the use of mixed logit models to reflect heterogeneity in capture recapture studies summary we examine issues in estimating population size n with capture recapture models when there is variable catchability among subjects we focus on a logistic normal mixed model for which the logit of the probability of capture is an additive function of a random subject and a fixed sampling occasion parameter when the probability of capture is small or the degree of heterogeneity is large the log likelihood surface is relatively flat and it is difficult to obtain much information about n we also discuss a latent class model and a log linear model that account for heterogeneity and show that the log linear model has greater scope models assuming homogeneity provide much narrower intervals for n but are usually highly overly optimistic the actual coverage probability being much lower than the nominal level

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

handling uncertain data in subspace detection abstract experimental data is subject to uncertainty as every measurement apparatus is inaccurate at some level however the design of most computer vision and pattern recognition techniques e g hough transform overlooks this fact and treats intensities locations and directions as precise values in order to take imprecisions into account entries are often resampled to create input datasets where the uncertainty of each original entry is characterized by as many exact elements as necessary clear disadvantages of the sampling based approach are the natural processing penalty imposed by a larger dataset and the difficulty of estimating the minimum number of required samples we present an improved voting scheme for the general framework for subspace detection hence to its particular case the hough transform that allows processing both exact and uncertain data our approach is based on an analytical derivation of the propagation of gaussian uncertainty from the input data into the distribution of votes in an auxiliary parameter space in this parameter space the uncertainty is also described by gaussian distributions in turn the votes are mapped to the actual parameter space as non gaussian distributions our results show that resulting accumulators have smoother distributions of votes and are in accordance with the ones obtained using the conventional sampling process thus safely replacing them with significant performance gains

3d reconstruction of free formed line like objects using nurbs representation 3d reconstruction of arbitrary free formed objects is an important and challenging problem in computer vision in this paper we first discuss the importance of primitive selection in 3d reconstruction subsequently a theorem which reveals the perspective invariance of nurbs is shown making it a good choice as primitive in 3d reconstruction consequently based on this theorem a new paradigm of free formed line like object reconstruction using nurbs as primitives is proposed furthermore an approach for determining weights for 3d nurbs is presented and the width effect of curved line like objects is analyzed finally experiments with line like objects and machine part demonstrate the feasibility of our approach and prove the superiority of our approach over the point or segment based approaches as well as the b spline based reconstruction approach in terms of robustness and accuracy

on comparison of mixture models for closed population capture recapture studies summary a mixture model is a natural choice to deal with individual heterogeneity in capture recapture studies pledger 2000 biometrics 56 434 442 2005 biometrics 61 868 876 advertised the use of the two point mixture model dorazio and royle 2003 biometrics 59 351 364 2005 biometrics 61 874 876 suggested that the beta binomial model has advantages the controversy is related to the nonidentifiability of the population size link 2003 biometrics 59 1123 1130 and certain boundary problems the total bias is decomposed into an intrinsic bias an approximation bias and an estimation bias we propose to assess the approximation bias the estimation bias and the variance with the intrinsic bias excluded when comparing different estimators the boundary problems in both models and their impacts are investigated real epidemiological and ecological examples are analyzed

real time detection of planar regions in unorganized point clouds automatic detection of planar regions in point clouds is an important step for many graphics image processing and computer vision applications while laser scanners and digital photography have allowed us to capture increasingly larger datasets previous techniques are computationally expensive being unable to achieve real time performance for datasets containing tens of thousands of points even when detection is performed in a non deterministic way we present a deterministic technique for plane detection in unorganized point clouds whose cost is o n log n in the number of input samples it is based on an efficient hough transform voting scheme and works by clustering approximately co planar points and by casting votes for these clusters on a spherical accumulator using a trivariate gaussian kernel a comparison with competing techniques shows that our approach is considerably faster and scales significantly better than previous ones being the first practical solution for deterministic plane detection in large unorganized point clouds highlights o n log n deterministic technique for plane detection in unorganized point clouds fast and robust clustering solution for detecting sets of almost coplanar points efficient voting scheme for detecting planar regions in unorganized point clouds real time plane detection in point clouds with up to 105 samples

higher homotopy commutativity of h spaces and the permuto associahedra in this paper we give a combinatorial definition of a higher homotopy commutativity of the multiplication for an an space to give the definition we use polyhedra called the permuto associahedra which are constructed by kapranov we also show that if a connected ap space has the finitely generated mod p cohomology for a prime p and the multiplication of it is homotopy commutative of the p th order then it has the mod p homotopy type of a finite product of eilenberg mac lane spaces k z 1 s k z 2 s and r z p i 1 s for i 1

estimating three dimensional motion parameters of a rigid planar patch ii singular value decomposition we show that the three dimensional 3 d motion parameters of a rigid planar patch can be determined by computing the singular value decomposition svd of a 3 3 matrix containing the eight so called pure parameters furthermore aside from a scale factor for the translation parameters the number of solutions is either one or two depending on the multiplicity of the singular values of the matrix

