an investigation of the nature of parameterization for the hough transform a novel parameterization method for the hough transform is reported instead of the conventional non parametric form the parametric form is used and copies of the transformed shape are plotted on two dimensional slices of the hough space it is shown that the corresponding parameterization has uniform precision with respect to translation and cancels out the quantization uncertainty due to image digitization a problem of the hough transform is discovered which is due to non uniform discretized voting it is shown that the above class of parameterizations avoids the problem finally a particular solution of the parameterization scheme is described which is called the fourier parameterization it is shown that the parameterization has uniform precision with respect to the affine transformation

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

modification of hough transform for object recognition using a 2 dimensional array abstract in this paper a technique which transforms ballard s 4 dimensional 4d parameters x y s to a 2d format x1 y1 x2 y2 namely 2 point parameterization is introduced this technique leads to new voting and detection rules for object recognition using hough transform due to the 2 point parameterization technique three algorithms namely rotation invariant hough transform rht scale invariant hough transform sht and rotation scale invariant hough transform rsht are proposed for object recognition to handle 1 when the scale s is known and x y are unknown 2 when the orientation is known and x y s are unknown and 3 when all x y s are unknown these proposed methods require only a 2 dimensional array for the accumulator which greatly reduces the memory required in using hough transform for object recognition

shapes recognition using the straight line hough transform theory and generalization a shape matching technique based on the straight line hough transform slht is presented in the theta rho space the transform can be expressed as the sum of the translation term and the intrinsic term this formulation allows the translation rotation and intrinsic parameters of the curve to be easily decoupled a shape signature called the scalable translation invariant rotation to shifting stirs signature is obtained from the theta rho space by computing the distances between pairs of points having the same theta value this signature is invariant to translation and can be easily normalized and rotation in the image space corresponds to circular shifting of the signature matching two signatures only amounts to computing a 1d correlation the height and location of a peak if it exists indicate the similarity and orientation of the test object with respect to the reference object the location of the test object is obtained once the orientation is known by an inverse transform voting from the theta rho space to the x y plane

natural representations for straight lines and the hough transform on discrete arrays the grid of discrete sampled data points in a digital image supports a limited set of lines at angles and displacements natural to that grid the effect of this implicit line quantization on the parametrization of the hough transform is presented the function describing the discrete hough transforms line detection sensitivity is derived expressions for the orientation frequency and popularity of lines in the natural set are given the results obtained are of importance to data arrays of small size the distribution of lines in the natural set is also important as it determines the precision and reliability with which straight lines can be measured on a discrete imaging array from the natural line set concept a general a d slope offset straight line parametrization is developed for which the hough transform is compact and fast to compute and which is as easy to interpret as the class p theta parametrization

dispersion operators and resistant second order functional data analysis inferences related to the second order properties of functional data as expressed by covariance structure can become unreliable when the data are non gaussian or contain unusual observations in the functional setting it is often difficult to identify atypical observations as their distinguishing characteristics can be manifold but subtle in this paper we introduce the notion of a dispersion operator investigate its use in probing the second order structure of functional data and develop a test for comparing the second order characteristics of two functional samples that is resistant to atypical observations and departures from normality the proposed test is a regularized m test based on a spectrally truncated version of the hilbert schmidt norm of a score operator defined via the dispersion operator we derive the asymptotic distribution of the test statistic investigate the behaviour of the test in a simulation study and illustrate the method on a structural biology dataset

a hough transform based line recognition method utilizing both parameter space and image space hough transform ht is recognized as a powerful tool for graphic element extraction from images due to its global vision and robustness in noisy or degraded environment however the application of ht has been limited to small size images for a long time besides the well known heavy computation in the accumulation the peak detection and the line verification become much more time consuming for large size images another limitation is that most existing ht based line recognition methods are not able to detect line thickness which is essential to large size images usually engineering drawings we believe these limitations arise from that these methods only work on the ht parameter space this paper therefore proposes a new ht based line recognition method which utilizes both the ht parameter space and the image space the proposed method devises an image based gradient prediction to accelerate the accumulation introduces a boundary recorder to eliminate redundant analyses in the line verification and develops an image based line verification algorithm to detect line thickness and reduce false detections as well it also proposes to use pixel removal to avoid overlapping lines instead of rigidly suppressing the nxn neighborhood we perform experiments on real images with different sizes in terms of speed and detection accuracy the experimental results demonstrate the significant performance improvement especially for large size images

