a signal processing approach to symmetry detection we present an algorithm that detects rotational and reflectional symmetries of two dimensional objects both symmetry types are effectively detected and analyzed using the angular correlation ac which measures the correlation between images in the angular direction the ac is accurately computed using the pseudopolar fourier transform which rapidly computes the fourier transform of an image on a near polar grid we prove that the ac of symmetric images is a periodic signal whose frequency is related to the order of the symmetry this frequency is recovered via spectrum estimation which is a proven technique in signal processing with a variety of efficient solutions we also provide a novel approach for finding the center of symmetry and demonstrate the applicability of our scheme to the analysis of real images

robust detection of skewed symmetries by combining local and semi local affine invariants abstract affine invariant feature vector ip and shen image vision comput 16 2 1998 135 146 that captures both local and semi local geometric features around each point of the object boundary is applied here for the detection of skewed symmetries based on the affine invariant shape representation the problem of detecting symmetry axes has been formulated as a problem of detecting lines with known orientations in a local similarity matrix of an object since the feature vector extracts sufficient local and semi local shape information for every point along the object boundary the process of checking symmetric point pairs is thus robust against both noises and deformations moreover our technique is able to detect all the local reflectional symmetries contained in the object various experimental results have shown the robustness and effectiveness of our method in detecting skewed symmetries from both self symmetric objects and generalized objects

projection based polygonality measurement measuring the degree to which a shape resembles a polygon referred to as polygonality is a difficult problem due to the intrinsic diversity in the form and distortion of shapes caused by digitization and similarity transformation this paper proposes a generic approach for this problem by performing the measurement in the projection space where the radon image of some primitive shapes which compose the shape becomes apparent the obtained measures take value in 0 1 with 1 corresponding to analytical polygons they are robust to additive noise and boundary distortion and is invariant to similarity transformation the new framework generalizes existing polygonal measures such as triangularity and quadrangularity in addition the ability to estimate polygon s geometric quantities in the projection space allows approximating a shape by analytical polygons the efficiency of the proposed approach is demonstrated through a number of experiments on both synthetic and real data sets

a new dea ranking system based on changing the reference set this research proposes a new ranking system for extreme efficient dmus decision making units based upon the omission of these efficient dmus from reference set of the inefficient dmus we state and prove some facts related to our model a numerical example where the proposed method is compared with traditional ranking approaches is shown

dynamics in a periodic competitive model with stage structure in this paper we consider a time delayed periodic system which describes the competition among mature populations by appealing to theories of monotone dynamical systems periodic semiflows and uniform persistence we analyze the evolutionary behavior of the system and establish sufficient conditions for competitive coexistence and exclusion

the existence of nonoscillatory solutions to a generalized nonautonomous delay logistic equation sufficient conditions for the existence of nonoscillatory solutions to the delay logistic equation x t r t x t 1 x g t k are obtained where 1

frequency domain classification of cyclic and dihedral symmetries of finite 2 d patterns this paper presents a very simple and effective algorithm for classifying cyclic and dihedral symmetries from images of finite two dimensional patterns it consists in an extension of a frequency domain algorithm proposed by the author for estimating two dimensional rotation of rigid objects within this framework the estimation of rotation is conveniently turned into the problem of detecting two orthogonal lines within the locus of the zero crossings of a certain function represented in orthogonal cartesian coordinates the main contribution of this paper is the use and interpretation of the ambiguities that arise in such a locus in the form of additional pairs of orthogonal lines when applied to symmetric patterns and the development of other algorithmic steps which allow a simple and fast discrimination between cyclic and dihedral symmetries unlike any other available method this algorithm does not require any conversion from cartesian to polar image representations besides classification reliability and consistency observed through several dozen testing experiments the nice features of this new method also include robustness to noise and ease of implementation with fast fourier transform algorithms which makes it amenable to almost real time pattern classifications applications several examples representative of the performance of the algorithm through extensive testing are reported and discussed in the paper

stability of a competition model with two stage structure a population model with stage structure which describes the competition of two species for space is considered the model is established under the assumptions that reproductive rates of two species are affected by competition and that the space occupied by one type of juveniles cannot be neglected estimates on the length of delays for which positive equilibrium of the model remains stable are given sufficient conditions are also derived that ensure global stability of positive equilibrium

optimal harvesting policy for single population with stage structure it is the purpose of this paper to analyze the exploitation of the stage structured singleautonomous population model we analyze the harvesting population equation and obtain existence local and global geometric properties of nonnegative equilibria explicit expressions are obtained for the optimal harvesting effort the maximum sustainable yield and the corresponding population level

