invariant to general linear transformations four of the latter invariants were presented originally by hu these are revised to take the correction to the fundamental theorem into account furthermore these four invariants are combined to yield three new invariants which are additionally invariant to changes in the illumination of an image

fuzzy artmap classification of invariant features derived using angle of rotation from a neural network conventional regular moment functions have been proposed as pattern sensitive features in image classification and recognition applications but conventional regular moments are only invariant to translation rotation and equal scaling it is shown that the conventional regular moment invariants remain no longer invariant when the image is scaled unequally in the x and y axis directions we address this problem by presenting a technique to make the regular moment functions invariant to unequal scaling however the technique produces a set of features that are only invariant to translation unequal equal scaling and reflection they are not invariant to rotation to make them invariant to rotation moments are calculated with respect to the principal axis of the image to perform this the exact angle of rotation must be known but the method of using the second order moments to determine this angle will also be inclusive of an undesired tilt angle therefore in order to correctly determine the amount of rotation the tilt angle which differs for different scaling factors in the x and y axis directions for the particular image must be obtained in order to solve this problem a neural network using the back propagation learning algorithm is trained to estimate the tilt angle of the image and from this the amount of rotation for the image can be determined next the new moments are derived and a fuzzy artmap network is used to classify these images into their respective classes sets of experiments involving images rotated and scaled unequally in the x and y axis directions are carried out to demonstrate the validity of the proposed technique

cross weighted moments and affine invariants for image registration and matching a framework for deriving a class of new global affine invariants for both object matching and positioning based on a novel concept of cross weighted moments with fractional weights is presented the fractional weight factor allows for a more flexible range to balance between the capability to discriminate between objects that differ only in small shape details and the sensitivity of small shape details to the presence of the noise moreover it makes it possible to arrive at low order zero order affine invariants that are more robust than those derived from higher order regular moments the affine transformation parameters are recovered from the zero and the first order cross weighted moments without requiring any feature point correspondence information the equations used to find the affine transformation parameters are linear algebraic the sensitivity of the cross weighted moment invariants to noise missing data and perspective effects is shown on real images

moment based image normalization with high noise tolerance in this paper the effects of noise with nonzero mean on existing moment based image normalization methods are studied several modifications to reduce noise sensitivity are presented and tested they involve nonlinear mapping and fractional and negative order moments

classification of invariant image representations using a neural network a neural network nn based approach for classification of images represented by translation scale and rotation invariant features is presented the utilized network is a multilayer perceptron mlp classifier with one hidden layer back propagation learning is used for its training two types of features are used moment invariants derived from geometrical moments of the image and features based on zernlike moments which are the mapping of the image onto a set of complex orthogonal polynomials the performance of the mlp is compared to the bayes nearest neighbor and minimum mean distance statistical classifiers through extensive experimentation with noiseless as well as noisy binary images of all english characters 26 classes the following conclusions are reached 1 the mlp outperforms the other three classifiers especially when noise is present 2 the nearest neighbor classifier performs about the same as the nn for the noiseless case 3 the nn can do well even with a very small number of training samples 4 the nn has a good degree of fault tolerance and 5 the zernlike moment based features possess strong class separability power and are more powerful than moment invariants

polynomial time recognition of minimal unsatisfiable formulas with fixed clause variable difference a formula in conjunctive normal form is said to be minimal unsatisfiable if it is unsatisfiable and deleting any clause makes it satisfiable the deficiency of a formula is the difference of the number of clauses and the number of variables it is known that every minimal unsatisfiable formula has positive deficiency until recently polynomial time algorithms were known to recognize minimal unsatisfiable formulas with deficiency 1 and 2 we state an algorithm which recognizes minimal unsatisfiable formulas with any fixed deficiency in polynomial time

the stability of special symmetric solutions of x t αf x t 1 with small amplitudes we consider the differential delay equation f x t f x t 1 with odd f c 3 r f 0 0 f 0 0 f 0 0 f 0 0 a theorem of kaplan and yorke 4 implies that 2f 0 is a bifurcation point where a certain class of periodic solutions bifurcates from the trivial zero solutions

center manifolds for periodic functional differential equations of mixed type abstract we study the behaviour of solutions to nonlinear functional differential equations of mixed type mfdes that remain sufficiently close to a prescribed periodic solution under a discreteness condition on the floquet spectrum we show that all such solutions can be captured on a finite dimensional invariant center manifold that inherits the smoothness of the nonlinearity this generalizes the results that were obtained previously in h j hupkes s m verduyn lunel center manifold theory for functional differential equations of mixed type j dynam differential equations 19 2007 497 560 for bifurcations around equilibrium solutions to mfdes

two dimensional object recognition using a two dimensional polar transform abstract a two dimensional 2d transform is proposed for the classification of planar objects with a centroid referenced polar representation it samples the multiple intersections of n radii with the object using the mass center translation invariance is achieved and with an appropriate amplitude normalization the transform is also made invariant to scaling the modules of its 2d fast fourier transform coefficients which are rotation invariant are used as the feature vector simultaneously translation scaling and rotation parameters are estimated the high performance of this algorithm is shown with computer simulations and its advantages and disadvantages are analysed in comparison with existing methods

a general approach to moment calculation for polygons and line segments abstract the calculation of moments from the boundary of a solid digital area is a quite useful technique used in pattern recognition a straightforward way of doing the calculation that does not have any numerical instabilities is presented all the symmetries available in moment calculations are preserved and it is shown how different moment formulas are related to each other this includes relations between different moments and the relationships among different methods for calculating moments finally a direct relation between the moment expansion of a polygonal area and a stick figure made from one dimensional lines embedded in a two dimensional plane is derived

