generalizing the hough transform to detect arbitrary shapes abstract the hough transform is a method for detecting curves by exploiting the duality between points on a curve and parameters of that curve the initial work showed how to detect both analytic curves 1 2 and non analytic curves 3 but these methods were restricted to binary edge images this work was generalized to the detection of some analytic curves in grey level images specifically lines 4 circles 5 and parabolas 6 the line detection case is the best known of these and has been ingeniously exploited in several applications 7 8 9 we show how the boundaries of an arbitrary non analytic shape can be used to construct a mapping between image space and hough transform space such a mapping can be exploited to detect instances of that particular shape in an image furthermore variations in the shape such as rotations scale changes or figure ground reversals correspond to straightforward transformations of this mapping however the most remarkable property is that such mappings can be composed to build mappings for complex shapes from the mappings of simpler component shapes this makes the generalized hough transform a kind of universal transform which can be used to find arbitrarily complex shapes

on the density of irreducible nfsrs let n be a positive integer an nfsr of n stages is called irreducible if the family of output sequences of any nfsr of stages less than n is not included in that of the nfsr in this paper we prove that the density of the irreducible nfsrs of n stages is larger than 0 39 this implies that it is expected to find an irreducible nfsr of n stages among three randomly chosen nfsrs of n stages

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

eigencurves for two parameter sturm liouville equations this paper concerns two parameter sturm liouville problems of the form p x y q x y lambda r x mu y quad a leqslant x leqslant b with self adjoint boundary conditions at a and b the set of lambda mu in bf r 2 for which there exists a nontrivial y satisfying the differential equation and the boundary conditions turns out to be a countable union of graphs of analytic functions our focus is on these graphs which are termed eigencurves in the literature although eigencurves have been used in a variety of ways for about a century they seem comparatively underdeveloped in their own right our plan is to give motivation for the topic elementary properties of eigencurves illustrations on a simple example first studied by richardson in 1918 and since then by several authors and some natural questions which may whet the reader s appetite some of these questions lead to new types of inverse sturm liouville problems

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

asymptotics of eigencurves for second order ordinary differential equations i abstract the regular two parameter sturm liouville equation py qy f r y is studied for l1 coefficients with p r 0 for each fixed number n of internal zeros of the eigenfunctions y n is analytic in necessary and sufficient conditions which are in fact independent of n are given for lim n gl to exist as or asymptotic expansions for n are derived in cases of existence and non existence of lim n

a survey of full length nonlinear shift register cycle algorithms shift registers have been used to generate sequences of 0 s and 1 s for over thirty years a wide variety of applications has been made of these sequences principally communications have made use of the sequences generated one particular class of shift register sequences for which applications exist is the full length nonlinear shift register sequences these sequences are periodic and of length 2 n and all 2 n different binary n tuples appear exactly one time in a periodic portion of the sequence in this paper we discuss various algorithms which have been suggested for generating these sequences

multiparameter definiteness conditions a previous attempt to systematize various conditions from multiparameter spectral theory is extended to weaker forms of definiteness the latter not only occur in the established literature but are also under active investigation at present several algebraic and geometrical formulations exist and questions concerning their equivalence are approached in a unified fashion where possible

a numerical algorithm for computing a basis for the root subspace at a nonderogatory eigenvalue of a multiparameter system abstract a numerical algorithm for the calculation of a basis for the root subspace at a nonderogatory eigenvalue of a finite dimensional multiparameter system is given it is based on the algorithm proposed by kosir 1 the perturbation theory for the algorithm is studied and a new stopping criterion is proposed at the end two numerical examples are given

a numerical method for the solution of two parameter eigenvalue problems abstract we consider a two parameter weakly coupled eigenvalue problem for matrix equations under known assumptions 4 such a problem can be reduced to a system of one parameter problems in a tensor product space after which it can be treated by known numerical methods the method is illustrated by a numerical example of the simple two parameter problem and the example of binding and browne 5 it turns out that the method is especially suitable for problems of smaller orders

