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

locating a changed segment in a sequence of bernoulli variables the theory underlying inferences about a single change point in a sequence of independent bernoulli variables is extended to the two change points problem where the distance between the two change points is known namely a changed segment both null and nonnull distributions of the log likelihood ratio for testing the hypothesis that there is no changed segment against the alternative that there is one of specified length are derived using recurrence equations the distribution of the maximum likelihood estimator of the location of the changed segment is derived

segmentation of range images as the search for geometric parametric models segmentation of range images has long been considered in computer vision as an important but extremely difficult problem in this paper we present a new paradigm for the segmentation of range images into piecewise continuous surfaces data aggregation is performed via model recovery in terms of variable order bi variate polynomials using iterative regression model recovery is initiated independently in regularly placed seed regions in the image all the recovered models are potential candidates for the final description of the data selection of the models is defined as a quadratic boolean problem and the solution is sought by the wta winner takes all technique which turns out to be a good compromise between the speed of computation and the accuracy of the solution the overall efficiency of the method is achieved by combining model recovery and model selection in an iterative way partial recovery of the models is followed by the selection optimization procedure and only the best models are allowed to develop further

two dimensional critical point configuration graphs the configuration of the critical points of a smooth function of two variables is studied under the assumption that the function is morse that is that all of its critical points are nondegenerate a critical point configuration graph cpcg is derived from the critical points ridge lines and course lines of the function then a result from the theory of critical points of morse functions is applied to obtain several constraints on the number and type of critical points that appear on cycles of a cpcg these constraints yield a catalog of equivalent cpcg cycles containing four entries the slope districts induced by a critical point configuration graph appear useful for describing the behavior of smooth functions of two variables such as surfaces images and the radius function of three dimensional symmetric axes

three dimensional shape description using the symmetric axis transform i theory blum s two dimensional shape description method based on the symmetric axis transform sat is generalized to three dimensions the method uniquely decomposes an object into a collection of sub objects each drawn from three separate but not completely independent primitive sets defined in the paper width primitives based on radius function properties axis primitives based on symmetric axis curvatures and boundary primitives based on boundary surface curvatures width primitives are themselves comprised of two components slope districts and curvature districts visualizing the radius function as if it were the height function of some mountainous terrain each slope district corresponds to a mountain face together with the valley below it curvature districts further partition each slope district into regions that are locally convex concave or saddle like similarly axis boundary primitives are regions of the symmetric surface where the symmetric surface boundary surfaces are locally convex concave or saddle like relations among the primitive sets are discussed

minimally selected p and other tests for a single abrupt changepoint in a binary sequence summary a novel changepoint statistic based on the minimum value over possible changepoint locations of fisher s exact test is introduced specific points in the exact distribution of the minimally selected fisher s value may be rapidly calculated as a lattice path counting problem via known recurrence methods the test is compared to the kolmogorov smirnov two sample test the maximally selected chi square and a likelihood ratio test the tests are applied to assessing recombination in genetic sequences of hiv

detection of random change point in one parameter exponential families abstract we consider a sequence x 1 x 2 x n of independent random variables which are susceptible to changing their distribution after the nt first observations where t is a random variable of a distribution known with support in 0 1 the object of this work is to detect the eventual change of distribution for that we study the performance of a test based on the statistic of log likelihood it shows that when the number of observations gets larger the distribution of the statistic log likelihood behaves like that of an affine function of the brownian motion this allows by using the concept of contiguity in the sense of lecam the evaluation of the asymptotic power function of the test

surface curvature as a measure of image texture methods from the theory of surfaces in differential geometry are applied to the gray tone intensity and absorbance surfaces defined by a digital image in particular the first fundamental form the second fundamental form the two principal curvatures the gaussian curvature and mean curvature from classical differential geometry are presented new curvatures are introduced which appear to be more appropriate for the purposes of image texture for each curvature a texture feature is generated these features are applied to biological cell nuclei and it is found that they are useful for purposes of discrimination

structure from motion using line correspondences a theory is presented for the computation of three dimensional motion and structure from dynamic imagery using only line correspondences the traditional approach of corresponding microfeatures interesting points highlights corners high curvature points etc is reviewed and its shortcomings are discussed then a theory is presented that describes a closed form solution to the motion and structure determination problem from line correspondences in three views the theory is compared with previous ones that are based on nonlinear equations and iterative methods