3 d symmetry detection and analysis using the pseudo polar fourier transform symmetry detection and analysis in 3d images is a fundamental task in a gamut of scientific fields such as computer vision medical imaging and pattern recognition to name a few in this work we present a computational approach to 3d symmetry detection and analysis our analysis is conducted in the fourier domain using the pseudo polar fourier transform the pseudo polar representation enables to efficiently and accurately analyze angular volumetric properties such as rotational symmetries our algorithm is based on the analysis of the angular correspondence rate of the given volume and its rotated and rotated inverted replicas in their pseudo polar representations we also derive a novel rigorous analysis of the inherent constraints of 3d symmetries via groups theory based analysis thus our algorithm starts by detecting the rotational symmetry group of a given volume and the rigorous analysis results pave the way to detect the rest of the symmetries the complexity of the algorithm is o n 3log n where n n n is the volumetric size in each direction this complexity is independent of the number of the detected symmetries we experimentally verified our approach by applying it to synthetic as well as real 3d objects

a procedure for ranking efficient units in data envelopment analysis data envelopment analysis dea evaluates the relative efficiency of decision making units dmus but does not allow for a ranking of the efficient units themselves a modified version of dea based upon comparison of efficient dmus relative to a reference technology spanned by all other units is developed the procedure provides a framework for ranking efficient units and facilitates comparison with rankings based on parametric methods

spectral symmetry analysis we present a spectral approach for detecting and analyzing rotational and reflectional symmetries in n dimensions our main contribution is the derivation of a symmetry detection and analysis scheme for sets of points irn and its extension to image analysis by way of local features each object is represented by a set of points s irn where the symmetry is manifested by the multiple self alignments of s the alignment problem is formulated as a quadratic binary optimization problem with an efficient solution via spectral relaxation for symmetric objects this results in a multiplicity of eigenvalues whose corresponding eigenvectors allow the detection and analysis of both types of symmetry we improve the scheme s robustness by incorporating geometrical constraints into the spectral analysis our approach is experimentally verified by applying it to 2d and 3d synthetic objects as well as real images

on state dependent delay partial neutral functional integro differential equations in this paper the existence of mild solutions for a class of abstract neutral integro differential equations with state dependent delay is studied

skewed rotation symmetry group detection we present a novel and effective algorithm for affinely skewed rotation symmetry group detection from real world images we define a complete skewed rotation symmetry detection problem as discovering five independent properties of a skewed rotation symmetry group 1 the center of rotation 2 the affine deformation 3 the type of the symmetry group 4 the cardinality of the symmetry group and 5 the supporting region of the symmetry group in the image we propose a frieze expansion fe method that transforms rotation symmetry group detection into a simple 1d translation symmetry detection problem we define and construct a pair of rotational symmetry saliency maps complemented by a local feature method frequency analysis using discrete fourier transform dft is applied to the frieze expansion patterns feps to uncover the types cyclic dihedral and o 2 the cardinalities and the corresponding supporting regions concentric or otherwise of multiple rotation symmetry groups in an image the phase information of the fep is used to rectify affinely skewed rotation symmetry groups our result advances the state of the art in symmetry detection by offering a unique combination of region based feature based and frequency based approaches experimental results on 170 synthetic and natural images demonstrate superior performance of our rotation symmetry detection algorithm over existing methods

wavefronts and global stability in a time delayed population model with stage structure we formulate and study a one dimensional single species diffusive delay population model the time delay is the time taken from birth to maturity without diffusion the delay differential model extends the well known logistic differential equation by allowing delayed constant birth processes and instantaneous quadratically regulated death processes this delayed model is known to have simple global dynamics similar to that of the logistic equation through the use of a sub supersolution pair method we show that the diffusive delay model continues to generate simple global dynamics this has the important biological implication that quadratically regulated death processes dramatically simplify the growth dynamics we also consider the possibility of travelling wavefront solutions of the scalar equation for the mature population connecting the zero solution of that equation with the positive steady state our main finding here is that our fronts appear to be all monotone regardless of the size of the delay this is in sharp contrast to the frequently reported findings that delay causes a loss of monotonicity with the front developing a prominent hump in some other delay models