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

deconstructing hopf spaces we characterize hopf spaces with finitely generated cohomology as an algebra over the steenrod algebra we deconstruct the original space into an h space y with finite mod p cohomology and a finite number of p torsion eilenberg mac lane spaces we give a precise description of homotopy commutative h spaces in this setting

catadioptric camera calibration using geometric invariants central catadioptric cameras are imaging devices that use mirrors to enhance the field of view while preserving a single effective viewpoint in this paper we propose a novel method for the calibration of central catadioptric cameras using geometric invariants lines and spheres in space are all projected into conics in the catadioptric image plane we prove that the projection of a line can provide three invariants whereas the projection of a sphere can only provide two from these invariants constraint equations for the intrinsic parameters of catadioptric camera are derived therefore there are two kinds of variants of this novel method the first one uses projections of lines and the second one uses projections of spheres in general the projections of two lines or three spheres are sufficient to achieve catadioptric camera calibration one important conclusion in this paper is that the method based on projections of spheres is more robust and has higher accuracy than that based on projections of lines the performances of our method are demonstrated by both the results of simulations and experiments with real images

motion estimation in image sequences using the deformation of apparent contours the problem of determining the camera motion from apparent contours or silhouettes of a priori unknown curved 3d surfaces is considered in a sequence of images it is shown how to use the generalized epipolar constraint on apparent contours one such constraint is obtained for each epipolar tangency point in each image pair an accurate algorithm for computing the motion is presented based on a maximum likelihood estimate it is shown how to generate initial estimates on the camera motion using only the tracked contours it is also shown that in theory the motion can be calculated from the deformation of a single contour the algorithm has been tested on several real image sequences for both euclidean and projective reconstruction the resulting motion estimate is compared to motion estimates calculated independently using standard feature based methods the motion estimate is also used to classify the silhouettes as curves or apparent contours the statistical evaluation shows that the technique gives accurate and stable results

a stratified approach for camera calibration using spheres this paper proposes a stratified approach for camera calibration using spheres previous works have exploited epipolar tangents to locate frontier points on spheres for estimating the epipolar geometry it is shown in this paper that other than the frontier points two additional point features can be obtained by considering the bitangent envelopes of a pair of spheres a simple method for locating the images of such point features and the sphere centers is presented an algorithm for recovering the fundamental matrix in a plane plus parallax representation using these recovered image points and the epipolar tangents from three spheres is developed a new formulation of the absolute dual quadric as a cone tangent to a dual sphere with the plane at infinity being its vertex is derived this allows the recovery of the absolute dual quadric which is used to upgrade the weak calibration to a full calibration experimental results on both synthetic and real data are presented which demonstrate the feasibility and the high precision achieved by our proposed algorithm

the performance of mixture models in heterogeneous closed population capture recapture summarydorazio and royle 2003 biometrics59 351 364 investigated the behavior of three mixture models for closed population capture recapture analysis in the presence of individual heterogeneity of capture probability their simulations were from the beta binomial distribution with analyses from the beta binomial the logit normal and the finite mixture latent class models in this response simulations from many different distributions give a broader picture of the relative value of the beta binomial and the finite mixture models and provide some preliminary insights into the situations in which these models are useful

estimating three dimensional motion parameters of a rigid planar patch iii finite point correspondences and the three view problem two results are presented in this paper first it is shown that in estimating three dimensional motion of a rigid planar patch the eight pure parameters used in 1 and 2 are uniquely determined from the image correspondences of four points no three collinear and can be estimated by solving a set of linear equations the second result concerns the three view problem it is proved that given four image point correspondences in three perspective views of a planar patch undergoing general three dimensional rigid body motion the number of solutions for the motion parameters is one as opposed to two 2 when only two perspective views are given

relative affine structure canonical model for 3d from 2d geometry and applications we propose an affine framework for perspective views captured by a single extremely simple equation based on a viewer centered invariant we call relative affine structure via a number of corollaries of our main results we show that our framework unifies previous work including euclidean projective and affine in a natural and simple way and introduces new extremely simple algorithms for the tasks of reconstruction from multiple views recognition by alignment and certain image coding applications

uniqueness and estimation of three dimensional motion parameters of rigid objects with curved surfaces two main results are established in this paper first we show that seven point correspondences are sufficient to uniquely determine from two perspective views the three dimensional motion parameters within a scale factor for the translations of a rigid object with curved surfaces the seven points should not be traversed by two planes with one plane containing the origin nor by a cone containing the origin second a set of essential parameters are introduced which uniquely determine the motion parameters up to a scale factor for the translations and can be estimated by solving a set of linear equations which are derived from the correspondences of eight image points the actual motion parameters can subsequently be determined by computing the singular value decomposition svd of a 3 3 matrix containing the essential parameters

real time line detection through an improved hough transform voting scheme the hough transform ht is a popular tool for line detection due to its robustness to noise and missing data however the computational cost associated to its voting scheme has prevented software implementations to achieve real time performance except for very small images many dedicated hardware designs have been proposed but such architectures restrict the image sizes they can handle we present an improved voting scheme for the ht that allows a software implementation to achieve real time performance even on relatively large images our approach operates on clusters of approximately collinear pixels for each cluster votes are cast using an oriented elliptical gaussian kernel that models the uncertainty associated with the best fitting line with respect to the corresponding cluster the proposed approach not only significantly improves the performance of the voting scheme but also produces a much cleaner voting map and makes the transform more robust to the detection of spurious lines