the adaptive hough transform we introduce the adaptive hough transform aht as an efficient way of implementing the hough transform ht method for the detection of 2 d shapes the aht uses a small accumulator array and the idea of a flexible iterative coarse to fine accumulation and search strategy to identify significant peaks in the hough parameter spaces the method is substantially superior to the standard ht implementation in both storage and computational requirements in this correspondence we illustrate the ideas of the aht by tackling the problem of identifying linear and circular segments in images by searching for clusters of evidence in 2 d parameter spaces we show that the method is robust to the addition of extraneous noise and can be used to analyze complex images containing more than one shape

use the fuzzy hough transform towards reduction of the precision uncertainty duality the hough transform is a popular method for detecting complex forms in digital images however the technique is not very robust since several parameters that determine the scope of the detection results such as quantization thresholds and intervals must first be defined in the present paper we propose to enhance shape detection with the hough transform through fuzzy analysis one chief drawback of the hough transform i e the uncertainty precision duality is thus reduced

using focus of attention with the hough transform for accurate line parameter estimation abstract in this paper we describe a hough transform algorithm for finding lines in an image that can have an order of magnitude denser sampling in both parameters of the parameter space without significant increase in required memory or overhead in cpu time by increasing the sampling density we determine the line parameters for each line segment much more accurately the method circumvents the problems of requiring large amounts of memory to store the accumulator array and is not significantly slower than other hough algorithms by using a focus of attention approach we illustrate the benefits that can be obtained on a wide variety of images and quantify the improvements in line parameter estimation by performing statistical tests we also discuss the benefits that can be obtained by algorithms attempting to locate higher level features in the image and determining the 3d model of the image scene

demiclosed principle and δ convergence theorems for total asymptotically nonexpansive mappings in cat 0 spaces abstract the purpose of this paper is to introduce the concept of total asymptotically nonexpansive mappings and to prove the demiclosed principle for this kind of mappings in cat 0 spaces as a consequence we obtain a convergence theorem of the krasnoselskii mann type iteration for total asymptotically nonexpansive mappings in this setting our results extend and improve the corresponding recent results announced by many authors

a hierarchical approach to feature extraction and grouping in this paper the problem of extracting and grouping image features from complex scenes is solved by a hierarchical approach based on two main processes voting and clustering voting is performed for assigning a score to both global and local features the score represents the evidential support provided by input data for the presence of a feature clustering aims at individuating a minimal set of significant local features by grouping together simpler correlated observations it is based on a spatial relation between simple observations on a fixed level i e the definition of a distance in an appropriate space as the multilevel structure of the system implies that input data for an intermediate level are outputs of the lower level voting can be seen as a functional representation of the part of relation between features at different abstraction levels the proposed approach has been tested on both synthetic and real images and compared with other existing feature grouping methods

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 nonparametric method for fitting a straight line to a noisy image in fitting a straight line to a noisy image the least squares method becomes highly unreliable either when the noise distribution is nonnormal or when it is contaminated by outliers the authors propose a nonparametric method the median of the intercepts to overcome these difficulties this method is free of assumptions about the noise distribution and insensitive to outliers and it does not require quantization of the parameter space thus unlike the hough transform its outcome does not depend on the bin size the method is efficient and its implementation does not involve practical difficulties such as local minima or poor convergence of iterative procedures

discretization errors in the hough transform abstract straight line segments in a two dimensional image can be detected with the hough transform by searching peaks in a parameter space the influence on the hough transform of the quantization of the parameter space the quantization of the image and the width of the line segment is investigated in this paper the hough transform was improved by o gorman and clowes by taking into account the gradient direction the resulting scatter of the peaks can be reduced by using a weighting function in the transform examples of asbestos preparations are given