robust rotation angle estimator the conventional method of estimating the rotation angle of a pattern using the principal axes is not suitable for circular symmetric patterns since their eigenvalues are similar in both directions in the paper a robust method of estimating a rotation angle using the phase information of zernike moments is presented the experimental results show that the proposed method estimates the rotation angle of the circular symmetric patterns more accurately than the principal axes method even in the presence of noise

the fractional fourier transform and applications this paper describes the fractional fourier transform which admits computation by an algorithm that has complexity proportional to the fast fourier transform algorithm whereas the discrete fourier transform dft is based on integral roots of unity e 2 pi i n the fractional fourier transform is based on fractional roots of unity e 2 pi i alpha where alpha is arbitrary the fractional fourier transform and the corresponding fast algorithm are useful for such applications as computing dfts of sequences with prime lengths computing dfts of sparse sequences analyzing sequences with noninteger periodicities performing high resolution trigonometric interpolation detecting lines in noisy images and detecting signals with linearly drifting frequencies in many cases the resulting algorithms are faster by arbitrarily large factors than conventional techniques

methods of critical value reduction for type 2 fuzzy variables and their applications a type 2 fuzzy variable is a map from a fuzzy possibility space to the real number space it is an appropriate tool for describing type 2 fuzziness this paper first presents three kinds of critical values cvs for a regular fuzzy variable rfv and proposes three novel methods of reduction for a type 2 fuzzy variable secondly this paper applies the reduction methods to data envelopment analysis dea models with type 2 fuzzy inputs and outputs and develops a new class of generalized credibility dea models according to the properties of generalized credibility when the inputs and outputs are mutually independent type 2 triangular fuzzy variables we can turn the proposed fuzzy dea model into its equivalent parametric programming problem in which the parameters can be used to characterize the degree of uncertainty about type 2 fuzziness for any given parameters the parametric programming model becomes a linear programming one that can be solved using standard optimization solvers finally one numerical example is provided to illustrate the modeling idea and the efficiency of the proposed dea model

dea and the discriminant analysis of ratios for ranking units the purpose of this study is to develop a new method which provides for given inputs and outputs the best common weights for all the units that discriminate optimally between the efficient and inefficient units as pregiven by the data envelopment analysis dea in order to rank all the units on the same scale this new method discriminant data envelopment analysis of ratios dr dea presents a further post optimality analysis of dea for organizational units when their multiple inputs and outputs are given we construct the ratio between the composite output and the composite input where their common weights are computed by a new non linear optimization of goodness of separation between the two pregiven groups a practical use of dr dea is that the common weights may be utilized for ranking the units on a unified scale dr dea is a new use of a two group discriminant criterion that has been presented here for ratios rather than the traditional discriminant analysis which applies to a linear function moreover non parametric statistical tests are employed to verify the consistency between the classification from dea efficient and inefficient units and the post classification as generated by dr dea

a unifying approach to moment based shape orientation and symmetry classification in this paper the problem of moment based shape orientation and symmetry classification is jointly considered a generalization and modification of current state of the art geometric moment based functions is introduced the properties of these functions are investigated thoroughly using fourier series analysis and several observations and closed form solutions are derived we demonstrate the connection between the results presented in this work and symmetry detection principles suggested from previous complex moment based formulations the proposed analysis offers a unifying framework for shape orientation symmetry detection in the context of symmetry classification and matching the second part of this work presents a frequency domain method aiming at computing a robust moment based feature set based on a true polar fourier representation of image complex gradients and a novel periodicity detection scheme using subspace analysis the proposed approach removes the requirement for accurate shape centroid estimation which is the main limitation of moment based methods operating in the image spatial domain the proposed framework demonstrated improved performance compared to state of the art methods

role of constant prey refuge on stage structure predator prey model with ratio dependent functional response abstract a constant prey refuge has been incorporated in a stage structured predator prey model with ratio dependent functional response sufficient conditions are obtained for the uniform persistence and global asymptotic stability by constructing suitable lyapunov function our model analysis demonstrates that the constant prey refuge plays an important role on the coexistence of stage structured predator prey species