on the reconstruction aspects of moment descriptors the problem of reconstruction of an image from discrete and noisy data by the method of moments is examined the set of orthogonal moments based on legendre polynomials is employed a general class of signal dependent noise models is taken into account an asymptotic expansion for the global reconstruction error is established this reveals mutual relationships between a number of moments the image smoothness sampling rate and noise model characteristics the problem of an automatic data driven section of an optimal number of moments is studied this is accomplished with the help of cross validation techniques

normalization and shape recognition of three dimensional objects by 3d moments abstract in this paper we are primarily concerned with the recognition of three dimensional 3d objects on the basis of the geometry of their physical surface the 3d moments are defined on the object s surface with two main aims 1 to derive a normalized version irrespective of position size and orientation for each imaged object and 2 to establish global descriptors extracted from normalized shapes in order to make up a representative feature vector to be used in recognition tasks the source data are multiple orthographic views of 3d objects with known viewpoint specifications a volume intersection procedure is used in the recovery of 3d object surface from two dimensional 2d data the problem of normalization to achieve recognition of 3d objects is dealt with and a heuristic solution is proposed to lessen the inherent ambiguity of the principal axes method for object orientation experimental results are described with ten object categories showing excellent percentage classification success rates by using only a small number of normalized moments as elements of the feature vector

recognition by symmetry derivatives and the generalized structure tensor we suggest a set of complex differential operators that can be used to produce and filter dense orientation tensor fields for feature extraction matching and pattern recognition we present results on the invariance properties of these operators that we call symmetry derivatives these show that in contrast to ordinary derivatives all orders of symmetry derivatives of gaussians yield a remarkable invariance they are obtained by replacing the original differential polynomial with the same polynomial but using ordinary coordinates x and y corresponding to partial derivatives moreover the symmetry derivatives of gaussians are closed under the convolution operator and they are invariant to the fourier transform the equivalent of the structure tensor representing and extracting orientations of curve patterns had previously been shown to hold in harmonic coordinates in a nearly identical manner as a result positions orientations and certainties of intricate patterns e g spirals crosses parabolic shapes can be modeled by use of symmetry derivatives of gaussians with greater analytical precision as well as computational efficiency since gaussians and their derivatives are utilized extensively in image processing the revealed properties have practical consequences for local orientation based feature extraction the usefulness of these results is demonstrated by two applications 1 tracking cross markers in long image sequences from vehicle crash tests and 2 alignment of noisy fingerprints

symmetric phase only matched filtering of fourier mellin transforms for image registration and recognition presents a new method to match a 2d image to a translated rotated and scaled reference image the approach consists of two steps the calculation of a fourier mellin invariant fmi descriptor for each image to be matched and the matching of the fmi descriptors the fmi descriptor is translation invariant and represents rotation and scaling as translations in parameter space the matching of the fmi descriptors is achieved using symmetric phase only matched filtering spomf the performance of the fmi spomf algorithm is the same or similar to that of phase only matched filtering when dealing with image translations the significant advantage of the new technique is its capability to match rotated and scaled images accurately and efficiently the innovation is the application of spomf to the fmi descriptors which guarantees high discriminating power and excellent robustness in the presence of noise this paper describes the principle of the new method and its discrete implementation for either image detection problems or image registration problems practical results are presented for various applications in medical imaging remote sensing fingerprint recognition and multiobject identification

orthogonal moment operators for subpixel edge detection abstract a new approach to detect step edges with subpixel accuracy is presented the proposed approach is based on a set of orthogonal complex moments of the image known as zernike moments an ideal two dimensional 2d step edge is modeled in terms of four parameters the background gray level the step size the distance of the edge from the center of the mask and the orientation of the edge discrete zernike moments are used to obtain a total of three complex masks to compute all the edge parameters for subpixel detection for pixel level edge detection only two masks one real and one complex are required the theoretical analysis of the influence of noise on the location and the orientation of an edge is presented this analysis reveals that the accuracy of the proposed approach is virtually unaffected by the additive noise the technique is effective in detecting both the pixel level and subpixel level edges experimental results are presented to demonstrate the efficacy of the proposed technique

binary object representation and recognition using the hilbert morphological skeleton transform abstract a binary shape representation called the hilbert morphological skeleton transform hmst is introduced this representation combines the morphological skeleton transform mst with the clustering capabilities of the hilbert transform the hmst preserves the skeleton properties including information preservation progressive visualization and compact representation then an object recognition algorithm the hilbert skeleton matching algorithm hsma is introduced this algorithm performs a single sweep over the hmst s and renders the similarity between them as a distance measure testing the hsma against the skeleton matching algorithm sma and invariant moments revealed that the hsma algorithm achieves slightly better object recognition rates while substantially reducing the complexity in an experiment of 14 400 shape matches the hsma achieved a 90 36 recognition rate as opposed to 89 76 for the sma and 89 49 for invariant moments on the other hand the hsma improved the sma processing more than 40