finding line segments by stick growing a method is described for extracting lineal features from an image using extended local information to provide robustness and sensitivity the method utilizes both gradient magnitude and direction information and incorporates explicit lineal and end stop terms these terms are combined nonlinearly to produce an energy landscape in which local minima correspond to lineal features called sticks that can be represented as line segments a hill climbing stick growing process is used to find these minima the method is compared to two others and found to have improved gap crossing characteristics

abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity critical point theorems and applications to some nonlinear problems with strong resonance at infinity p bartolo and v benci istituto di matematica applicata via re david x0 bari ital and istituto di analisi matematica palazzo ateneo l ia scolai 2 bari italy received in revised form 20 december 1952

a metric for line segments this correspondence presents a metric for describing line segments this metric measures how well two line segments can be replaced by a single longer one this depends for example on collinearity and nearness of the line segments the metric is constructed using a new technique using so called neighborhood functions the behavior of the metric depends on the neighborhood function chosen in this correspondence an appropriate choice for the case of line segments is presented the quality of the metric is verified by using it in a simple clustering algorithm that groups line segments found by an edge detection algorithm in an image the fact that the clustering algorithm can detect long linear structures in an image shows that the metric is a good measure for the groupability of line segments

a ground truth based vanishing point detection algorithm a bayesian probability based vanishing point detection algorithm is presented which introduces the use of multiple features and training with ground truth data to determine vanishing point locations the vanishing points of 352 images were manually identified to create ground truth data each intersection is assigned a probability of being coincident with a ground truth vanishing point based upon conditional probabilities of a number of features the results of this algorithm are demonstrated to be superior to the results of a similar algorithm where each intersection is considered to be of equal importance the advantage of this algorithm is that multiple features derived from ground truth training are used to determine vanishing point location

using angular dispersion of gradient direction for detecting edge ribbons edges in a scene generally project to smooth continuous curves nearly everywhere in the image which results in low angular deviation of the intensity gradients in small neighborhoods straddling edges angular deviation is shown to be a measure of snr a theoretical analysis of angular deviation arising due to independent and identically distributed n 0 sigma sup 2 random noise is presented angular deviation thresholds for neighborhood sizes from 3 3 to 11 11 pixels are determined both from this analysis and numerical examples the proposed gradient angular dispersion detection algorithm detects edge elements by comparing the measured angular deviation with values computed for the minimum acceptable snr low values of deviation violate the no edge hypothesis the algorithm is shown to make good use of the limited dynamic range of the imaging system the sensitivity and selectivity of the strategy are both shown to be high

existence of a nontrivial solution for a class of superquadratic elliptic problems abstract a nontrivial solution is obtained for a class of superquadratic elliptic problems by variational methods

likelihood ratio tests for a change in the multivariate normal mean abstract a sequence of independent multivariate normal vectors with equal but possibly unknown variance matrices are hypothesized to have equal mean vectors and we wish to test that the mean vectors have changed after an unknown point in the sequence the likelihood ratio test is based on the maximum hotelling t 2 for the sequences before and after the change point the main result is a conservative approximation for its null distribution based on an improved bonferroni inequality if the change is judged significant then further changes are estimated by splitting the two subsequences formed by the first change point the methods can also be used to test for a change in row probabilities of a contingency table allowing for extramultinomial variation the results are used to find changes in a set of geological data previously analyzed by chernoff 1973 by the faces method and to find changes in the frequencies of pronouns in the plays of shakespeare

motion and structure from line correspondences closed form solution uniqueness and optimization this work discusses estimating motion and structure parameters from line correspondences of a rigid scene the authors present a closed form solution to motion and structure parameters from line correspondences through three monocular perspective views the algorithm makes use of redundancy in the data to improve the accuracy of the solutions the uniqueness of the solution is established and necessary and sufficient conditions for degenerate spatial line configurations are given optimization has been employed to further improve the accuracy of the estimates in the presence of noise simulations have shown that the errors of the optimized estimates are close to the theoretical lower error bound

the power of likelihood ratio and cumulative sum tests for a change in a binomial probability summary a simple iterative procedure is found for the exact null and alternative distributions of likelihood ratio cumulative sum and related statistics for testing for a change in probability of a sequence of independent binomial random variables it is concluded that the likelihood ratio test is slightly less powerful than the cumulative sum test near the middle of the sequence but that the likelihood ratio test is much more powerful near the ends an example from epidemiology is used to illustrate the results under certain conditions the cumulative sum test is identical to a two sample kolmogorov smirnov test and so the iterative procedure can be used to find the null distribution of kolmogorov smirnov and related statistics