finite h spaces and algebras over the steenrod algebra a correction we are grateful to k ishiguro for pointing out a regrettable fallacy which vitiates a passage of our paper 1 starting with p 141 line 3 on the other hand and finishing with p 141 line 21 thus i wi is prime to p we wish to replace this passage with the following argument let h and k be the graded fields of fractions of h and k respectively we recall from 1 8 that k is integral over h it follows that foreachx oink wecanfindy oink suchthatxyeh it is now easy to choose elements ui ui2 me in k which form a base for k over t in particular the elements u u2 ye u generate over h a free module m whose poincare series has the form f t k t where k t is a polynomial with k l m by 1 8 again k is finitely generated as a module over h and so choosing a common denominator a 0 in h we can arrange that k is contained in m or equivalently ak c m from the inclusions

closed form line segment extraction using the hough transform this paper proposes a novel closed form solution to complete line segment extraction given a voting angle in image space the voting distribution is analyzed and two functional relationships are deduced regarding the corresponding column in hough space voting along the distance axis is considered as being a random variable and voting values in cells are considered as forming a probability distribution statistical characteristics of this distribution are used to fit a quadratic polynomial curve and a linear curve direction length and width of a line segment are simultaneously computed in a closed form based on coefficients of fitted quadratic polynomial curves the midpoint of a line segment is determined based on the fitted linear curve the method is tested on simulated and real world images results show that the proposed closed form solution is feasible in the presence of quantization errors or image noise highlightswe proposed a method for obtaining the complete set of line segment parameters the direction length and width of a line segment are extracted simul taneously in a closed form we provided a complete theoretical derivation of voting variance with respect to voting angle the midpoint of a line segment is determined by the coefficients of the fitted linear curve parallel crossing and aligned line segments are discussed by analysing events in image space and hough space

projective reconstruction and invariants from multiple images this correspondence investigates projective reconstruction of geometric configurations seen in two or more perspective views and the computation of projective invariants of these configurations from their images a basic tool in this investigation is the fundamental matrix that describes the epipolar correspondence between image pairs it is proven that once the epipolar geometry is known the configurations of many geometric structures for instance sets of points or lines are determined up to a collineation of projective 3 space spl pscrsup 3 by their projection in two independent images this theorem is the key to a method for the computation of invariants of the geometry invariants of six points in spl pscrsup 3 and of four lines in spl pscrsup 3 are defined and discussed an example with real images shows that they are effective in distinguishing different geometrical configurations since the fundamental matrix is a basic tool in the computation of these invariants new methods of computing the fundamental matrix from seven point correspondences in two images or six point correspondences in three images are given

capture recapture estimation using finite mixtures of arbitrary dimension reversible jump markov chain monte carlo rjmcmc methods are used to fit bayesian capture recapture models incorporating heterogeneity in individuals and samples heterogeneity in capture probabilities comes from finite mixtures and or fixed sample effects allowing for interactions estimation by rjmcmc allows automatic model selection and or model averaging priors on the parameters stabilize the estimates and produce realistic credible intervals for population size for overparameterized models in contrast to likelihood based methods to demonstrate the approach we analyze the standard snowshoe hare and cottontail rabbit data sets from ecology a reliability testing data set

collinear segment detection using ht neighborhoods in this paper geometrical analysis is used to extract novel straight line segment features from the wings around the peaks of the hough transform ht based on these features a practical segment detection method is proposed which has the ability to determine complete straight line segment parameters including the location of the center length slope and the euclidean distance to the origin the proposed method does not rely on edge point verification in the image space i e the complete set of segment features are determined only using the information embodied in the ht data the proposed method can distinguish between highly collinear straight line segments segment detection is robust to disturbing edge points especially ones collinear with the object a predefined collinear segment resolution that provides a theoretical criterion to determine straight line contiguity is derived image processing and analysis experiments show consistent robust performance

a general framework for subspace detection in unordered multidimensional data the analysis of large volumes of unordered multidimensional data is a problem confronted by scientists and data analysts every day often it involves searching for data alignments that emerge as well defined structures or geometric patterns in datasets for example straight lines circles and ellipses represent meaningful structures in data collected from electron backscatter diffraction particle accelerators and clonogenic assays also customers with similar behavior describe linear correlations in e commerce databases we describe a general approach for detecting data alignments in large unordered noisy multidimensional datasets in contrast to classical techniques such as the hough transforms which are designed for detecting a specific type of alignment on a given type of input our approach is independent of the geometric properties of the alignments to be detected as well as independent of the type of input data thus it allows concurrent detection of multiple kinds of data alignments in datasets containing multiple types of data given its general nature optimizations developed for our technique immediately benefit all its applications regardless the type of input data

nonidentifiability of population size from capture recapture data with heterogeneous detection probabilities heterogeneity in detection probabilities has long been recognized as problematic in mark recapture studies and numerous models developed to accommodate its effects individual heterogeneity is especially problematic in that reasonable alternative models may predict essentially identical observations from populations of substantially different sizes thus even with very large samples the analyst will not be able to distinguish among reasonable models of heterogeneity even though these yield quite distinct inferences about population size the problem is illustrated with models for closed and open populations