simple and fast computation of moments abstract in this paper we address the problem of efficient computation of moments from the boundary of a digital area boundary based computation is superior to usual region based approaches as the data dimension of boundary representations is substantially smaller than that of region representations we investigate the inter order relationship of moments one of our results is that moments of higher order can be computed from moments of lower order based on this relationship a simple iterative algorithm is proposed for the computation of moments from a polygonal approximation of the boundary in comparison with a direct computation method our algorithm is simpler to program the memory requirement is minimum simulation results show that a speed up of factor 8 can be achieved using our algorithm a special version of the algorithm can be utilized to compute moments from the run length chain code of the boundary our algorithm can be applied to compute the most popular geometric moments as well as other types of moments like legendre zernike rotational and complex moments

fast computation of geometric moments using a symmetric kernel this paper presents a novel set of geometric moments with symmetric kernel sgm obtained using an appropriate transformation of image coordinates by using this image transformation the computational complexity of geometric moments gm is reduced significantly through the embedded symmetry and separability properties in addition it minimizes the numerical instability problem that occurs in high order gm computation the novelty of the method proposed in this paper lies in the transformation of gm kernel from interval 0 to interval 1 1 the transformed gm monomials are symmetry at the origin of principal cartesian coordinate axes and hence possess symmetrical property the computational complexity of sgm is reduced significantly from order o n 4 using the original form of computation to order o n 3 for the proposed symmetry separable approach experimental results show that the percentage of reduction in computation time of the proposed sgm over the original gm is very significant at about 75 0 and 50 0 for square and non square images respectively furthermore the invariant properties of translation scaling and rotation in hu s moment invariants are maintained the advantages of applying sgm over gm in zernike moments computation in terms of efficient representation and computation have been shown through experimental results

recognitive aspects of moment invariants moment invariants are evaluated as a feature space for pattern recognition in terms of discrimination power and noise tolerance the notion of complex moments is introduced as a simple and straightforward way to derive moment invariants through this relation properties of complex moments are used to characterize moment invariants aspects of information loss suppression and redundancy encountered in moment invariants are investigated and significant results are derived the behavior of moment invariants in the presence of additive noise is also described

pattern recognition with moment invariants a comparative study and new results abstract moment invariants have been proposed as pattern sensitive features in classification and recognition applications in this paper the authors present a comprehensive study of the effectiveness of different moment invariants in pattern recognition applications by considering two sets of data handwritten numerals and aircrafts the authors also present a detailed study of zernike and pseudo zernike moment invariants including a new procedure for deriving the moment invariants in addition the authors introduce a new normalization scheme that reduces the large dynamic range of these invariants as well as implicit redundancies in these invariants based on a comprehensive study with both handwritten numerals and aircraft data the authors show that the new method of deriving zernike moment invariants along with the new normalization scheme yield the best overall performance even when the data are degraded by additive noise

numerical stability of fast computation algorithms of zernike moments abstract a detailed comparative study of the numerical stability of the recursive algorithms widely used to calculate the zernike moments of an image is presented in this paper while many papers introducing fast algorithms for the computation of zernike moments have been presented in the literature there is not any work studying the numerical behaviour of these methods these algorithms have been in the past compared to each other only according to their computational complexity without been given the appropriate attention as far as their numerical stability is concerned being the most significant part of the algorithms reliability the present contribution attempts to fill this gap in the literature since it mainly demonstrates that the usefulness of a recursive algorithm is defined not only by its low computational complexity but most of all by its numerical robustness this paper exhaustively compares some well known recursive algorithms for the computation of zernike moments and sets the appropriate conditions in which each algorithm may fall in an unstable state the experiments show that any of these algorithms can be unstable under some conditions and thus the need to develop more stable algorithms is of major importance

a potential based approach for shape matching and recognition this paper presents a novel potential based approach for recognizing the shape of a two dimensional 2d region by identifying the best match from a selected group of shape templates the proposed model assumes that the border of every 2d region is uniformly charged an initially small shape template placed inside a shape sample will experience the repulsive force and torque arising from the potential field a better match in the shape between the template and the sample can be obtained if the template translates and reorients itself to reduce the potential while growing in size the shape template with the largest final size corresponds to the best match and represents the shape of the given sample the potential and the associated repulsive force and torque between the polygonal contours are analytically tractable hence resulting in high computational efficiency of the matching process the proposed approach is intrinsically invariant under translation rotation and size changes of the shape sample moreover not only can the matching be carried out directly for shape contours at different viewscales but the contours can also be unconnected provided that the template is confined within the shape sample throughout the matching process

extraction of shift invariant wavelet features for classification of images with different sizes an effective shift invariant wavelet feature extraction method for classification of images with different sizes is proposed the feature extraction process involves a normalization followed by an adaptive shift invariant wavelet packet transform an energy signature is computed for each subband of these invariant wavelet coefficients a reduced subset of energy signatures is selected as the feature vector for classification of images with different sizes experimental results show that the proposed method can achieve high classification accuracy of 98 5 percent and outperforms the other two image classification methods

accurate calculation of zernike moments zernike moments zms are very effective global image descriptors which are used in many digital image processing applications the digitization process compromises the accuracy of the moments and therefore several of its properties are affected there are two major discretization errors namely the geometric error and numerical integration error in this paper we propose two new algorithms which eliminate these errors the first algorithm performs the exact computation of geometric moments gms over a unit disk and then uses gms to zms relationship to compute the latter this algorithm is computationally more expensive and it becomes numerically instable for higher order moments therefore we develop a second algorithm based on gaussian quadrature numerical integration the second algorithm reduces both the errors simultaneously and its accuracy increases as the degree of gaussian quadrature numerical integration increases the proposed algorithms are observed to provide very accurate zms which result in improved image reconstruction reduction in reconstruction error and improvement in rotation and scale invariance exhaustive experiments are provided to support improved accuracy of zms and time complexity analysis is performed for the existing and the proposed methods