a hybrid method for ellipse detection in industrial images a hybrid method with high reliability to detect ellipses in low snr industrial images is proposed using candidate elliptic arcs with high fitting precision as seed arcs to group with other arcs a novel method to extract regions which may contain one ellipse is proposed new selection scores for evaluating hypothetical ellipse are used experimental results show high reliability of proposed method many ellipse detection methods have been proposed for detecting ellipses in images however they are unsuitable for industrial images due to low signal to noise ratios snr this paper presents an ellipse detection method combining the advantages of hough transform ht based methods and the advantages of edge following methods which is capable of detecting fragmented ellipses and is both computational and memory efficient our method works in two steps in the first step an edge following method is proposed to quickly and accurately extract the majority of ellipses for ellipses missed in the first step candidate regions where each may contain one missed ellipse are extracted in the second step using cluster analysis and then a ht based method is performed on these regions to extract the missed ellipses this can not only guarantee the accuracy of the ht based method but also save the memory and computation time we test the performance of our method using both synthetic images and low snr industrial images experimental results demonstrate that the proposed method performs far better than existing methods in terms of recall precision f measure and reliability especially in term of reliability our method has achieved a very high value close to 1 while the reliabilities of state of the art methods are almost less than 0 5

deb definite error bounded tangent estimator for digital curves we propose a simple and fast method for tangent estimation of digital curves this geometric based method uses a small local region for tangent estimation and has a definite upper bound error for continuous as well as digital conics i e circles ellipses parabolas and hyperbolas explicit expressions of the upper bounds for continuous and digitized curves are derived which can also be applied to nonconic curves our approach is benchmarked against 72 contemporary tangent estimation methods and demonstrates good performance for conic nonconic and noisy curves in addition we demonstrate a good multigrid and isotropic performance and low computational complexity of o 1 and better performance than most methods in terms of maximum and average errors in tangent computation for a large variety of digital curves

further results on the decomposition of an nfsr into the cascade connection of an nfsr into an lfsr nonlinear feedback shift registers nfsrs are widely used in stream cipher design as building blocks in this paper we study the problem of decomposing an nfsr into the cascade connection of an nfsr into a linear feedback shift register lfsr which is a kind of concatenation of an nfsr and lfsr a necessary and sufficient condition for such decomposition is provided and other algebraic properties about such decomposition are also studied based on these theoretical results a binary decision diagram bdd based algorithm for such decomposition is proposed compared with the previous algorithm proposed by ma et al our algorithm can find more accurate candidate lfsr and the algebraic properties presented in this paper guarantee that the memory requirement during our verification is linear in the size of the bdd of the nfsrs characteristic function

on minimum period of nonlinear feedback shift registers in grain like structure grain is one of three hardware oriented finalists of the estream project a nonlinear feedback shift register nfsr in grain like structure is a cascade connection of a linear feedback shift register lfsr into an nfsr in which the characteristic polynomial of the lfsr is primitive and the feedback function of the nfsr is nonsingular in 2011 hu and gong pointed out that the period of the sequence generated by an nfsr in grain like structure is a multiple of the period of the sequence generated by its lfsr if the initial state of the lfsr is nonzero meanwhile they proposed an open problem for fixed feedback functions of an nfsr and an lfsr determine whether the sequences generated by the nfsr in grain like structure can achieve the minimum period i e the period of the lfsr when the initial state of the lfsr is nonzero and if they can achieve provide at least one pair of the initial states of the nfsr and lfsr clearly from a security point of view it is not preferable if the sequences generated by an nfsr in grain like structure achieve the minimum period this paper converts the open problem into a problem of solving an integer equation with respect to two unknown integers that uniquely correspond to the initial states of the nfsr and lfsr by viewing the nfsr as a boolean control network based on the integer equation this paper shows that for any given initial state of an n stage nfsr and any given nonzero initial state of an m stage lfsr the probability that the sequence generated by the nfsr in grain like structure achieves the minimum period 2 m 1 is at most 2 n this implies that the probability of the cascade connection used in grain achieving the minimum period is very small