motion from flow along contours a note on robustness and ambiguous cases the projected contours of a rigid body in motion define a velocity field a flow in the image plane where the tangential components are invisible we investigate robustness when estimating motion parameters from the normal components of velocity along contours ambiguous curves are contours for which no unique motion can be recovered from normal flow we show that they are field lines of some extra velocity field which causes an invisible motion when added on top of the actual velocity field these field lines coincide with the contour this is an analytical description of what waxman and wohn 1984 called the aperture problem in the large which actually was studied by lie 1893 under the concept of self projective curves if we specialize to a planar surface patch we make a catalogue of the class of ambiguous curves we study the robustness of motion parameters obtained by least squares estimation by calculating the a mount by which noise in the normal flow is magnified for simple curves and a motion model with four unknowns two translation components rotation and expansion there are explicit formulas relating the robustness of motion parameters to how large a portion of the contour we use sometimes it helps to use more global information a larger portion of e g a closed contour and sometimes there is no way out because we are working with contour segments that too closely resemble ambiguous curves neither is there any hope to recover the true velocity field from normal flow locally since any contour falls into one of the ill conditioned contours

nonparametric mle under two closed capture recapture models with heterogeneity we conduct nonparametric maximum likelihood estimation under two common heterogeneous closed population capture recapture models our models specify mixture models as did previous researchers models which have a common generating distribution say f for the capture probabilities using lindsay and roeder s 1992 journal of the american statistical association 87 785 794 mixture model results and the em algorithm a nonparametric maximum likelihood estimator mle of f for any specified population size n is obtained then the nonparametric mle of the n f pair and thus for n is determined perhaps most importantly since our mle pair maximizes the likelihood under the entire nonparametric probability model it provides an excellent foundation for estimating properties of estimators conducting a goodness of fit test and performing a likelihood ratio test these are illustrated in the paper

when is it possible to identify 3d objects from single images using class constraints one approach to recognizing objects seen from arbitrary viewpoint is by extracting invariant properties of the objects from single images such properties are found in images of 3d objects only when the objects are constrained to belong to certain classes e g bilaterally symmetric objects existing studies that follow this approach propose how to compute invariant representations for a handful of classes of objects a fundamental question regarding the invariance approach is whether it can be applied to a wide range of classes to answer this question it is essential to study the set of classes for which invariance exists this paper introduces a new method for determining the existence of invariant functions for classes of objects together with the set of images from which these invariants can be computed we develop algebraic tests that determine whether the objects in a given class can be identified from single images these tests apply to classes of objects undergoing affine projection in addition these tests allow us to determine the set of views of the objects which are degenerate we apply these tests to several classes of objects and determine which of them is identifiable and which of their views are degenerate

geometry of single axis motions using conic fitting previous algorithms for recovering 3d geometry from an uncalibrated image sequence of a single axis motion of unknown rotation angles are mainly based on the computation of two view fundamental matrices and three view trifocal tensors we propose three new methods that are based on fitting a conic locus to corresponding image points over multiple views the main advantage is that determining only five parameters of a conic from one corresponding point over at least five views is simpler and more robust than determining a fundamental matrix from two views or a trifocal tensor from three views it is shown that the geometry of single axis motion can be recovered either by computing one conic locus and one fundamental matrix or by computing at least two conic loci a maximum likelihood solution based on this parametrization of the single axis motion is also described for optimal estimation using three or more loci the experiments on real image sequences demonstrate the simplicity accuracy and robustness of the new methods

geometric and algebraic constraints of projected concentric circles and their applications to camera calibration we investigate the projective properties of the feature consisting of two concentric circles we demonstrate there exist geometric and algebraic constraints on its projection we show how these constraints greatly simplify the recoveries of the affine and euclidean structures of a 3d plane as an application we assess the performances of two camera calibration algorithms

on the exterior calculus of invariant theory the full extent of the tragedy of hermann grassmann which has been unfolding since his death by a succession of misadventures and misunderstandings of his work unique in the history of modern mathematics is yet to be fully realized it began with a deliberate ambiguity on the part of the author of the ausdehnungslehre whereby one and the same notation was chosen to designate two different algebraic operations originally known as the progressive and the regressive product this choice was not an oversight on grassmann s part as we shall see but was rather dictated by the author s deep understanding of the philosophical reach of his discovery an understanding which lay well beyond the powers of the

homotopy nilpotency in p regular loop spaces we consider the problem how far from being homotopy commutative is a loop space having the homotopy type of the p completion of a product of finite numbers of spheres we determine the homotopy nilpotency of those loop spaces as an answer to this problem

statistical bias of conic fitting and renormalization introducing a statistical model of noise in terms of the covariance matrix of the n vector we point out that the least squares conic fitting is statistically biased we present a new fitting scheme called renormalization for computing an unbiased estimate by automatically adjusting to noise relationships to existing methods are discussed and our method is tested using real and synthetic data

new memory and computation efficient hough transform for detecting lines the slope intercept hough transform siht is one of the two types of line detection methods however the disadvantage of the siht is its low memory utilization say 50 based on the affine transformation this paper presents a new method to improve the memory utilization of the siht from 50 to 100 according to the proposed affine transformation we first present a basic siht based algorithm for detecting lines instead of concerning floating point operations in the basic siht based algorithm an improved siht based algorithm which mainly concerns integer operations is presented besides the memory utilization advantage experimental results reveal that the improved siht based algorithm has more than 60 execution time improvement ratio when compared to the basic siht based algorithm and has more than 33 execution time improvement ratio when compared to another type of line detection methods such as the r based ht algorithm and its variant the detailed complexity analyses for all the related algorithms are also investigated and we show that the time complexity required in the improved siht based algorithm is the least