combined invariants to similarity transformation and to blur using orthogonal zernike moments the derivation of moment invariants has been extensively investigated in the past decades in this paper we construct a set of invariants derived from zernike moments which is simultaneously invariant to similarity transformation and to convolution with circularly symmetric point spread function psf two main contributions are provided the theoretical framework for deriving the zernike moments of a blurred image and the way to construct the combined geometric blur invariants the performance of the proposed descriptors is evaluated with various psfs and similarity transformations the comparison of the proposed method with the existing ones is also provided in terms of pattern recognition accuracy template matching and robustness to noise experimental results show that the proposed descriptors perform on the overall better

homoclinic solution and chaos in xf x 0 is followed by a move in the opposite direction i t 0 however there are equations 1 2 which are closely related to applications and where the negative feedback condition 3 is only true in a certain neighbourhood of x 0 furumochi 3 studied equation

fast and accurate method for high order zernike moments computation abstract zernike moments zms which belong to a class of circularly orthogonal rotation invariant moments are very useful image descriptors for various image processing applications they however suffer from various errors such as discretization error geometric error and numerical integration error in this paper we present an approach for their computation which reduces geometric error and numerical integration error geometric error is reduced by performing exact mapping of a square grid domain into a circular grid by using both the square and arc grids numerical integration error is reduced by resorting to gaussian numerical integration over the square and arc grids it is observed that the contribution of numerical integration error to the total error is much more than the geometric error the effect of these two errors is more significant in small images as compared to large images the use of numerical integration however enhances the time complexity this problem is resolved by using recursive algorithms for the computation of radial polynomials 8 way symmetry of radial polynomials and 8 way symmetry anti symmetry of angular part of the kernel function exhaustive experiments on synthetic and real images are performed to demonstrate the effectiveness of the proposed approach

two dimensional rigid body kinematics using image contour registration a method for calculating two dimensional rigid body kinematic parameters using shape features is presented proposed applications include the noninvasive quantification of planar joint motion in vivo by using digitized images computed tomographs radiographs etc of a bone contour at two positions the contour curvatures can be best fit to obtain a one to one mapping or registration of the bone images this produces a dense field of displacement vectors from which planar rigid body kinematic parameters can be estimated accuracy was studied using radiographic images of cadaveric femoral bone the two motions of pure rotation with a fixed center of rotation and of pure translation were simulated for pure rotation error in rotation was independent of the rotation magnitude with an average n 10 error of 0 3 0 8 degrees the translation error averaged 0 9 0 5 mm for pure translation the error in rotation was 0 01 0 69 degrees and the error in translation was 0 62 0 98 mm n 10 this novel method has broad applications in the field of planar kinematics especially in cases for which marker fixation is neither possible nor practical

existence of chaos in control systems with delayed feedback here f r r denotes some nonlinear function a a positive constant t e r is the independent variable x e r the dependent variable and 1 dx dt the investigation is motivated i by the applications eq 1 1 has found in several areas of applied sciences and ii by the observation of intensely structured periodic and aperiodic oscillations in numerical simulations for a certain class of nonlinearities f we show that these structures are not numerical artefacts but properties of the solution manifold of eq 1 1 in the applications eq 1 1 has been used to explain normal and pathological behavior of control systems in the physiology of blood cell production and respiration 7 8 10 111 and periodic 2 or irregular s activity in neural networks computer simulations to eq 1 1 may be found in 3 the mathematical analysis of this equation so far has been restricted to prove the existence of slowly oscillating simple periodic solutions 1 4 61 a periodic solution is called slowly oscillating if successive

translation rotation and scale invariant pattern recognition by high order neural networks and moment classifiers the classification and recognition of two dimensional patterns independently of their position orientation and size by using high order networks are discussed a method is introduced for reducing and controlling the number of weights of a third order network used for invariant pattern recognition the method leads to economical networks that exhibit high recognition rates for translated rotated and scaled as well as locally distorted patterns the performance of these networks at recognizing types and handwritten numerals independently of their position size and orientation is compared with and found superior to the performance of a layered feedforward network to which image features extracted by the method of moments are presented as input

three dimensional shape analysis using moments and fourier descriptors a procedure for using moment based feature vectors to identify a three dimensional object from a two dimensional image recorded at an arbitrary viewing angle and range is presented a moment form called standard moments rather than the usual moment invariants is considered a standard six airplane experiment was used to compare different techniques fourier descriptors and moment invariants were both compared to the present scheme for normalized moments various experiments were conducted using mixtures of silhouette and boundary moments and different normalization techniques standard moments gave slightly better results than fourier descriptors for this experiment both of these techniques were much better than moment invariants

radial and angular moment invariants for image identification radial and angular moments of images are presented and methods are shown for deriving moment functions that are invariant with respect to rotation translation reflection and size changes without the aid of the theory of algebraic invariants hu s invariants are expressed in terms of these radial and angular moments and it is claimed that this facilitates visual inspection of invariance properties

reforming the theory of invariant moments for pattern recognition abstract the relationship between the algebraic invariants and the fourier mellin spectrum of an image irradiance distribution is clarified and a new approach for generating the two dimensional 2d invariant moments is proposed fifty two invariant functions of the second to the ninth order image moments are tabulated which are invariant with respect to image translation shift orientation and size changes and can be used as library functions in computer programs for automatic image identification the invariant functions derived in this study are shown useful in a numerical example concerned with a character recognition model