kronecker product graph matching abstract in this paper the interpolator based kronecker product graph matching ibkpgm algorithm for performing attributed graph matching is presented the ibkpgm algorithm is based on the kronecker product graph matching kpgm formulation this new formulation incorporates a general approach to a wide class of graph matching problems based on attributed graphs allowing the structure of the graphs to be based on multiple sets of attributes salient features of the ibkpgm algorithm are that no assumption is made about the adjacency structure of the graphs to be matched and that the explicit calculation of compatibility values between all vertices of the reference and input graphs as well as between all edges of the reference and input graphs are avoided

rank tests for changepoint problems summary we consider procedures based on quadratic form rank statistics to test for one or more changepoints in a series of independent observations models incorporating both smooth and abrupt changes are introduced various test statistics are suggested their asymptotic null distributions are derived and tables of significance points are given a monte carlo study shows that the asymptotic significance points are applicable to moderately sized samples

infinitely many solutions of a symmetric dirichlet problem here q is a bounded domain in r with smooth boundary and f i r is c and satisfies certain growth conditions if m 1 and f is an even function hence f r r is an odd function then ambrosetti and rabinowitz l 21 proved the existence of infinitely many weak solutions of d using a symmetric version of the mountain pass theorem a similar result is due to michalek 3 who considered the case where m 21 rm s c and f is invariant under a free action of the cyclic group z p on c here z p is considered as a subgroup of s c c acting essentially via scalar multiplication on c in this paper we want to investigate which kind of symmetries guarantee the existence of infinitely many solutions of d let g be a compact lie group and p g o m an orthogonal representation of g on lrm then g acts on irm via the map g x ir ir g u y gv p g v we write v for the space rm considered as a g space do there exist infinitely many solutions of d if f is invariant under this symmetry i e f gu f u for all g e g and u e v without further assumptions on p the answer to this question is no in general for example if p g id for all g e g then there is no symmetry at all and one cannot expect infinitely many solutions more generally one should exclude the existence of fixed points vg u e vi gu u for all g e g 0 our first result says that there exist infinitely many solutions of d if the following condition is satisfied

an algebraic method for detection and recognition of polyhedral objects from a single image abstract this paper proposes an algorithm to recognize rotated scaled or overlapping polyhedral objects using only one orthographic projection the procedure is not based on the numerical solution of nonlinear equations and does not require any a priori knowledge it is an algebraic method for testing whether a cluster of edges and vertices in a line drawing correspond to an orthographic view of a given 3d model it has the advantage of being based on simple algebraic equations which are easy to solve and do not require time consuming numerical procedures

pattern spectrum and multiscale shape representation the results of a study on multiscale shape description smoothing and representation are reported multiscale nonlinear smoothing filters are first developed using morphological opening and closings g matheron 1975 used openings and closings to obtain probabilistic size distributions of euclidean space sets continuous binary images these distributions are used to develop a concept of pattern spectrum a shape size descriptor a pattern spectrum is introduced for continuous graytone images and arbitrary multilevel signals as well as for discrete images by developing a discrete size family of patterns large jumps in the pattern spectrum at a certain scale indicate the existence of major protruding or intruding substructures of the signal at the scale an entropy like shape size complexity measure is also developed based on the pattern spectrum for shape representation a reduced morphological skeleton transform is introduced for discrete binary and graytone images this transform is a sequence of skeleton components sparse images which represent the original shape at various scales it is shown that the partially reconstructed images from the inverse transform on subsequences of skeleton components are the openings of the image at a scale determined by the number of eliminated components in addition two way correspondences are established among the degree of shape smoothing via multiscale openings or closings the pattern spectrum zero values and the elimination or nonexistence of skeleton components at certain scales

3d object classification using multi object kohonen networks the problem of three dimensional planar faced opaque object recognition from one single perspective view is addressed in this paper a view parameterization based on hough transform is described classification is accomplished by multiple multi object kohonen networks a new object grouping criterion has been investigated to assign disjoint subsets of objects to each kohonen network of the system on the basis of input space topology recognition tests are presented on both synthetic and real world 3d objects even in the presence of partial occlusion

extracting straight lines this paper presents a new approach to the extraction of straight lines in intensity images pixels are grouped into line support regions of similar gradient orientation and then the structure of the associated intensity surface is used to determine the location and properties of the edge the resulting regions and extracted edge parameters form a low level representation of the intensity variations in the image that can be used for a variety of purposes the algorithm appears to be more effective than previous techniques for two key reasons 1 the gradient orientation rather than gradient magnitude is used as the initial organizing criterion prior to the extraction of straight lines and 2 the global context of the intensity variations associated with a straight line is determined prior to any local decisions about participating edge elements

