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

inherent bias and noise in the hough transform considering the hough transformation as a linear imaging process recasts certain well known problems provides a useful vocab ulary and possibly indicates a source of applicable literature on the behavior of the hough transformation in various forms of noise a consideration of the analytic form of peaks in parameter space sets the stage for the idea of using complementary negative votes to cancel off peak positive votes in parameter space thus sharpening peaks and reducing bias

conformal spherical representation of 3d genus zero meshes this paper describes an approach of representing 3d shape by using a set of invariant spherical harmonic sh coefficients after conformal mapping specifically a genus zero 3d mesh object is first conformally mapped onto the unit sphere by using a modified discrete conformal mapping where the modification is based on mobius factorization and aims at obtaining a canonical conformal mapping then a sh analysis is applied to the resulting conformal spherical mesh the obtained sh coefficients are further made invariant to translation and rotation while at the same time retain the completeness thanks to which the original shape information has been faithfully preserved

stationary random fields arising from second order partial differential equations on compact lie groups wide sense stationary processes are a mainstay of classical signal processing it is well known that they can be obtained by solving ordinary differential equations with constant coefficients whose right hand side is a white noise this paper addresses the extension of this construction to random fields defined on compact lie groups on an underlying compact lie group the paper studies left invariant second order elliptic partial differential equations whose right hand side is a spatial white noise quite often the solution of a partial differential equation is not defined as a function but as a distribution to adapt to this situation the paper introduces a definition of wide sense stationary distributions on a compact lie group this is shown to be consistent with the more restricted definition of wide sense stationary fields given in a classic paper by yaglom it is proved that the solution of a partial differential equation of the kind being studied is a wide sense stationary distribution whose covariance structure is determined by the fundamental solution of the equation as a concrete example this paper describes the fundamental solution of the helmholtz equation on the rotation group and the resulting covariance structure

linear deterministic multi bottom up tree transducers in general top down and bottom up tree transducers lead to incomparable classes of tree transformations both for the nondeterministic and the deterministic case if deterministic top down tree transducers are extended by the capability to recognize regular tree properties and deterministic bottom up tree transducers are generalized by allowing states with arbitrary finite rank then the two devices now called deterministic top down tree transducers with regular look ahead and deterministic multi bottom up tree transducers respectively become equivalent z fulop a kuhnemann h vogler a bottom up characterization of deterministic top down tree transducers with regular look ahead inform process lett 91 2004 57 67 in this paper we focus on the class ld mbot of tree transformations which are computed by linear deterministic multi bottom up tree transducers we investigate the relationship among ld mbot and the classes of tree transformations computed by restricted deterministic bottom up tree transducers and by restricted deterministic top down tree transducers with regular look ahead in fact we show the inclusion diagram of nine such classes

optimal estimation and detection in homogeneous spaces this paper presents estimation and detection techniques in homogeneous spaces that are optimal under the squared error loss function the data is collected on a manifold which forms a homogeneous space under the transitive action of a compact lie group signal estimation problems are addressed by formulating wiener hopf equations for homogeneous spaces the coefficient functions of these equations are the signal correlations which are assumed to be known the resulting coupled integral equations on the manifold are converted to wiener hopf convolutional integral equations on the group these are solved using the peter weyl theory of fourier transform on compact lie groups the computational complexity of this algorithm is reduced using the bi invariance of the correlations with respect to a stabilizer subgroup the theory of matched filtering for isotropic signal fields is developed for signal classification where given a set of template signals on the manifold and a noisy test signal the objective is to optimally detect the template buried in the test signal this is accomplished by designing a filter on the manifold that maximizes the signal to noise ratio snr of the filtered output an expression for the snr is obtained as a ratio of quadratic forms expressed as haar integrals over the transformation group these integrals are expressed in the fourier domain as infinite sums over the irreducible representations simplification of these sums is achieved by invariance properties of the signal function and the noise correlation function the wiener filter and matched filter are developed for an abstract homogeneous space and then specialized to the case of spherical signals under the action of the rotation group applications of these algorithms to denoising of 3d surface data visual navigation with omnidirectional camera and detection of compact embedded objects in the stochastic background are discussed with experimental results

optimization algorithms exploiting unitary constraints this paper presents novel algorithms that iteratively converge to a local minimum of a real valued function f x subject to the constraint that the columns of the complex valued matrix x are mutually orthogonal and have unit norm the algorithms are derived by reformulating the constrained optimization problem as an unconstrained one on a suitable manifold this significantly reduces the dimensionality of the optimization problem pertinent features of the proposed framework are illustrated by using the framework to derive an algorithm for computing the eigenvector associated with either the largest or the smallest eigenvalue of a hermitian matrix