the geometry and matching of lines and curves over multiple views this paper describes the geometry of imaged curves in two and three views multi view relationships are developed for lines conics and non algebraic curves the new relationships focus on determining the plane of the curve in a projective reconstruction and in particular using the homography induced by this plane for transfer from one image to another it is shown that given the fundamental matrix between two views and images of the curve in each view then the plane of a conic may be determined up to a two fold ambiguity but local curvature of a curve uniquely determines the plane it is then shown that given the trifocal tensor between three views this plane defines a homography map which may be used to transfer a conic or the curvature from two views to a third simple expressions are developed for the plane and homography in each case a set of algorithms are then described for automatically matching individual line segments and curves between images the algorithms use both photometric information and the multiple view geometric relationships for image pairs the homography facilitates the computation of a neighbourhood cross correlation based matching score for putative line curve correspondences for image triplets cross correlation matching scores are used in conjunction with line curve transfer based on the trifocal geometry to disambiguate matches algorithms are developed for both short and wide baselines the algorithms are robust to deficiencies in the segment extraction and partial occlusion experimental results are given for image pairs and triplets for varying motions between views and for different scene types the methods are applicable to line curve matching in stereo and trinocular rigs and as a starting point for line curve matching through monocular image sequences

mixture models for estimating the size of a closed population when capture rates vary among individuals nous developpons une parametrisation du melange de lois beta et binomiale qui fournit un cadre inferentiel approprie pour estimer l effectif d une population fermee lorsque les probabilites de capture ou de detection varient entre individus nous ajustons trois classes de modeles de melange beta binomiale logistique normale et modele a classes latentes d une part a des donnees de recapture de lievres d amerique pour en estimer l abondance et d autre part a des comptages d especes d oiseaux pour estimer la richesse specifique dans les deux jeux de donnees les taux de detection varient davantage entre individus lievres ou especes qu entre occasions ou lieux de capture les estimateurs de l effectif de la population et de la richesse specifique sont sensibles aux hypotheses faites sur la distribution sous jacente des probabilites individuelles de detection nous montrons par simulations que les outils habituels d evaluation de la qualite du modele comme la deviance ne sont pas fiables pour choisir entre des modeles de melanges celui qui fournit une inference correcte de l effectif de la population lorsqu elles existent des connaissances a priori sur les causes d heterogeneite des taux de detection doivent etre utilisees pour aider a choisir quelle classe de modeles de melanges utiliser pour l inference

reconstruction of general curves using factorization and bundle adjustment in this paper we extend the notion of affine shape introduced by sparr from finite point sets to curves the extension makes it possible to reconstruct 3d curves up to projective transformations from a number of their 2d projections we also extend the bundle adjustment technique from point features to curves the first step of the curve reconstruction algorithm is based on affine shape it is independent of choice of coordinates is robust does not rely on any preselected parameters and works for an arbitrary number of images in particular this means that except for a small set of curves e g a moving line a solution is given to the aperture problem of finding point correspondences between curves the second step takes advantage of any knowledge of measurement errors in the images this is possible by extending the bundle adjustment technique to curves finally experiments are performed on both synthetic and real data to show the performance and applicability of the algorithm

accurate and robust line segment extraction using minimum entropy with hough transform the hough transform is a popular technique used in the field of image processing and computer vision with a hough transform technique not only the normal angle and distance of a line but also the line segment s length and midpoint centroid can be extracted by analysing the voting distribution around a peak in the hough space in this paper a method based on minimum entropy analysis is proposed to extract the set of parameters of a line segment in each column around a peak in hough space the voting values specify probabilistic distributions the corresponding entropies and statistical means are computed the line segment s normal angle and length are simultaneously computed by fitting a quadratic polynomial curve to the voting entropies the line segment s midpoint and normal distance are computed by fitting and interpolating a linear curve to the voting means the proposed method is tested on simulated images for detection accuracy by providing comparative results experimental results on real world images verify the method as well the proposed method for line segment detection is both accurate and robust in the presence of quantization error background noise or pixel disturbances

otlines a novel line detection algorithm without the interference of smooth curves abstract we propose a novel line detection algorithm that avoids interpreting a smooth curve in an image as many straight segments the algorithm starts from a contiguous connected set of edge chains extracted by the edge drawing parameter free edpf algorithm such that a problem of line detection in the image space is transformed to a problem of line segments and circular arcs identified for each edge chain the core of our approach is the proposed orientation transformation ot algorithm based on principal component analysis hence our algorithm is named otlines with the ot algorithm each edge chain is not only decomposed into a series of straight line segments and smooth curve candidates at the estimated corners but is also mapped to a series of oblique lines and horizontal lines in a new space called the orientation space based on the results of the transformation line segments and circular arcs can be detected simultaneously in both the orientation and image spaces using principal component analysis the performance of our proposed algorithm is validated using a set of typical images we also compare our algorithm with existing algorithms our novel algorithm is very effective at segmenting the lines in synthetic and natural images no parameters in the proposed algorithm must be tuned during its application