edge detection and linear feature extraction using a 2 d random field model the edge detection problem is posed as one of detecting step discontinuities in the observed correlated image using directional derivatives estimated with a random field model specifically the method consists of representing the pixels in a local window by a 2 d causal autoregressive ar model whose parameters are adaptively estimated using a recursive least squares algorithm the directional derivatives are functions of parameter estimates an edge is detected if the second derivative in the direction of the estimated maximum gradient is negatively sloped and the first directional derivative and a local estimate of variance satisfy some conditions because the ordered edge detector may not detect edges of all orientations well the image scanned in four different directions and the union of the four edge images is taken as the final output the performance of the edge detector is illustrated using synthetic and real images comparisons to other edge detectors are given a linear feature extractor that operates on the edges produced by the ar model is presented

advanced hough transform using a multilayer fractional fourier method the hough transform ht is a commonly used technique for the identification of straight lines in an image the hough transform can be equivalently computed using the radon transform rt by performing line detection in the frequency domain through use of central slice theorem in this research an advanced radon transform is developed using a multilayer fractional fourier transform a cartesian to polar mapping and 1 d inverse fourier transforms followed by peak detection in the sinogram the multilayer fractional fourier transform achieves a more accurate sampling in the frequency domain and requires no zero padding at the stage of cartesian to polar coordinate mapping our experiments were conducted on mix shape images noisy images mixed thickness lines and a large data set consisting of 751 000 handwritten chinese characters the experimental results have shown that our proposed method outperforms all known representative line detection methods based on the standard hough transform or the fourier transform

multiscale medial loci and their properties blum s medial axes have great strengths in principle in intuitively describing object shape in terms of a quasi hierarchy of figures but it is well known that derived from a boundary they are damagingly sensitive to detail in that boundary the development of notions of spatial scale has led to some definitions of multiscale medial axes different from the blum medial axis that considerably overcame the weakness three major multiscale medial axes have been proposed iteratively pruned trees of voronoi edges ogniewicz 1993 szekely 1996 naf 1996 shock loci of reaction diffusion equations kimia et al 1995 siddiqi and kimia 1996 and height ridges of medialness cores fritsch et al 1994 morse et al 1993 pizer et al 1998 these are different from the blum medial axis and each has different mathematical properties of generic branching and ending properties singular transitions and geometry of implied boundary and they have different strengths and weaknesses for computing object descriptions from images or from object boundaries these mathematical properties and computational abilities are laid out and compared and contrasted in this paper

analyzing image structure by multidimensional frequency modulation we develop a mathematical framework for quantifying and understanding multidimensional frequency modulations in digital images we begin with the widely accepted definition of the instantaneous frequency vector if as the gradient of the phase and define the instantaneous frequency gradient tensor ifgt as the tensor of component derivatives of the if vector frequency modulation bounds are derived and interpreted in terms of the eigendecomposition of the ifgt using the ifgt we derive the ordinary differential equations odes that describe image flowlines we study the diagonalization of the odes of multidimensional frequency modulation on the ifgt eigenvector coordinate system and suggest that separable transforms can be computed along these coordinates we illustrate these new methods of image pattern analysis on textured and fingerprint images we envision that this work will find value in applications involving the analysis of image textures that are nonstationary yet exhibit local regularity examples of such textures abound in nature

applications of local linking to critical point theory we prove the existence of nontrivial critical points of functionals with a local linking at 0 applications to elliptic boundary value problems and to hamiltonian systems are given c 1995 academic press inc

discrete active models and applications abstract optimization processes based on active models play central roles in many areas of computational vision as well as computational geometry unfortunately current models usually require highly complex and sophisticated mathematical machinery and at the same time they suffer from a number of limitations which impose restrictions on their applicability in this paper a simple class of discrete active models called migration processes mps is presented the processes are based on iterated averaging over neighborhoods defined by constant geodesic distance it is demonstrated that the mp model a system of self organizing active particles has a number of advantages over previous models both parametric active models snakes and implicit contour evolution models due to the generality of the mp model the process can be applied to derive natural solutions to a variety of optimization problems including defining minimal surface patches given their boundary curves finding shortest paths joining sets of points and decomposing objects into primitive parts