elliptical object detection by using its geometric properties abstract a simple algorithm for ellipse detection in an image is proposed the new method consists of three steps 1 detect the elliptical center by using its symmetrical property 2 identify the elliptical points by using a simple geometric property and 3 estimate the five parameters x c y c a b by using a least sum of squares fitting method the new method has been tested on both the synthetic and real images the experimental results show that the method is reliable and accurate

catadioptric projective geometry catadioptric sensors are devices which utilize mirrors and lenses to form a projection onto the image plane of a camera central catadioptric sensors are the class of these devices having a single effective viewpoint in this paper we propose a unifying model for the projective geometry induced by these devices and we study its properties as well as its practical implications we show that a central catadioptric projection is equivalent to a two step mapping via the sphere the second step is equivalent to a stereographic projection in the case of parabolic mirrors conventional lens based perspective cameras are also central catadioptric devices with a virtual planar mirror and are thus covered by the unifying model we prove that for each catadioptric projection there exists a dual catadioptric projection based on the duality between points and line images conics it turns out that planar and parabolic mirrors build a dual catadioptric projection pair as a practical example we describe a procedure to estimate focal length and image center from a single view of lines in arbitrary position for a parabolic catadioptric system

a windowing approach to detecting line segments using hough transform abstract a new approach for using the hough transform to detect line segments is presented this approach is efficient in both space and time strategies combining the features of the intersection point ben tzvi leavers and sandler proc 5th intl conf image anal 152 159 1990 xu oja and kultannen pattern recognition lett 11 331 338 1990 and dual plane conker comput vis graphics image process 43 115 132 1988 methods are used to calculate the hough transform a dense set of small overlapping windows are used to restrict the pairs of inage pixels that are evaluated experimental results indicate that this method reduces the time and space requirements significantly

a novel hough transform based on eliminating particle swarm optimization and its applications hough transform ht is a well established method for curve detection and recognition due to its robustness and parallel processing capability however ht is quite time consuming in this paper an eliminating particle swarm optimization epso algorithm is employed to improve the speed of a ht the parameters of the solution after hough transformation are considered as the particle positions and the epso algorithm searches the optimum solution by eliminating the weakest particles to speed up the computation an accumulation array in hough transformation is utilized as a fitness function of the epso algorithm the experiments on numerous images show that the proposed approach can detect curves or contours of both noise free and noisy images with much better performance especially for noisy images it can archive much better results than that obtained by using the existing ht algorithms

robust ellipse detection with gaussian mixture models the euclidian distance between gaussian mixtures has been shown to be robust to perform point set registration jian and vemuri 2011 we propose to extend this idea for robustly matching a family of shapes ellipses optimisation is performed with an annealing strategy and the search for occurrences is repeated several times to detect multiple instances of the shape of interest we compare experimentally our approach to other state of the art techniques on a benchmark database for ellipses and demonstrate the good performance of our approach highlightswe extend the framework based on l2 to estimate a parametric family of curves we propose a non isotropic and multidimensional modeling for the density functions we propose a method for detecting multiple instances of an ellipse

a split and merge based ellipse detector with self correcting capability a novel ellipse detector based upon edge following is proposed in this paper the detector models edge connectivity by line segments and exploits these line segments to construct a set of elliptical arcs disconnected elliptical arcs which describe the same ellipse are identified and grouped together by incrementally finding optimal pairings of elliptical arcs we extract hypothetical ellipses of an image by fitting an ellipse to the elliptical arcs of each group finally a feedback loop is developed to sieve out low confidence hypothetical ellipses and to regenerate a better set of hypothetical ellipses in this aspect the proposed algorithm performs self correction and homes in on difficult ellipses detailed evaluation on synthetic images shows that the algorithm outperforms existing methods substantially in terms of recall and precision scores under the scenarios of image cluttering salt and pepper noise and partial occlusion additionally we apply the detector on a set of challenging real world images successful detection of ellipses present in these images is demonstrated we are not aware of any other work that can detect ellipses from such difficult images therefore this work presents a significant contribution towards ellipse detection

stochastic deconvolution over groups in this paper we address a class of inverse problems that are formulated as group convolutions this is a rich area of research with applications to radon transform inversion for tomography wide band and narrow band signal processing inverse rendering in computer graphics and channel estimation in communications as well as robotics and polymer science we present a group theoretic framework for signal modeling and analysis for such problems and propose a minimum mean square error mmse deconvolution method in a probabilistic setting key components of our approach are group representation theory and the concept of group stationarity the proposed deconvolution method incorporates a priori information and noise statistics into the inversion process which leads to a natural regularized solution we present recovery of self similar processes that are blurred and embedded in noise as a demonstration example the method is applicable to a wide range of inverse problems involving both commutative and noncommutative groups including finite compact and majority of well behaved locally compact groups