efficient radar target recognition using the music algorithm and invariant features an efficient technique is developed to recognize target type using one dimensional range profiles the proposed technique utilizes the multiple signal classification algorithm to generate superresolved range profiles their central moments are calculated to provide translation invariant and level invariant feature vectors next the computed central moments are mapped into values between zero and unity followed by a principal component analysis to eliminate the redundancy of feature vectors the obtained features are classified based on the bayes classifier which is one of the statistical classifiers recognition results using five different aircraft models measured at compact range are presented to assess the effectiveness of the proposed technique and they are compared with those of the conventional range profiles obtained by inverse fast fourier transform

fast computation of 2 d image moments using biaxial transform abstract in this paper a new transform is introduced this transform is based on dividing the image into four quadrants the transform can be generated by adding or subtracting the gray levels of each two axially symmetric points in the original image the addition or subtraction is dependent on the quadrant position the newly transformed quadrants can then be used to compute the moments only one quadrant of transformed image is needed to compute the moments of specific orders this can lead to considerable savings in both processing time as well as storage other advantages of this transform such as image reconstruction and using multiple filters on the same image frame to remove noise are also explored

invariant pattern recognition a review in this document we review and compare some of the classical and modern techniques for solving the problem of invariant pattern recognition such techniques include integral transforms construction of algebraic moments and the use of structured neural networks in all cases we assume that the nature of the invariance group is known a priori many of the methods described apply to specific geometrical transformation groups however some of the techniques are highly general and applicable to large classes of invariance groups we also review some results regarding the existence and structure of invariants under certain kinds of groups

complexity of partial satisfaction a conjunctive normal form expression cnf is said to be 2 satisfiable if and only if any two of its clauses are simultaneously satisfiable it is shown that every 2 satisfiable cnf has a truth assignment that satisfies at least the fraction h of its clauses where h sqrt 5 1 2 sim 0 618 the reciprocal of the golden ratio the proof is constructive in that it provides a polynomial time algorithm that will find for any 2 satisfiable cnf a truth assignment satisfying at least the fraction h of its clauses furthermore this result is optimal in that the constant h is as large as possible it is shown that for any rational h h the set of all 2 satisfiable cnfs that have truth assignments satisfying at least the fraction h of their clauses is an np complete set

fuzzy artmap a neural network architecture for incremental supervised learning of analog multidimensional maps a neural network architecture is introduced for incremental supervised learning of recognition categories and multidimensional maps in response to arbitrary sequences of analog or binary input vectors which may represent fuzzy or crisp sets of features the architecture called fuzzy artmap achieves a synthesis of fuzzy logic and adaptive resonance theory art neural networks by exploiting a close formal similarity between the computations of fuzzy subsethood and art category choice resonance and learning four classes of simulation illustrated fuzzy artmap performance in relation to benchmark backpropagation and generic algorithm systems these simulations include finding points inside versus outside a circle learning to tell two spirals apart incremental approximation of a piecewise continuous function and a letter recognition database the fuzzy artmap system is also compared with salzberg s nge systems and with simpson s fmmc system

a new bound for 3 satisfiable maxsat and its algorithmic application let f be a cnf formula with n variables and m clauses f is 3 satisfiable if for any 3 clauses in f there is a truth assignment which satisfies all of them lieberherr and specker 1982 and later yannakakis 1994 proved that in each 3 satisfiable cnf formula at least 23 of its clauses can be satisfied by a truth assignment we improve this result by showing that every 3 satisfiable cnf formula f contains a subset of variables u such that some truth assignment t will satisfy at least 23m 13m u rn clauses where m is the number of clauses of f m u is the number of clauses of f containing a variable from u n is the total number of variables in clauses not containing a variable in u and r is a positive absolute constant both u and t can be found in polynomial time we use our result to show that the following parameterized problem is fixed parameter tractable and moreover has a kernel with a linear number of variables in 3 s maxsat ae we are given a 3 satisfiable cnf formula f with m clauses and asked to determine whether there is an assignment which satisfies at least 23m k clauses where k is the parameter

smooth bifurcation of symmetric periodic solutions of functional differential equations with odd f c r in contrast to the one dimensional ordinary differential equation this equation can have periodic solutions as the example i t 7r 2 x t 1 with solutions x t z sin rc 2 t z 0 shows numerical bifurcation diagrams e g 6 143 indicate a complicated structure of the period solutions depending on the delay parameter u one finds various intersecting smooth curves one task of mathematics is to prove the existence of periodic solutions in this paper we are mainly interested in symmetric periodic solutions i e solutions x of c which fultil the symmetry property

contour sequence moments for the classification of closed planar shapes abstract a technique for classifying closed planar shapes is described in which a shape is characterized by a one dimensional sequence that represents the euclidean distance between the centroid and all contour pixels of the shape contour sequences obtained from shapes belonging to the same class are similar and are considered to be different realizations of a stochastic process statistical moment functions derived from contour sequences are used to characterize the process and hence the shapes it is shown that these moment functions are invariant to shape translation rotation and scale transformations examples are presented to illustrate the performance of these moment functions in the classification of noisy shapes