the ovuscule we propose an active contour a k a snake that takes the shape of an ellipse its evolution is driven by surface terms made of two contributions the integral of the data over an inner ellipse counterbalanced by the integral of the data over an outer elliptical shell we iteratively adapt the active contour to maximize the contrast between the two domains which results in a snake that seeks elliptical bright blobs we provide analytic expressions for the gradient of the snake with respect to its defining parameters which allows for the use of efficient optimizers an important contribution here is the parameterization of the ellipse which we define in such a way that all parameters have equal importance this creates a favorable landscape for the proceedings of the optimizer we validate our construct with synthetic data and illustrate its use on real data as well

a probabilistic hough transform abstract the hough transform for straight line detection is considered it is shown that if just a small subset of the edge points in the image selected at random is used as input for the hough transform the performance is often only slightly impaired thus the execution time can be considerably shortened the performance of the resulting probabilistic hough transform is analysed the analysis is supported by experimental evidence

spectral properties of two parameter eigenvalue problems ii we study the self adjoint eigenvalue problem w x 0 in hilbert space for one equation in two parameters here is bounded below with compact resolvent for each 1 2 we give necessary and sufficient conditions for the existence of so that holds with w 0 and we investigate the geometry of the set z 0 of such we also discuss higher order solution sets z i where the ith eigenvalue of w vanishes deriving various asymptotic results in a unified fashion

dual variational approaches to multiparameter eigenvalue problems abstract we study the abstract multiparameter problem t m x m k n 1 n v mn x m 0 x m h m m 1 k for selfadjoint operators t m and v mn on separable hilbert spaces h m we develop dual variational approaches related to the polar duality between certain convex sets the primal approach has been the basis of several investigations particularly in the so called right definite case here we use the dual approach to derive existence and comparison results for the left definite case

existence conditions for higher order eigensets of multiparameter operators we consider classes of self adjoint operators for which the nonpositive part of the spectrum consists of eigenvalues 0 1 repeated according to multiplicity the sets of where i is negative and zero are labelled n i and z i respectively and p i k n i z i we study conditions on the v j sufficient to ensure nonemptiness of at least one of n i z i and p i for all t or for all positive definite t as well as conditions which are necessary in the sense that failure permits emptiness for at least one t as an example of our results we show in the sturm liouville case with l coefficients and separated end conditions that nonemptiness of z i for all t i e for all p 0 all q and all boundary data is equivalent to the i independent condition that the ft j do not vanish simultaneously on a set of positive measure

eigencurves for two parameter self adjoint ordinary differential equations of even order abstract the eigenvalue problem ly x x r x y x is considered for a self adjoint 2nth order operator l which is bounded below with compact resolvent on l2 a b and for real functions f r with certain restrictions it is shown that the eigencurves are piecewise analytic with no line segments unless s f r is constant a e when the curves are lines and possesses left right hand asymptotes iff s attains its minimum maximum value a e on some interval the asymptote equations are given explicitly in terms of the eigenvalues of certain simpler boundary value problems the second order case is discussed in detail

instability results for the damped wave equation in unbounded domains abstract we extend some previous results for the damped wave equation in bounded domains in r d to the unbounded case in particular we show that if the damping term is of the form a with bounded a taking on negative values on a set of positive measure then there will always exist unbounded solutions for sufficiently large positive in order to prove these results we generalize some existing results on the asymptotic behaviour of eigencurves of one parameter families of schrodinger operators to the unbounded case which we believe to be of interest in their own right

classification of eigentuples for uniformly elliptic multiparameter problems abstract let tm vmn be self adjoint operators in hilbert spaces hm the t3 having compact resolvents and lower bounds m 0 and the vmn satisfying uniform ellipticity 1 m n k when m 0 for each m these conditions are called uniform left definiteness and guarantee that all eigenvalues for the simultaneous equations wm xm 0 xm 0 wm tm n 1k nvmn belong to r k and are semi simple in an appropriate sense when some m 0 these conclusions may fail and we use an embedding technique to discuss for example algebraic multiplicities of eigenvalues transitions between real and non real eigenvalues and bounds for the numbers of eigenvalues of various types