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

3d model retrieval using principal plane analysis and dynamic programming three dimensional models play an important role in many applications the problem is how to select the appropriate models from a 3d database rapidly and accurately in recent years a variety of shape representations statistical methods and geometric algorithms have been proposed for matching 3d shapes or models in this paper we propose a 3d shape representation scheme based on a combination of principal plane analysis and dynamic programming the proposed 3d shape representation scheme consists of three steps first a 3d model is transformed into a 2d image by projecting the vertices of the model onto its principal plane second the convex hall of the 2d shape of the model is further segmented into multiple disjoint triangles using dynamic programming finally for each triangle a projection score histogram and moments are extracted as the feature vectors for similarity searching experimental results showed the robustness of the proposed scheme which resists translation rotation scaling noise and destructive attacks the proposed 3d model retrieval method performs fairly well in retrieving models having similar characteristics from a database of 3d models

determining the geometry of boundaries of objects from medial data we consider a region in r2 or r3 with generic smooth boundary b and blum medial axis m on which is defined a multivalued radial vector field u from points x on m to the points of tangency of the sphere at x with b we introduce a radial shape operator srad and an edge shape operator se which measure how u bends along m these are not traditional differential geometric shape operators nonetheless we derive all local differential geometric invariants of b from these operators this allows us to define from m u a geometric medial map on m which corresponds via a radial map from m to b to the differential geometric properties of b the geometric medial map also includes a description of the relative geometry of b this is defined using the relative critical set of the radius function r on m this set consists of a network of curves on m which describe where b is thickest and thinnest it is computed using the covariant derivative of the tangential component of the unit radial vector field we further determine how these invariants are related to the differential geometric invariants of m and how these invariants change under deforming diffeomorphisms of m

robin problems with a general potential and a superlinear reaction abstract we consider semilinear robin problems driven by the negative laplacian plus an indefinite potential and with a superlinear reaction term which need not satisfy the ambrosetti rabinowitz condition we prove existence and multiplicity theorems producing also an infinity of smooth solutions using variational tools truncation and perturbation techniques and morse theory critical groups

multiplicity of solutions for a class of elliptic boundary value problems abstract in this paper we study the existence of infinitely many solutions for a class of elliptic boundary value problems the existence results include both superlinear case and an asymptotically linear case our arguments are based on a recently given new fountain theorem due to zou w zou variant fountain theorems and their applications manuscripta math 104 2001 343 358

multiple solutions for a class of semilinear elliptic equations with general potentials abstract in this paper we study the existence of infinitely many nontrivial solutions for a class of semilinear elliptic equations u a x u g x u in a bounded smooth domain of r n n 3 with the dirichlet boundary value where the primitive of the nonlinearity g is of superquadratic growth near infinity in u and the potential a is allowed to be sign changing recent results in the literature are generalized and significantly improved

boundary crossing probabilities and statistical applications abstract this paper surveys recent results involving boundary crossing probabilities and related statistical applications the first part is concerned with problems of sequential analysis especially repeated significance tests and their application to sequential clinical trials involving survival data the second part develops the probability theory motivated by the problems of part 1 a method for computing first passage distributions of brownian motion to linear boundaries is introduced and then modified to handle problems in discrete time and those involving nonlinear boundaries the third part is concerned with fixed sample statistical problems especially change point problems which involve boundary crossing probabilities examples are given of problems for which methods of part 2 appear adequate and of problems which require new methods

standing wave solutions for generalized quasilinear schrodinger equations with critical growth abstract we study the existence of standing wave solutions for generalized quasilinear schrodinger equations involving critical sobolev exponents we use the variational methods to obtain a nonexistence theorem and two existence results

new prospects in line detection by dynamic programming the detection of lines in satellite images has drawn a lot of attention within the last 15 years problems of resolution noise and image understanding are involved and one of the best methods developed so far is the f algorithm of fischler which achieves robustness rightness and rapidity like other methods of dynamic programming it consists of defining a cost which depends on local information then a summation minimization process in the image is performed the authors present herein a mathematical formalization of the f algorithm which allows them to extend the cost both to cliques of more than two points to deal with the contrast and to neighborhoods of size larger than one to take into account the curvature thus all the needed information contrast grey level curvature is synthesized in a unique cost function defined on the digital original image this cost is used to detect roads and valleys in satellite images spot