open capture recapture models with heterogeneity ii jolly seber model summary estimation of abundance is important in both open and closed population capture recapture analysis but unmodeled heterogeneity of capture probability leads to negative bias in abundance estimates this article defines and develops a suite of open population capture recapture models using finite mixtures to model heterogeneity of capture and survival probabilities model comparisons and parameter estimation use likelihood based methods a real example is analyzed and simulations are used to check the main features of the heterogeneous models especially the quality of estimation of abundance survival recruitment and turnover the two major advances in this article are the provision of realistic abundance estimates that take account of heterogenetiy of capture and an appraisal of the amount of overestimation of survival arising from conditioning on the first capture when heterogeneity of survival is present

the quadrifocal variety abstract multi view geometry is reviewed from an algebraic geometry perspective and multi focal tensors are constructed as equivariant projections of the grassmannian a connection to the principal minor assignment problem is made by considering several flatlander cameras the ideal of the quadrifocal variety is computed up to degree 8 and partially in degree 9 using the representations of gl 3 4 in the polynomial ring on the space of 3 3 3 3 tensors further representation theoretic analysis gives a lower bound for the number of minimal generators

projective reconstruction of ellipses from multiple images this paper presents a new approach for reconstructing 3d ellipses including circles from a sequence of 2d images taken by uncalibrated cameras our strategy is to estimate an ellipse in 3d space by reconstructing n 5 3d points called representative points on it where the representative points are reconstructed by minimizing the distances from their projections to the measured 2d ellipses on different images i e 2d reprojection error this minimization problem is transformed into a sequence of minimization sub problems that can be readily solved by an algorithm which is guaranteed to converge to a local minimum of the 2d reprojection error our method can reconstruct multiple 3d ellipses simultaneously from multiple images and it readily handles images with missing and or partially occluded ellipses the proposed method is evaluated using both synthetic and real data

linear pose estimate from corresponding conics we propose here a new method to recover the orientation and position of a plane by matching at least three projections of a conic lying on the plane itself the procedure is based on rearranging the conic projection equations such that the non linear terms are eliminated it works with any kind of conic and does not require that the shape of the conic is known a priori the method was extensively tested using ellipses but it can also be used for hyperbolas and parabolas it was further applied to pairs of lines which can be viewed as a degenerate case of hyperbola without requiring the correspondence problem to be solved first critical configurations and numerical stability have been analyzed through simulations the accuracy of the proposed algorithm was compared to that of traditional algorithms and of a trinocular vision system using a set of landmarks

applications and extensions of chao s moment estimator for the size of a closed population summary this article revisits chao s 1989 biometrics 45 427 438 lower bound estimator for the size of a closed population in a mark recapture experiment where the capture probabilities vary between animals model mh first an extension of the lower bound to models featuring a time effect and heterogeneity in capture probabilities mth is proposed the biases of these lower bounds are shown to be a function of the heterogeneity parameter for several loglinear models for mth small sample bias reduction techniques for chao s lower bound estimator are also derived the application of the loglinear model underlying chao s estimator when heterogeneity has been detected in the primary periods of a robust design is then investigated a test for the null hypothesis that chao s loglinear model provides unbiased abundance estimators is provided the strategy of systematically using chao s loglinear model in the primary periods of a robust design where heterogeneity has been detected is investigated in a monte carlo experiment its impact on the estimation of the population sizes and of the survival rates is evaluated in a monte carlo experiment

invariant descriptors for 3d object recognition and pose invariant descriptors are shape descriptors that are unaffected by object pose by perspective projection or by the intrinsic parameters of the camera these descriptors can be constructed using the methods of invariant theory which are briefly surveyed a range of applications of invariant descriptors in 3d model based vision is demonstrated first a model based vision system that recognizes curved plane objects irrespective of their pose is demonstrated curves are not reduced to polyhedral approximations but are handled as objects in their own right models are generated directly from image data once objects have been recognized their pose can be computed invariant descriptors for 3d objects with plane faces are described all these ideas are demonstrated using images of real scenes the stability of a range of invariant descriptors to measurement error is treated in detail

estimating three dimensional motion parameters of a rigid planar patch we present a new direct method of estimating the three dimensional motion parameters of a rigid planar patch from two time sequential perspective views image frames first a set of eight pure parameters are defined these parameters can be determined uniquely from the two given image frames by solving a set of linear equations then the actual motion parameters are determined from these pure parameters by a method which requires the solution of a sixth order polynomial of one variable only and there exists a certain efficient algorithm for solving a sixth order polynomial aside from a scale factor for the translation parameters the number of real solutions never exceeds two in the special case of three dimensional translation the motion parameters can be expressed directly as some simple functions of the eight pure parameters thus only a few arithmetic operations are needed

conic reconstruction and correspondence from two views conics are widely accepted as one of the most fundamental image features together with points and line segments the problem of space reconstruction and correspondence of two conics from two views is addressed in this paper it is shown that there are two independent polynomial conditions on the corresponding pair of conics across two views given the relative orientation of the two views these two correspondence conditions are derived algebraically and one of them is shown to be fundamental in establishing the correspondences of conics a unified closed form solution is also developed for both projective reconstruction of conics in space from two uncalibrated camera views and metric reconstruction from two calibrated camera views experiments are conducted to demonstrate the discriminality of the correspondence conditions and the accuracy and stability of the reconstruction both for simulated and real images