nested analysis of variance with autocorrelated errors summary in this paper we consider the problem where there is a randomized experimental design with several successive time measurements on each experimental unit one approach to the analysis of such data is to treat time as the subplot treatment and to use a split plot analysis of variance alternatively the problem may be considered in a more general multivariate framework here we recognize the timeinduced correlations and apply an autoregressive time series modelling approach estimation and testing are addressed two examples are presented to illustrate the practicality of our procedure some extensions are also considered briefly frequently data arise from a randomized experimental design where several successive measurements over time are made on each experimental unit there are many examples such as the following i in medical trials observations may be taken on each subject at regular time intervals ii in wildlife radio telemetry studies the distance moved by each animal may be tracked during successive periods of a day iii in plant animal experiments observations may be taken on the same plant animal as it grows and changes over time in all cases there will be a correlation between observations taken on the same experimental unit at different time points it is also likely that there is a decay in the correlation with increasing time lags in other words observations on the same experimental unit which are close together should be more highly correlated than those that are far apart in time this is contrary to the assumption of constant correlation between all time points subplots within a unit whole plot made by the traditional split plot analysis an alternative approach is to consider a general multivariate analysis of variance manova model which assumes an arbitrary covariance matrix for the observations see timm 1980 however we believe that the multivariate model is overparametrized and also it cannot easily incorporate missing values therefore we consider a time series modelling approach to the problem which serves as a compromise we now present the time series model that we consider for analyzing such data we denote the variable under study by the letter y with two subscripts where the first subscript refers to the individual experimental units and the second subscript refers to the successive measurements for the particular individual we assume that n individuals are selected at random and that measurements are taken at ti consecutive time points on the ith individual we consider a linear model r

hypothesis testing a framework for analyzing and optimizing hough transform performance in this paper a formal quantitative approach to designing optimum hough transform ht algorithms is proposed this approach takes the view that a ht is a hypothesis testing method each sample in the ht array implements a test to determine whether a curve with the given parameters fits the edge point data this view allows the performance of ht algorithms to be quantified the power function which gives the probability of rejection as a function of the underlying parametric distribution of data points is shown to be the fundamentally important characteristic of ht behaviour attempting to make the power function narrow is a formal approach to optimizing ht performance to illustrate how this framework is useful the particular problem of line detection is discussed in detail it is shown that the hypothesis testing framework leads to a redefinition of the ht in which the values are a measure of the distribution of points around a curve rather than the number of points on a curve this change dramatically improves the sensitivity of the method to small structures the solution to many ht design problems can be posed within the framework including optimal quantizations and optimum sampling of the parameter space in this paper the authors consider the design of optimum i d filters which can be used to sharpen the peak structure in parameter space results on several real images illustrate the improvements obtained

hough transform modified by line connectivity and line thickness a modified hough transform based on a likelihood principle of connectivity and thickness is proposed for line detection it makes short as well as thick line segments easier to detect in a noisy image certain desirable properties of the new method are justified by theory and simulations

a fast digital radon transform an efficient means for evaluating the hough transform a fast digital radon transform based on recursively defined digital straight lines is described which has the sequential complexity of n 2 log n additions for an n x n image this transform can be used to evaluate the hough transform to detect straight lines in a digital image whilst a parallel implementation of the hough transform algorithm is difficult because of global memory access requirements the fast digital radon transform is vectorizable and therefore well suited for parallel computation the structure of the fast algorithm is shown to be quite similar to the fft algorithm for decimation in frequency it is demonstrated that even for sequential computation the fast radon transform is an attractive alternative to the classical hough transform algorithm

multiresolution hough transform an efficient method of detecting patterns in images a new multiresolution coarse to fine search algorithm for efficient computation of the hough transform is proposed the algorithm uses multiresolution images and parameter arrays logarithmic range reduction is proposed to achieve faster convergence discretization errors are taken into consideration when accumulating the parameter array this permits the use of a very simple peak detection algorithm comparative results using three peak detection methods are presented tests on synthetic and real world images show that the parameters converge rapidly toward the true value the errors in rho and theta as well as the computation time are much lower than those obtained by other methods since the multiresolution hough transform mht uses a simple peak detection algorithm the computation time will be significantly lower than other algorithms if the time for peak detection is also taken into account the algorithm can be generalized for patterns with any number of parameters