determining straight line correspondences from intensity images abstract this paper presents an algorithm for straight edge extraction from intensity images and an algorithm for straight line matching in the first part of the paper straight edge extraction is described image data are first processed by the operation of edge support focusing to remove unnecessary image details an edge support is formed in this process then straight edges are extracted from line support regions which are segmented from the edge support in the second part of this paper we describe straight line matching using a matching function which characterizes the similarity of edge lines of two images and is based on not only the geometrical relations of the lines but also the information from the intensity images a technique of two step matching is applied to reduce the cost of computation the motivation behind this paper is our work on motion estimation from line correspondences of sequential images where straight edge extraction and matching is an essential first step the output data of the algorithm can also be used for calibration of stereo camera setups the results of experiments using indoor and outdoor scene images are shown

structure and motion from straight line segments abstract a method to determine both the camera location and scene structure from image straight segment correspondences is presented the proposed method considers the finite segment length in order to use stronger constraints than do those that use the infinite line that supports the image segment the constraints between image segments involve a weak pairing between image segment midpoints this allows deviations of the midpoint only in the segment direction experimental results are presented of structure and motion computations from the image straight line segment matching using two real images

infinitely many solutions for a class of semilinear elliptic equations abstract in this paper we find some new conditions to ensure the existence of infinitely many nontrivial solutions for the dirichlet boundary value problems of the form u a x u g x u in a bounded smooth domain conditions s 1 s 3 in the present paper are somewhat weaker than the famous ambrosetti rabinowitz type superquadratic condition here we assume that the primitive of the nonlinearity g is either asymptotically quadratic or superquadratic as u

an error analysis for surface orientation from vanishing points given two parallel lines in a plane their images formed by central projection onto the viewing plane intersect at a vanishing point which provides a constraint on the orientation of the plane two such independent constraints define a vanishing line and thereby determine the orientation of the plane uniquely in order to effectively use this information an estimate of its accuracy must be incorporated in the approach suggested line directions and surface normal vectors are represented as points on a gaussian sphere and the error bounds are computed as regions on the sphere information from multiple vanishing points and surfaces is combined by intersecting the corresponding regions in addition constraints based on real world knowledge can be introduced to improve the accuracy some experimental results on natural images re presented to illustrate this method

three dimensional reconstruction of points and lines with unknown correspondence across images three dimensional reconstruction from a set of images is an important and difficult problem in computer vision in this paper we address the problem of determining image feature correspondences while simultaneously reconstructing the corresponding 3d features given the camera poses of disparate monocular views first two new affinity measures are presented that capture the degree to which candidate features from different images consistently represent the projection of the same 3d point or 3d line an affinity measure for point features in two different views is defined with respect to their distance from a hypothetical projected 3d pseudo intersection point similarly an affinity measure for 2d image line segments across three views is defined with respect to a 3d pseudo intersection line these affinity measures provide a foundation for determining unknown correspondences using weighted bipartite graphs representing candidate point and line matches across different images as a result of this graph representation a standard graph theoretic algorithm can provide an optimal simultaneous matching and triangulation of points across two views and lines across three views experimental results on synthetic and real data demonstrate the effectiveness of the approach

a martingale approach to the changepoint problem abstract the changepoint problem for a binary sequence is considered a test statistic based on recursive residuals is compared to the test statistic suggested by pettitt the new test statistic has more interesting properties for use in sequential testing however neither of the two test statistics dominates the other sequential versions of the martingale based test forward and reverse are given and compared to other tests by means of a simulation study the reverse martingale tests detect a shift earlier if it is detected the price to be paid is a slightly higher probability of not detecting a shift

bayesian analysis of a poisson process with a change point summary a bayesian approach to estimation and hypothesis testing for a poisson process with a change point is developed and an example given

multiscale change point inference summary we introduce a new estimator the simultaneous multiscale change point estimator smuce for the change point problem in exponential family regression an unknown step function is estimated by minimizing the number of change points over the acceptance region of a multiscale test at a level the probability of overestimating the true number of change points k is controlled by the asymptotic null distribution of the multiscale test statistic further we derive exponential bounds for the probability of underestimating k by balancing these quantities will be chosen such that the probability of correctly estimating k is maximized all results are even non asymptotic for the normal case on the basis of these bounds we construct asymptotically honest confidence sets for the unknown step function and its change points at the same time we obtain exponential bounds for estimating the change point locations which for example yield the minimax rate up to a log term finally the simultaneous multiscale change point estimator achieves the optimal detection rate of vanishing signals as n even for an unbounded number of change points we illustrate how dynamic programming techniques can be employed for efficient computation of estimators and confidence regions the performance of the multiscale approach proposed is illustrated by simulations and in two cutting edge applications from genetic engineering and photoemission spectroscopy