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

simple capture recapture models permitting unequal catchability and variable sampling effort we consider two capture recapture models that imply that the logit of the probability of capture is an additive function of an animal catchability parameter and a parameter reflecting the sampling effort the models are special cases of the rasch model and satisfy the property of quasi symmetry one model is log linear and the other is a latent class model for the log linear model point and interval estimates of the population size are easily obtained using standard software such as glim

a class of latent markov models for capture recapture data allowing for time heterogeneity and behavior effects we propose an extension of the latent class model for the analysis of capture recapture data which allows us to take into account the effect of a capture on the behavior of a subject with respect to future captures the approach is based on the assumption that the variable indexing the latent class of a subject follows a markov chain with transition probabilities depending on the previous capture history several constraints are allowed on these transition probabilities and on the parameters of the conditional distribution of the capture configuration given the latent process we also allow for the presence of discrete explanatory variables which may affect the parameters of the latent process to estimate the resulting models we rely on the conditional maximum likelihood approach and for this aim we outline an em algorithm we also give some simple rules for point and interval estimation of the population size the approach is illustrated by applying it to two data sets concerning small mammal populations

on identifiability in capture recapture models we study the issue of identifiability of mixture models in the context of capture recapture abundance estimation for closed populations such models are used to take account of individual heterogeneity in capture probabilities but their validity was recently questioned by link 2003 biometrics 59 1123 1130 on the basis of their nonidentifiability we give a general criterion for identifiability of the mixing distribution and apply it to establish identifiability within families of mixing distributions that are commonly used in this context including finite and beta mixtures our analysis covers binomial and geometrically distributed outcomes in an example we highlight the difference between the identifiability issue considered here and that in classical binomial mixture models

a theory of self calibration of a moving camera there is a close connection between the calibration of a single camera and the epipolar transformation obtained when the camera undergoes a displacement the epipolar transformation imposes two algebraic constraints on the camera calibration if two epipolar transformations arising from different camera displacements are available then the compatible camera calibrations are parameterized by an algebraic curve of genus four the curve can be represented either by a space curve of degree seven contained in the intersection of two cubic surfaces or by a curve of degree six in the dual of the image plane the curve in the dual plane has one singular point of order three and three singular points of order two if three epipolar transformations are available then two curves of degree six can be obtained in the dual plane such that one of the real intersections of the two yields the correct camera calibration the two curves have a common singular point of order three experimental results are given to demonstrate the feasibility of camera calibration based on the epipolar transformation the real intersections of the two dual curves are found by locating the zeros of a function defined on the interval 0 2 the intersection yielding the correct camera calibration is picked out by referring back to the three epipolar transformations

low risk population size estimates in the presence of capture heterogeneity summary population estimation methods are used for estimating the size of a population from samples of individuals in many applications the probability of being observed in the sample varies across individuals resulting in sampling bias we show that in this setting estimators of the population size have high and sometimes infinite risk leading to large uncertainty in the population size as an alternative we propose estimating the population of individuals with observation probability exceeding a small threshold we show that estimators of this quantity have lower risk than estimators of the total population size the proposed approach is shown empirically to result in large reductions in mean squared error in a common model for capture recapture population estimation with heterogeneous capture probabilities

unified maximum likelihood estimates for closed capture recapture models using mixtures summary agresti 1994 biometrics50 494 500 and norris and pollock 1996a biometrics52 639 649 suggested using methods of finite mixtures to partition the animals in a closed capture recapture experiment into two or more groups with relatively homogeneous capture probabilities this enabled them to fit the models mh mbh norris and pollock and mth agresti of otis et al 1978 wildlife monographs62 1 135 in this article finite mixture partitions of animals and or samples are used to give a unified linear logistic framework for fitting all eight models of otis et al by maximum likelihood likelihood ratio tests are available for model comparisons for many data sets a simple dichotomy of animals is enough to substantially correct for heterogeneity induced bias in the estimation of population size although there is the option of fitting more than two groups if the data warrant it

a contour based recovery of image flow iterative transformation method the authors present an iterative algorithm for the recovery of 2 d motion i e for the determination of a transformation that maps one image onto another the local ambiguity in measuring the motion of contour segments the aperture problem implies a reliance on measurements along the normal direction since the measured normal flow does not agree with the actual normal flow the full flow recovered from this erroneous flow also possesses substantial error and any attempt to recover the 3 d motion from such full flow fails the proposed method is based on the observation that a polynomial approximation of the image flow provides sufficient information for 3 d motion computation the use of an explicit flow model results in improved normal flow estimates through an iterative process the authors discuss the adequacy and the convergence of the algorithm the algorithm was tested on some synthetic and some simple natural time varying images the image flow recovered from this scheme is sufficiently accurate to be useful in 3 d structure and motion computation

interval estimation for mark recapture studies of closed populations textbooks continue to recommend the use of an asymptotic normal distribution to provide an interval estimate for the unknown size n of a closed population studied by a mark recapture experiment or multiple record system a likelihood interval approach is proposed and its implementation demonstrated for a range of models for such studies including all main effect and interaction models for incomplete contingency tables

the quadric reference surface theory and applications the conceptual component of this work is about reference surfaces which are the analogous to reference frames often used for shape representation purposes the theoretical component of this work involves the question of whether one can find a unique and simple mapping that aligns two arbitrary perspective views of an opaque textured quadric surface in 3d given i few corresponding points in the two views or ii the outline conic of the surface in one view only and few corresponding points in the two views the practical component of this work is concerned with applying the theoretical results as tools for the task of achieving full correspondence between views of arbitrary objects