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

efficient sampling strategy and refinement strategy for randomized circle detection circle detection is fundamental in pattern recognition and computer vision the randomized approach has received much attention for its computational benefit when compared with the hough transform in this paper a multiple evidence based sampling strategy is proposed to speed up the randomized approach next an efficient refinement strategy is proposed to improve the accuracy based on different kinds of ten test images experimental results demonstrate the computation saving and accuracy effects when plugging the proposed strategies into three existing circle detection methods

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

expression invariant representations of faces addressed here is the problem of constructing and analyzing expression invariant representations of human faces we demonstrate and justify experimentally a simple geometric model that allows to describe facial expressions as isometric deformations of the facial surface the main step in the construction of expression invariant representation of a face involves embedding of the facial intrinsic geometric structure into some low dimensional space we study the influence of the embedding space geometry and dimensionality choice on the representation accuracy and argue that compared to its euclidean counterpart spherical embedding leads to notably smaller metric distortions we experimentally support our claim showing that a smaller embedding error leads to better recognition

a method for solving the multiple ellipses detection problem in this paper the multiple ellipses detection problem on the basis of a data points set coming from a number of ellipses in the plane not known in advance is considered an ellipse is considered as a mahalanobis circle with some positive definite matrix a very efficient method for solving this problem is proposed this method very successfully combines the well known direct least squares method and the ransac algorithm with a realistic statistical model of multiple ellipses in the plane the method is illustrated and tested on numerous synthetic and real world applications the method was also compared with other similar methods in the case when a data points set comes from a number of ellipses with clear edges the proposed method gives results similar to other known methods however when a data points set comes from a number of ellipses with noisy edges the proposed method performs significantly better than the other methods we should emphasize the advantage and utility of the proposed methods in a variety of applications such as medical image analysis and ultrasound image segmentation highlightsransac based method for solving the multiple ellipses detection problem is proposed the proposed method shows high efficiency the method has the potential to solve real time applications data is considered as a realization of a realistic statistical model pseudocodes of all proposed algorithms are provided

spherical diffusion for 3d surface smoothing a diffusion based approach to surface smoothing is presented surfaces are represented as scalar functions defined on the sphere the approach is equivalent to gaussian smoothing on the sphere and is computationally efficient since it does not require iterative smoothing furthermore it does not suffer from the well known shrinkage problem evolution of important shape features parabolic curves under diffusion is demonstrated a nonlinear modification of the diffusion process is introduced in order to improve smoothing behavior of elongated and poorly centered objects

a high speed algorithm for elliptical object detection a high speed method for elliptical object location is proposed through the use of the geometric symmetry it first locates the centers of elliptical objects and classifies the boundary points then each point possible on an elliptical object boundary is used to obtain the remaining three parameters of the elliptical object since each boundary point is at most transformed to one point on the parameter space the proposed method is very fast some experimental results are also given to show that the proposed method is better than some existing methods under the consideration of space and storage

power histogram for circle detection on images the detection of circles from digital images is very important to shape recognition in this paper we propose and analyze a novel method based on power histograms to detect circles in an image the key idea is to transform an image into several power histograms that are computed from the pairwise distance products referring to the rays emanated from some reference points on the image according to the circle power theorem the edge pixels on a circle share the same circle powers with respect to an arbitrary point on the image the peaks in the power histograms provide strong evidence for the existence of real circles a multi reference cross validation among various peaks can systematically remove randomness and eliminate false detections experimental results over several synthetic as well as natural images with varying ranges of complexity validate the efficacy of the proposed method in terms of its accuracy simplicity and robustness highlightsa new and simple circle detector based on the power theorem of circles is proposed transforms the edge pixel pairs into 1d power space and detects peaks in power histogram for circle locating incorporates the inherent geometric properties of circle and generates only a few number of candidate circles for validation a robust peak detection and cross validation algorithm for enhancing the robustness of the method experiments on synthetic hand sketched and natural images are carried out

detection of incomplete ellipse in images with strong noise by iterative randomized hough transform irht an iterative randomized hough transform irht is developed for detection of incomplete ellipses in images with strong noise the irht iteratively applies the randomized hough transform rht to a region of interest in the image space the region of interest is determined from the latest estimation of ellipse parameters the irht zooms in on the target curve by iterative parameter adjustments and reciprocating use of the image and parameter spaces during the iteration process noise pixels are gradually excluded from the region of interest and the estimation becomes progressively close to the target the irht retains the advantages of rht of high parameter resolution computational simplicity and small storage while overcoming the noise susceptibility of rht indivisible multiple instances of ellipse can be sequentially detected the irht was first tested for ellipse detection with synthesized images it was then applied to fetal head detection in medical ultrasound images the results demonstrate that the irht is a robust and efficient ellipse detection method for real world applications