the cusum test of homogeneity with an application in spontaneous abortion epidemiology we test the hypothesis of homogeneity over time in the rate of an event with a modification of page s cumulative sum cusum procedure the modification draws on an indifference zone approach to testing that is well suited to the epidemiologic study of retrospective data we provide procedures for evaluating the significance level of the largest observed cusum value occurring in a sequence of fixed length we draw inferences unconditionally with a known baseline rate of the event and conditionally on observed margins with unknown baseline rate data collected over a five year period from one new york city hospital serve to illustrate the modified cusum test in a study of fluctuations in the proportions of chromosomally normal trisomic x monosomic and triploid spontaneous abortions

reeb graphs for shape analysis and applications reeb graphs are compact shape descriptors which convey topological information related to the level sets of a function defined on the shape their definition dates back to 1946 and finds its root in morse theory reeb graphs as shape descriptors have been proposed to solve different problems arising in computer graphics and nowadays they play a fundamental role in the field of computational topology for shape analysis this paper provides an overview of the mathematical properties of reeb graphs and reconstructs its history in the computer graphics context with an eye towards directions of future research

lsd a fast line segment detector with a false detection control we propose a linear time line segment detector that gives accurate results a controlled number of false detections and requires no parameter tuning this algorithm is tested and compared to state of the art algorithms on a wide set of natural images

correction to on testing trained vector quantizer codebooks this correspondence formally defines partial radon trans forms for functions of more than two dimensions it shows that a generalized projection slice theorem exists which connects planar and hy perplanar projections of a function to its fourier transform in addition a general theoretical framework is provided for carrying out dimensional backprojection reconstruction in a multistage fashion through the use of the partial radon transform

und unite and divide method in fourier and radon domains for line segment detection in this paper we extend our previously proposed line detection method to line segmentation using a so called unite and divide und approach the methodology includes two phases namely the union of spectra in the frequency domain and the division of the sinogram in radon space in the union phase given an image its sinogram is obtained by parallel 2d multilayer fourier transforms cartesian to polar mapping and 1d inverse fourier transform in the division phase the edges of butterfly wings in the neighborhood of every sinogram peak are firstly specified with each neighborhood area corresponding to a window in image space by applying the separated sinogram of each such windowed image we can extract the line segments the division phase identifies the edges of butterfly wings in the neighborhood of every sinogram peak such that each neighborhood area corresponds to a window in image space line segments are extracted by applying the separated sinogram of each windowed image our experiments are conducted on benchmark images and the results reveal that the und method yields higher accuracy has lower computational cost and is more robust to noise compared to existing state of the art methods

a robust line extraction method by unsupervised line clustering abstract this paper describes a new method of extracting straight lines based on unsupervised line clustering it is assumed that each line support region lsr in an image is composed of pixels that share similar gradient orientation values therefore by an appropriate partitioning of gradient space the sets of parallel lines can be more easily extracted previous works on partitioning gradient space however relied on ad hoc methods and cannot be used as reliable tools for the extraction of the number of clusters in gradient space in order to handle such a clustering issue the bhattacharyya distance is introduced to define a measure for cluster separability and thereafter to estimate the number of inherent clusters subsequent to the clustering stage each extracted line support region undergoes a consistency test to evaluate its validity in terms of uncertainty descriptors for the consistency test an entropy based line selection scheme is formulated and a theory from robust statistics is adopted the feasibility of the proposed line extraction method is assessed by considering the issue of vanishing point detection

singularities of principal direction fields from 3 d images generic singularities can provide position independent information about the qualitative shape of surfaces the authors determine the singularities of the principal direction fields of a surface its umbilic points from a computation of the index of the fields the authors present examples both for 3 d synthetic images to which noise has been added and for clinical magnetic resonance images

a method for shift rotation and scale invariant pattern recognition using the form and arrangement of pattern specific features abstract a new computer based method for visual pattern recognition is described the process extracts shape features from binary edge images represented in either real valued or discrete coordinates both separate and overlapping features are extracted maximizing their completeness and continuity without using templates or mathematical feature descriptions these features and their arrangement are encoded in a shift rotation and scale invariant manner and used to recognize incoming patterns from a set of previously encoded patterns stored in memory new patterns may be automatically classified and stored in memory allowing the system to learn and generalize without operator intervention testing shows the system to be completely shift rotation and scale invariant and insensitive to local image distortion