new computational methods for full and subset zernike moments the computation of zernike radial polynomials contributes most of the computation time in computing the zernike moments due to the involvement of factorial terms the common approaches used in fast computation of zernike moments are kintner s prata s coefficient and q recursive methods in this paper we propose faster methods to derive the full set of zernike moments as well as a subset of zernike moments a hybrid algorithm that uses prata s simplified kintner s and coefficient methods is used to derive the full set of zernike moments in the computation of a subset of zernike moments we propose using the combination of prata s simplified kintner s coefficient and q recursive methods fast computation is achieved by using the recurrence relations between the zernike radial polynomials of successive order without any involvement of factorial terms in the first and second experiments we show both the hybrid algorithms take lesser computation time than the existing methods in computing the full set of zernike moments and a selected subset of zernike moments which are not in successive sequence both hybrid algorithms have been applied in real world application in the classification of rice grains using full set and subset of zernike moments the classification performance using optimal subset of zernike moments is better than using full set of zernike moments

3 d moment forms their construction and application to object identification and positioning the 3 d moment method is applied to object identification and positioning a general theory of deriving 3 d moments invariants is proposed the notion of complex moments is introduced complex moments are defined as linear combinations of moments with complex coefficients and are collected into multiplets such that each multiplet transforms irreducibly under 3 d rotations the application of the 3 d moment method to motion estimation is also discussed using group theoretic techniques various invariant scalars are extracted from compounds of complex moments via clebsch gordon expansion twelve moment invariants consisting of the second order and third order moments are explicitly derived based on a perturbation formula it is shown that the second order moment invariants can be used to predict whether the estimation using noisy data is reliable or not the new derivation of vector forms also facilities the calculation of motion estimation in a tensor approach vectors consisting of the third order moments can be derived in a similar manner

fast computation of exact zernike moments using cascaded digital filters zernike moments have been extensively used and have received much research attention in a number of fields object recognition image reconstruction image segmentation edge detection and biomedical imaging however computation of these moments is time consuming thus we present a fast computation technique to calculate exact zernike moments by using cascaded digital filters the novelty of the method proposed in this paper lies in the computation of exact geometric moments directly from digital filter outputs without the need to first compute geometric moments the mathematical relationship between digital filter outputs and exact geometric moments is derived and then they are used in the formulation of exact zernike moments a comparison of the speed of performance of the proposed algorithm with other state of the art alternatives shows that the proposed algorithm betters current computation time and uses less memory

auto regressive shape classifiers in time varying noise abstract good results have been reported in a number of recent studies where auto regressive shape classifiers have been used to allocate objects to a pre determined number of classes it is shown that this approach may give unsatisfactory results when applied to imaging systems whose noise characteristics vary substantially over time such variation may be due to changes in atmospheric conditions or the relative effect of discretization errors observations are based on the reconstruction of a number of noisy synthetic templates

invariant pattern recognition by moment fourier descriptor abstract this paper proposes a new shape descriptor called moment fourier descriptor which can describe a complex object composed by a set of closed regions this descriptor is shown to be independent of object s translation rotation and scaling the essential advantage of moment fourier descriptor is that it can be used to recognize more complex patterns than the traditional fourier descriptors simulations are given to show the high performance of the proposed approach

applications of tensor theory to object recognition and orientation determination a method is developed by which images resulting from orthogonal projection of rigid planar patch objects arbitrarily oriented in three dimensional 3 d space may be used to form systems of linear equations which are solved for the affine transform relating the images the technique is applicable to complete images and to unlabeled feature sets derived from images and with small modification may be used to transform images of unknown objects such that they represent images of those objects from a known orientation for use in object identification no knowledge of point correspondence between images is required theoretical development of the method and experimental results are presented the method is shown to be computationally efficient requiring o n multiplications and additions where depending on the computation algorithm n may equal the number of object or edge picture elements

invariant image classification using triple correlation based neural networks triple correlation based neural networks are introduced and used in this paper for invariant classification of 2d gray scale images third order correlations of an image are appropriately clustered in spatial or spectral domain to generate an equivalent image representation that is invariant with respect to translation rotation and dilation an efficient implementation scheme is also proposed which is robust to distortions insensitive to additive noise and classifies the original image using adequate neural network architectures applied directly to 2d image representations third order neural networks are shown to be a specific category of triple correlation based networks applied either to binary or gray scale images a simulation study is given which illustrates the theoretical developments using synthetic and real image data

fast and numerically stable methods for the computation of zernike moments zernike moments zms are used in many image processing applications due to their superior performance over other moments however they suffer from high computation cost and numerical instability at high order of moments in the past many recursive methods have been developed to improve their speed performance and considerable success has been achieved the analysis of numerical stability has also gained momentum as it affects the accuracy of moments and their invariance property there are three recursive methods which are normally used in zms calculation prata s kintner s and q recursive methods the earlier studies have found the q recursive method outperforming the two other methods in this paper we modify prata s method and present a recursive relation which is proved to be faster than the q recursive method numerical instability is observed at high orders of moments with the q recursive method suffering from the underflow problem while the modified prata s method suffering from finite precision error the modified kintner s method is the least susceptible to these errors keeping in view the better numerical stability we further make the modified kintner s method marginally faster than the q recursive method we recommend the modified prata s method for low orders 90 and kintner s fast method for high orders 90 of zms