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

unbalanced repeated measures models with structured covariance matrices the question of how to analyze unbalanced or incomplete repeated measures data is a common problem facing analysts we address this problem through maximum likelihood analysis using a general linear model for expected responses and arbitrary structural models for the within subject covariances models that can be fit include standard univariate and multivariate models with incomplete data random effects models and models with time series and factor analytic error structures we describe newton raphson and fisher scoring algorithms for computing maximum likelihood estimates and generalized em algorithms for computing restricted and unrestricted maximum likelihood estimates an example fitting several models to a set of growth data is included

relative sensitivity of a family of closet point graphs in computer vision applications abstract various graph theoretic definitions of neighborhood have been used in the past in computer vision and clustering applications in this paper we study the properties of a set of four related closest point graphs using monte carlo methods i the delaunay triangulation dt and its dual voronoi tessellation ii the gabriel graph gg iii the relative neighborhood graph rng and iv the minimum spanning tree mst we examine the suitability of these graphs in the detection of structure in noisy images using the hough transform we also explore each graph s structural stability under random positional noise delaunay triangulation is shown to be the least sensitive to such noisy conditions

improvements and systolic implementation of the hough transformation for straight line detection abstract hough transformation ht is an efficient method to detect straight lines in digital pictures in the conventional ht pixel contiguity is not taken into account and this leads to the following drawbacks 1 actual length of line segments cannot be computed 2 colinear line segments cannot be distinguished and 3 very often false lines are detected and short lines go undetected this paper proposes a modified hough transformation which performs contiguity check in a simple and efficient way a systolic architecture that implements this modified transform is presented the systolic array takes the bit map of the binary picture as input and processes one row column of pixels concurrently the area time complexity of the proposed architecture is shown to be superior to the conventional sequential algorithm preliminary simulation results are presented

robust methods for testing the pattern of a single covariance matrix summary patterns for a single covariance matrix may be studied using likelihood ratio or quadratic form test statistics typically these tests have an asymptotic chi squared distribution when the data are normally distributed but the asymptotic distribution is sensitive to nonnormality this paper suggests two ways to robustify inference for patterned matrices i estimate the critical values of normal theory test statistics using a new bootstrap procedure which takes advantage of certain invariances under ho and ii modify the statistics so that an asymptotic chi squared distribution holds even under nonnormality

bootstrap methods for testing homogeneity of variances this article describes the use of bootstrap methods for the problem of testing homogeneity of variances when means are not assumed equal or known the methods are new in this context and allow the use of normal theory test statistics such as f s 2 1 s 2 2 without the normality assumption that is crucial for validity of critical values obtained from the f distribution both asymptotic analysis and monte carlo sampling show that the new resampling procedures compare favorably with older methods in terms of test validity and power

biometrika centenary nonparametrics summary contributions in biometrika to nonparametric statistics are surveyed with particular emphasis on more recent work it is argued that even in the journal s very early years it had interests in smoothing methods for density estimation and in techniques for nonparametric regression in addition to its more obvious focus on classical nonparametric statistics such as ranking methods biometrika s early involvement with permutation testing has links to its contemporary work on bootstrap methods emphases on different types of nonparametric statistics have evolved over time however a rapidly increasing proportion of the journal s pages is devoted to papers that include some use of nonparametric ideas or methods

on the inverse hough transform in this paper an inverse hough transform algorithm is proposed this algorithm reconstructs correctly the original image using only the data of the hough transform space and it is applicable to any binary image as a first application the inverse hough transform algorithm is used for straight line detection and filtering the lines are detected not just as continuous straight lines which is the case of the standard hough transform but as they really appear in the original image i e pixel by pixel to avoid the quantization effects in the hough transform space inversion conditions are defined which are associated only with the dimensions of the images experimental results indicate that the inverse hough transform algorithm is robust and accurate