the likelihood ratio test for a change point in simple linear regression summary we consider likelihood ratio tests to detect a change point in simple linear regression a when the alternative specifies that only the intercept changes and b when the alternative permits the intercept and the slope to change approximations for the significance level are obtained under reasonably general assumptions about the empirical distribution of the independent variable the approximations are compared with simulations in order to assess their accuracy for the model in which only the intercept is allowed to change a confidence region for the change point and an approximate joint confidence region for the change point the difference in intercepts and the slope are obtained by inversion of the appropriate likelihood ratio tests

statistical method for detecting structural change in the growth process due to competition among individual trees and other exogenous factors that change the growth environment each tree grows following its own growth trend with some structural changes in growth over time in the present article a new method is proposed to detect a structural change in the growth process we formulate the method as a simple statistical test for signal detection without constructing any specific model for the structural change to evaluate the p value of the test the tube method is developed because the regular distribution theory is insufficient using two sets of tree diameter growth data sampled from planted forest stands of cryptomeria japonica in japan we conduct an analysis of identifying the effect of thinning on the growth process as a structural change our results demonstrate that the proposed method is useful to identify the structural change caused by thinning we also provide the properties of the method in terms of the size and power of the test

hierarchical shape description via the multiresolution symmetric axis transform a method is proposed that produces a shape description in the form of a hierarchy by scale of simple symmetric axis sequences an axis segment that is a child of another has smaller scale and is seen as a branch of its parent the scale value and parent child relationship are induced by following the symmetric axis under successive reduction of resolution the result in two or three dimensions is a figure rather than boundary oriented shape description that has natural segments and is insensitive to noise in the object description the general approach of hierarchy production by following a feature through successive resolution reduction will be presented as will methods of resolution reduction and computer implementation also the relation of this figure based shape description to those based on boundary curvature will be briefly discussed

edge expression based on tree structure abstract it is a difficult problem to construct the edge structure of an object from its defective line drawing after the low level image processing phase a tree structure edge expression is proposed in which the tree expresses the contiguous line segments and all the trees constitute a forest for the object some medium level processing algorithms such as line connecting pruning and appending are derived by using the tree structure experiments are conducted which show the advantages of the expression and corresponding algorithms

how easy is matching 2d line models using local search local search is a well established and highly effective method for solving complex combinatorial optimization problems here local search is adapted to solve difficult geometric matching problems matching is posed as the problem of finding the optimal many to many correspondence mapping between a line segment model and image line segments image data is assumed to be fragmented noisy and cluttered the algorithms presented have been used for robot navigation photo interpretation and scene understanding this paper explores how local search performs as model complexity increases image clutter increases and additional model instances are added to the image data expected run times to find optimal matches with 95 percent confidence are determined for 48 distinct problems involving six models nonlinear regression is used to estimate run time growth as a function of problem size both polynomial and exponential growth models are fit to the run time data for problems with random clutter the polynomial model fits better and growth is comparable to that for tree search for problems involving symmetric models and multiple model instances where tree search is exponential the polynomial growth model is superior to the exponential growth model for one search algorithm and comparable for another

structure from motion with line segments under relaxed endpoint constraints we present a novel structure from motion pipeline which estimates motion and wiry 3d structure from imaged line segments across multiple views although the position and orientation of line segments can be determined more accurately than point features the instability of their endpoints and the fact that lines are not constrained by epipolar geometry diverted most research focus away to point based methods in our approach we tackle the problem of instable endpoints by utilizing relaxed constraints on their positions both during matching and as well in the following bundle adjustment stage furthermore we gain efficiency in estimating trifocal image relations by decoupling rotation and translation to this end a novel linear solver for relative translation estimation given rotations from five line correspondences in three views is introduced extensive experiments on long image sequences show that our line based structure from motion pipeline advantageously complements point based methods giving more meaningful 3d representation for indoor scenarios

numerically efficient angle width offset and discontinuity determination of straight lines by the discrete fourier bilinear transformation algorithm we introduce a new method for determining the number of straight lines line angles offsets widths and discontinuities in complicated images in this method line angles are obtained by searching the peaks of a hybrid discrete fourier and bilinear transformed line angle spectrum numerical advantages and performance are demonstrated

early image representation using regions defined by maximum gradient paths between singular points abstract a representation for images is described that is intended to be interposed between the pixel data and marr s primal sketch the image is segmented into regions named slope districts which are defined by maximum gradient paths between singular points a rich data structure is formed containing the regions their boundary components overall attributes and relationships with their neighbours this representation provides a framework to simplify the interaction between bottom up and top down processes examples are given using simple grouping rules to construct more complex elements like those in the primal sketch