using zernike moments for the illumination and geometry invariant classification of multispectral texture we develop a method for recognizing color texture independent of rotation scale and illumination color texture is modeled using spatial correlation functions defined within and between sensor bands using a linear model for surface spectral reflectance with the same number of parameters as the number of sensor classes we show that illumination and geometry changes in the scene correspond to a linear transformation of the correlation functions and a linear transformation of their coordinates a several step algorithm that includes scale estimation and correlation moment computation is used to achieve the invariance the key to the method is the new result that illumination rotation and scale changes in the scene correspond to a specific transformation of correlation function zernike moment matrices these matrices can be estimated from a color image this relationship is used to derive an efficient algorithm for recognition the algorithm is substantiated using classification results on over 200 images of color textures obtained under various illumination conditions and geometric configurations

moments and moment invariants in the radon space radon transform has been acknowledged as the promising solution for image processing due to its high noise robustness and the ability of converting the rotation scaling and translation operations on a pattern image into translations and scaling in the radon image recently several transforms widely employed in signal processing have been introduced in images radon space for pattern recognition however moments and especially moment invariants in the radon space have not been thoroughly investigated in this paper we introduce a mathematical framework of constructing moments and moment invariants in the radon space first rotational moments which represent non orthogonal moments and legendre fourier moments which represent orthogonal moments are introduced in the radon space respectively on this basis we propose a method to obtain rotation scaling and translation as well as affine invariance of these moments in the radon space second we prove that the proposed moments in the radon space can be represented by a linear combination of classical geometric moments with this property the implementation time of the moments in the radon space can be significantly reduced and the recognition accuracy can also be greatly improved since no numerical approximation is involved theoretical and experimental analysis on invariant recognition accuracy noise robustness image blur distortion and computational time also shows the superiority of the proposed methods highlightsa framework of constructing moments and moment invariants in the radon space is introduced a method to obtain rst and affine invariance of moments in the radon space is proposed the implementation time of the proposed moments can be significantly reduced the recognition accuracy of the proposed moments can also be increased

on image analysis by the methods of moments various types of moments have been used to recognize image patterns in a number of applications a number of moments are evaluated and some fundamental questions are addressed such as image representation ability noise sensitivity and information redundancy moments considered include regular moments legendre moments zernike moments pseudo zernike moments rotational moments and complex moments properties of these moments are examined in detail and the interrelationships among them are discussed both theoretical and experimental results are presented

implications of forbidden structures for extremal algorithmic problems abstract we develop and analyze p optimal approximation algorithms for various generalized satisfiability problems and determine the corresponding p optimal thresholds the most novel aspect of the paper is that we develop new p optimal algorithms for restricted generalized satisfiability problems which are defined by forbidden subformulas all our algorithms run in linear time on a ram

characteristic multipliers and stability of symmetric periodic solutions of x t g x t 1 on etudie l equation differentielle scalaire a retard x t g x t 1 a retroaction negative on suppose que la fonction non lineaire g est impaire et monotone on demontre que des solutions periodiques x t de type legerement oscillant satisfaisant la condition de symetrie x t x t 2 t r sont non degenerees et ont toutes des multiplicateurs de floquet non triviaux dans le cercle unite

n folded symmetries by complex moments in gabor space and their application to unsupervised texture segmentation complex moments of the gabor power spectrum yield estimates of the n folded symmetry of the local image content at different frequency scales that is they allow to detect linear rectangular hexagonal triangular and so on structures with very fine to very coarse resolutions results from experiments on the unsupervised segmentation of real textures indicate their importance for image processing applications real geometric moments computed in gabor space also provide for very powerful texture features but lack the clear geometrical interpretation of complex moments

a new class of zernike moments for computer vision applications a modified direct method for the computation of the zernike moments is presented in this paper the presence of many factorial terms in the direct method for computing the zernike moments makes their computation process a very time consuming task although the computational power of the modern computers is impressively increasing the calculation of the factorial of a big number is still an inaccurate numerical procedure the main concept of the present paper is that by using stirling s approximation formula for the factorial and by applying some suitable mathematical properties a novel factorial free direct method can be developed the resulted moments are not equal to those computed by the original direct method but they are a sufficiently accurate approximation of them besides their variability does not affect their ability to describe uniquely and distinguish the objects they represent this is verified by pattern recognition simulation examples

binary shape recognition using the morphological skeleton transform abstract binary image representation by its morphological skeleton transform has been proposed in the past as an information preserving representation in this paper this skeleton representation is adopted as the start point for the development of a binary shape recognition scheme a skeleton matching algorithm is presented that efficiently characterizes the similarity between two skeletons as a distance measure this skeleton matching algorithm resembles the well known from speech processing elastic matching technique

detection of composite edges the paper presents a new parametric model based approach to high precision composite edge detection using orthogonal zernike moment based operators it deals with two types of composite edges a generalized step and b pulse staircase edges a 2 d generalized step edge is modeled in terms of five parameters two gradients on two sides of the edge the distance from the center of the candidate pixel the orientation of the edge and the step size at the location of the edge a 2 d pulse staircase edge is modeled in terms of two steps located at two positions within the mask and the edge orientation a pulse edge is formed if the steps are of opposite polarities whereas a staircase edge results from two steps having the same polarity two complex and two real zernike moment based masks are designed to determine parameters of both the 2 d edge models for a given edge model estimated parameter values at a point are used to detect the presence or absence of that type of edge extensive noise analysis is performed to demonstrate the robustness of the proposed operators experimental results with intensity and range images are included to demonstrate the efficacy of the proposed edge detection technique as well as to compare its performance with the geometric moment based step edge detection technique and canny s 1986 edge detector