analysis of a model representing stage structured population growth with state dependent time delay a stage structured model of population growth is proposed where the time to ma turity is itself state dependent it is shown that under appropriate assumptions all solutions are positive and bounded criteria for the existence of positive equilibria and further conditions for the uniqueness of the equilibria are given the stability of the equilibria are also discussed in addition an attracting region is determined for solutions such that this region collapses to the unique positive equilibrium in the state independent case

a framework for discrete integral transformations i the pseudopolar fourier transform the fourier transform of a continuous function evaluated at frequencies expressed in polar coordinates is an important conceptual tool for understanding physical continuum phenomena an analogous tool suitable for computations on discrete grids could be very useful however no exact analogue exists in the discrete case in this paper we present the notion of pseudopolar grid pp grid and the pseudopolar fourier transform ppft which evaluates the discrete fourier transform at points of the pp grid the pp grid is a type of concentric squares grid in which the radial density of squares is twice as high as usual the pp grid consists of equally spaced samples along rays where different rays are equally spaced in slope rather than angle we develop a fast algorithm for the ppft with the same complexity order as the cartesian fast fourier transform the algorithm is stable invertible requires only one dimensional operations and uses no approximate interpolations we prove that the ppft is invertible and develop two algorithms for its inversion iterative and direct both with complexity o n 2 log n where n times n is the size of the reconstructed image the iterative algorithm applies conjugate gradients to the gram operator of the ppft since the transform is ill conditioned we introduce a preconditioner which significantly accelerates the convergence the direct inversion algorithm utilizes the special frequency domain structure of the transform in two steps first it resamples the pp grid to a cartesian frequency grid and then recovers the image from the cartesian frequency grid

testing for image symmetries with application to confocal microscopy statistical tests are introduced for checking whether an image function f x y defined on the unit disc d x y x 2 y 2 les 1 is invariant under certain symmetry transformations of d given that discrete and noisy data are observed invariance under reflections or under rotations by rational angles is considered as well as rotational invariance these symmetry relations can be naturally expressed as restrictions for the zernike moments of f x y therefore the test statistics are based on the l 2 distance between zernike series estimates of the image function itself and its version obtained after applying the symmetry transformation the asymptotic distribution of the test statistics under both the hypothesis of symmetry as well as under fixed alternatives is derived furthermore the quality of the asymptotic approximations via simulation studies is investigated the usefulness of our theory is verified by examining an important problem in confocal microscopy i e possible imprecise alignments in the optical path of the microscope are investigated for optical systems with rotational symmetry the theoretical point spread function psf is reflection symmetric with respect to two orthogonal axes and rotationally invariant if the detector plane matches the optical plane of the microscope the tests are used to investigate whether the required symmetries can indeed be detected in the empirical psf

finding axes of symmetry from potential fields this paper addresses the problem of detecting axes of bilateral symmetry in images in order to achieve robustness to variation in illumination only edge gradient information is used to overcome the problem of edge breaks a potential field is developed from the edge map which spreads the information in the image plane pairs of points in the image plane are made to vote for their axes of symmetry with some confidence values to make the method robust to overlapping objects only local features in the form of taylor coefficients are used for quantifying symmetry we define an axis of symmetry histogram which is used to accumulate the weighted votes for all possible axes of symmetry to reduce the computational complexity of voting a hashing scheme is proposed wherein pairs of points whose potential fields are too asymmetric are pruned by not being counted for the vote experimental results indicate that the proposed method is fairly robust to edge breaks and is able to detect symmetries even when only 0 05 of the possible pairs are used for voting

detection of rotational symmetry in curves represented by the slope chain code abstract we present a new approach based on the slope chain code to determine whether a curve is rotational symmetrical and its order of symmetry the proposed approach works for open and closed perfectly symmetrical or quasi symmetrical 2d curves simple operations on the scc and its invariant properties are central to our methodology to evaluate the proposed methodology we use 1400 curves from a public database for the symmetrical asymmetrical classification task a recall r of 0 86 a balanced accuracy ba of 0 92 and a precision p of 0 87 were obtained for the quasi symmetrical quasi asymmetrical classification task r 0 77 ba 0 83 and p 0 70 were obtained for the order of rotational symmetry detection task the following performance was achieved r 0 97 ba 0 98 and p 0 95 for a symmetrical set of curves and r 0 98 ba 0 98 and p 0 90 for a quasi symmetrical set of curves we conclude our presentation demonstrating the usefulness of our methodology with three practical applications