a quadratic rate of asymptotic regularity for cat 0 spaces abstract in this paper we obtain a quadratic bound on the rate of asymptotic regularity for the krasnoselski mann iterations of nonexpansive mappings in cat 0 spaces whereas previous results guarantee only exponential bounds the method we use is to extend to the more general setting of uniformly convex hyperbolic spaces a quantitative version of a strengthening of groetsch s theorem obtained by kohlenbach using methods from mathematical logic so called proof mining

bartlett adjustments to the likelihood ratio statistic and the distribution of the maximum likelihood estimator for rather general parametric models a simple connection is established between the bartlett adjustment factor of the log likelihood ratio statistic and the normalizing constant c of the formula c i i 1 2l for the conditional distribution of a maximum likelihood estimator as applied to the full model and the model of the hypothesis tested this leads to a relatively simple demonstration that division of the likelihood ratio statistic by a suitable constant or estimated factor improves the chi squared approximation to its distribution various expressions for these quantities are discussed in particular for the case of a one dimensional parameter an approximation to the constants involved is derived which does not require integration over the sample space

perspective transformation invariant generalized hough transform for perspective planar shape detection and matching abstract in the real world most object shapes are perspectively transformed when imaged how to recognize or locate such shapes in images is interesting and important the conventional generalized hough transform ght is useful for detecting or locating translated two dimensional 2d planar shapes however it cannot be used for detecting perspectively transformed planar shapes a new version of the ght called perspective transformation invariant generalized hough transform ptight is proposed to remove this weakness the ptight is based on the use of a new perspective reference table that is built up by applying both forward and inverse perspective transformations on a given template shape image from all viewing directions and positions due to the use of the point spread function to express the perspective reference table the required dimensionality of the hough counting space hcs for the ptight is reduced to 2d after performing the ptight on an input image the peaks in the hcs whose values are larger than a threshold is picked out as the candidate locations of the perspective shape to be detected in the input images by performing an inverse ptight on the candidates one of the candidate locations whose corresponding shape matches best with the input shape is selected and the desired parameters of the perspective transformation can be obtained some experimental results are included to demonstrate the applicability of the proposed ptight

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

lim s theorems for multivalued mappings in cat 0 spaces let x be a complete cat 0 space we prove that if e is a nonempty bounded closed convex subset of x and t e k x a nonexpansive mapping satisfying the weakly inward condition i e there exists p e such that p 1 tx ie x x e 0 1 then t has a fixed point in banach spaces this is a result of lim on asymptotic centers and fixed points of nonexpansive mappings canad j math 32 1980 421 430 the related result for unbounded r trees is given

the vector gradient hough transform the paper presents a new transform called vector gradient hough transform for identifying elongated shapes in gray scale images this goal is achieved not only by collecting information on the edges of the objects but also by reconstructing their transversal profile of luminosity the main features of the new approach are related to its vector space formulation and the associated capability of exploiting all the vector information of the luminosity gradient

a note on fixed point sets in cat 0 spaces we show that the fixed point set of a quasi nonexpansive selfmap of a nonempty convex subset of a cat 0 space is always closed convex and contractible moreover we give a construction of a continuous selfmap of a cat 0 space whose fixed point set is prescribed

on the sensitivity of the hough transform for object recognition object recognition from sensory data involves in part determining the pose of a model with respect to a scene a common method for finding an object s pose is the generalized hough transform which accumulates evidence for possible coordinate transformations in a parameter space whose axes are the quantized transformation parameters large clusters of similar transformations in that space are taken as evidence of a correct match a theoretical analysis of the behavior of such methods is presented the authors derive bounds on the set of transformations consistent with each pairing of data and model features in the presence of noise and occlusion in the image bounds are provided on the likelihood of false peaks in the parameter space as a function of noise occlusion and tessellation effects it is argued that haphazardly applying such methods to complex recognition tasks is risky as the probability of false positives can be very high