orthogonal moment features for use with parametric and non parametric classifiers this research examines a variety of approaches for using two dimensional orthogonal polynomials for the recognition of handwritten arabic numerals it also makes use of parametric and non parametric statistical and neural network classifiers polynomials including legendre zernike and pseudo zernike are used to generate moment based features which are invariant to location size and optionally rotation an efficient method for computing the moments via geometric moments is presented a side effect of this method also yields scale invariance a new approach to location invariance using a minimum bounding circle is presented and a detailed analysis of the rotational properties of the moments is given data partitioning tests are performed to evaluate the various feature types and classifiers for rotational invariant character recognition the highest percentage of correctly classified characters was 91 7 and for non rotational invariant recognition it was 97 6 this compares with a previous effort using the same data and test conditions of 94 8 the techniques developed here should also be applicable to other areas of shape recognition

parameterized complexity of maxsat above average in maxsat we are given a cnf formula f with n variables and m clauses the task is to find a truth assignment satisfying the maximum number of clauses let r 1 r m be the number of literals in the clauses of f then asat f email protected i 1 m 1 2 r i is the expected number of clauses satisfied by a random truth assignment when the truth values to the variables are distributed uniformly and independently it is well known that in polynomial time one can find a truth assignment satisfying at least asat f clauses in the parameterized problem maxsat aa we are to decide whether there is a truth assignment satisfying at least asat f k clauses where k is the nonnegative parameter we prove that maxsat aa is para np complete and thus maxsat aa is not fixed parameter tractable unless p np this is in sharp contrast to the similar problem maxlin 2 aa which was recently proved to be fixed parameter tractable by crowston et al fsttcs 2011 in fact we consider a more refined version of maxsat aa max r n sat aa where r email protected r n for each j alon et al soda 2010 proved that if r r n is a constant then max r sat aa is fixed parameter tractable we prove that max r n sat aa is para np complete for any r n email protected email protected we also prove that assuming the exponential time hypothesis max r n sat aa is not even in xp for any integral r n email protected n where f n is any real valued unbounded strictly increasing computable function this lower bound on r n cannot be decreased much further as we prove that max r n sat aa is i in xp for any r n loglogn logloglogn and ii fixed parameter tractable for any r n email protected n where f n is any real valued unbounded strictly increasing computable function the proof uses some results on maxlin 2 aa

coexistence of infinitely many large stable rapidly oscillating periodic solutions in time delayed duffing oscillators abstract we explore stability and instability of rapidly oscillating solutions x t for the hard spring delayed duffing oscillator x t a x t b x t t x 3 t 0 fix t 0 we target periodic solutions x n t of small minimal periods p n 2 t n for integer n and with correspondingly large amplitudes note how x n t are also marginally stable solutions respectively of the two standard non delayed hamiltonian duffing oscillators x a x 1 n b x x 3 0 stability changes for the delayed duffing oscillator simultaneously for all sufficiently large n n 0 we obtain local exponential stability for 1 n b 0 and exponential instability for 1 n b 0 provided that 0 1 n 1 b t 2 3 2 2 we interpret our results in terms of noninvasive delayed feedback stabilization and destabilization for large amplitude rapidly periodic solutions of the standard duffing oscillators we conclude with numerical illustrations of our results for small and moderate n which also indicate a neimark sacker torus bifurcation at the validity boundary of our theoretical results

non conventional algorithm for representing and recognizing complicated two dimensional objects abstract a non conventional method for representing and recognizing shape descriptions is described for any shape s a modified cobweb form representation which is referred to as a shell descriptor sd is established for the most significant vertex v the shell descriptor is then used as a registered description for the shape s at vertex v this method is computationally efficient as compared to most of the conventional techniques in shape recognition the new algorithm provides an effective and reliable tool for shape representation and classification especially for complicated objects such as logos

efficient computation of radial moment functions using symmetrical property the applications of radial moment functions such as orthogonal zernike and pseudo zernike moments in real world have been limited by the computational complexity of their radial polynomials the common approaches used in reducing the computational complexity include the application of recurrence relations between successive radial polynomials and coefficients in this paper a novel approach is proposed to further reduce the computation complexity of zernike and pseudo zernike polynomials based on the symmetrical property of radial polynomials by using this symmetrical property the real valued radial polynomials computation is reduced to about one eighth of the full set polynomials while the computation of the exponential angle values is reduced by half this technique can be integrated with existing fast computation methods to further improve the computation speed besides significant reduction in computation complexity it also provides vast reduction in memory storage

combining color and shape information for illumination viewpoint invariant object recognition in this paper we propose a new scheme that merges color and shape invariant information for object recognition to obtain robustness against photometric changes color invariant derivatives are computed first color invariance is an important aspect of any object recognition scheme as color changes considerably with the variation in illumination object pose and camera viewpoint these color invariant derivatives are then used to obtain similarity invariant shape descriptors shape invariance is equally important as under a change in camera viewpoint and object pose the shape of a rigid object undergoes a perspective projection on the image plane then the color and shape invariants are combined in a multidimensional color shape context which is subsequently used as an index as the indexing scheme makes use of a color shape invariant context it provides a high discriminative information cue robust against varying imaging conditions the matching function of the color shape context allows for fast recognition even in the presence of object occlusion and cluttering from the experimental results it is shown that the method recognizes rigid objects with high accuracy in 3 d complex scenes and is robust against changing illumination camera viewpoint object pose and noise