ranking decision making units by imposing a minimum weight restriction in the data envelopment analysis it has been widely recognized that data envelopment analysis dea lacks discrimination power to distinguish between dea efficient units this paper proposes a new methodology for ranking decision making units dmus the new methodology ranks dmus by imposing an appropriate minimum weight restriction on all inputs and outputs which is decided by a decision maker dm or an assessor in terms of the solutions to a series of linear programming lp models that are specially constructed to determine a maximin weight for each dea efficient unit the dm can decide how many dmus to be retained as dea efficient in final efficiency ranking according to the requirement of real applications which provides flexibility for dea ranking three numerical examples are investigated using the proposed ranking methodology to illustrate its power in discriminating between dmus particularly dea efficient units

scaling units via the canonical correlation analysis in the dea context abstract this paper deals with the evaluation of decision making units which have multiple inputs and outputs a new method cca dea is developed where the canonical correlation analysis cca is utilized to provide a full rank scaling for all the units rather than a categorical classification for efficient and inefficient units as done by the data envelopment analysis dea the cca dea approach is an attempt to bridge the gap between the frontier approach of dea and the average tendencies of statistics econometrics nonparametric statistical tests are employed to validate the consistency between the classification from the dea and the postclassification that was generated by the cca dea

boundary layer phenomena for differential delay equations with state dependent time lags iii in this paper we begin a study of the differential delay equation varepsilon x t x t f x t r r r x t

symmetry as a continuous feature symmetry is treated as a continuous feature and a continuous measure of distance from symmetry in shapes is defined the symmetry distance sd of a shape is defined to be the minimum mean squared distance required to move points of the original shape in order to obtain a symmetrical shape this general definition of a symmetry measure enables a comparison of the amount of symmetry of different shapes and the amount of different symmetries of a single shape this measure is applicable to any type of symmetry in any dimension the symmetry distance gives rise to a method of reconstructing symmetry of occluded shapes the authors extend the method to deal with symmetries of noisy and fuzzy data finally the authors consider grayscale images as 3d shapes and use the symmetry distance to find the orientation of symmetric objects from their images and to find locally symmetric regions in images

stage structured models of intra and inter specific competition within age classes abstract in some species larvae and adults experience competition in completely different ways simple stage structured models without larval competition usually yield a single delay equation for the adults using an age structured system incorporating competition among both larvae and adults we derive a system of distributed delay equations for the numbers of larvae and adults the system is neither cooperative nor reducible to a single equation for either variable positivity boundedness and uniform strong persistence are established linear stability analysis of equilibria is difficult due to the strong coupling but results are proved for small delays using monotone systems theory and exponential ordering for small delay we prove a theorem on generic convergence to equilibria which does not directly follow from standard theory but can be proved indirectly using comparison arguments finally we consider an extension to two strain competition and prove theorems on the linear stability of the boundary equilibria

permanence and stability of a predator prey system with stage structure for predator a stage structured predator prey system with delays for prey and predator respectively is proposed and analyzed mathematical analysis of the model equations with regard to boundedness of solutions permanence and stability are analyzed some sufficient conditions which guarantee the permanence of the system and the global asymptotic stability of the boundary and positive equilibrium respectively are obtained

the dynamics of a mutual interference age structured predator prey model with time delay and impulsive perturbations on predators in this paper we introduce a mutual interference age structured predator prey natural enemy pest model with constant maturation time delay for the prey and then propose a pest management strategy by constant periodic releasing for the predator we show that there exists a global attractive pest eradication periodic solution when the periodic releasing amount m 1 and m 2 are lager than some critical value further to obtain a more effective pest control strategy we give the conditions involving the estimate of m 1 and m 2 in which the model is uniformly permanent and the pest population is under the economic threshold level we believe that the results will provide reliable tactic basis for the practical pest management