a flexible ratio regression approach for zero truncated capture recapture counts capture recapture methods are used to estimate the size of a population of interest which is only partially observed in such studies each member of the population carries a count of the number of times it has been identified during the observational period in real life applications only positive counts are recorded and we get a truncated at zero observed distribution we need to use the truncated count distribution to estimate the number of unobserved units we consider ratios of neighboring count probabilities estimated by ratios of observed frequencies regardless of whether we have a zero truncated or an untruncated distribution rocchetti et al 2011 have shown that for densities in the katz family these ratios can be modeled by a regression approach and rocchetti et al 2014 have specialized the approach to the beta binomial distribution once the regression model has been estimated the unobserved frequency of zero counts can be simply derived the guiding principle is that it is often easier to find an appropriate regression model than a proper model for the count distribution however a full analysis of the connection between the regression model and the associated count distribution has been missing in this manuscript we fill the gap and show that the regression model approach leads under general conditions to a valid count distribution we also consider a wider class of regression models based on fractional polynomials the proposed approach is illustrated by analyzing various empirical applications and by means of a simulation study

noncombinatorial detection of regular repetitions under perspective skew we present a geometric framework for the efficient detection of regular repetitions of planar but not necessarily coplanar patterns at the heart of our system lie the fixed structures of the transformations that describe these regular configurations the approach detects a number of symmetric configurations that have traditionally been dealt with separately in that all configurations corresponding to planar homologies are detected these include important cases such as periodicities mirror symmetries and reflections about a point the approach can handle perspective distortions it avoids to get trapped in combinatorics through invariant based hashing for pattern matching and through hough transforms for the detection of fixed structures additional efficiency and robustness are obtained from the system s ability to reason about the consistency of multiple homologies the performance of the system is demonstrated with several examples

interpretation of conic motion and its applications the indeterminacy of conic motion is analyzed in terms of lie group theory it is shown that an image motion of a conic is associated with a group ofinvisible motions that do not cause a visible change of the conic all such groups are isomorphic to the group associated with a special conic called thestandard circle for which the group of invisible motions is the three dimensional lorentz group similar results are obtained forinvisible optical flows finally our analysis is extended toconic stereo the 3 d position and orientation of a conic in the scene are computed from two projections this algorithm also works with one camera if a circular pattern is projected from a light source

enclosure transform for interest point detection from speckle imagery we present a fast enclosure transform et to localize complex objects of interest from speckle imagery this approach explores the spatial confinement on regional features from a sparse image feature representation unrelated broken ridge features surrounding an object are organized collaboratively giving rise to the enclosureness of the object three enclosure likelihood measures are constructed consisting of the enclosure force potential energy and encloser count in the transform domain the local maxima manifest the locations of objects of interest for which only the intrinsic dimension is known a priori the discrete et algorithm is computationally efficient being on the order of o mn using n measuring distances across an image of m ridge pixels it involves easy and few parameter settings we demonstrate and assess the performance of et on the automatic detection of the prostate locations from supra pubic ultrasound images et yields superior results in terms of positive detection rate accuracy and coverage

a generalization of chao s estimator for covariate information this note generalizes chao s estimator of population size for closed capture recapture studies if covariates are available chao s estimator was developed under unobserved heterogeneity in which case it represents a lower bound of the population size if observed heterogeneity is available in form of covariates we show how this information can be used to reduce the bias of chao s estimator the key element in this development is the understanding and placement of chao s estimator in a truncated poisson likelihood it is shown that a truncated poisson likelihood with log link with all counts truncated besides ones and twos is equivalent to a binomial likelihood with logit link this enables the development of a generalized chao estimator as the estimated expected value of the frequency of zero counts under a truncated all counts truncated except ones and twos poisson regression model if the regression model accounts for the heterogeneity entirely the generalized chao estimator is asymptotically unbiased a simulation study illustrates the potential in gain of bias reduction comparisons of the generalized chao estimator with the homogeneous zero truncated poisson regression approach are supplied as well the method is applied to a surveillance study on the completeness of farm submissions in great britain

multiple view geometry of general algebraic curves we introduce a number of new results in the context of multi view geometry from general algebraic curves we start with the recovery of camera geometry from matching curves we first show how one can compute without any knowledge on the camera the homography induced by a single planar curve then we continue with the derivation of the extended kruppa s equations which are responsible for describing the epipolar constraint of two projections of a general algebraic curve as part of the derivation of those constraints we address the issue of dimension analysis and as a result establish the minimal number of algebraic curves required for a solution of the epipolar geometry as a function of their degree and genus we then establish new results on the reconstruction of general algebraic curves from multiple views we address three different representations of curves i the regular point representation in which we show that the reconstruction from two views of a curve of degree d admits two solutions one of degree d and the other of degree d d 1 moreover using this representation we address the problem of homography recovery for planar curves ii dual space representation tangents for which we derive a lower bound for the number of views necessary for reconstruction as a function of the curve degree and genus and iii a new representation to computer vision based on the set of lines meeting the curve which does not require any curve fitting in image space for which we also derive lower bounds for the number of views necessary for reconstruction as a function of curve degree alone