segmentation and classification of range images the recognition of objects in three dimensional space is a desirable capability of a computer vision system range images which directly measure 3 d surface coordinates of a scene are well suited for this task in this paper we report a procedure to detect connected planar convex and concave surfaces of 3 d objects this is accomplished in three stages the first stage segments the range image into surface patches by a square error criterion clustering algorithm using surface points and associated surface normals the second stage classifies these patches as planar convex or concave based on a non parametric statistical test for trend curvature values and eigenvalue analysis in the final stage boundaries between adjacent surface patches are classified as crease or noncrease edges and this information is used to merge compatible patches to produce reasonable faces of the object s this procedure has been successfully applied to a large number of real and synthetic images four of which we present in this paper

fully automatic clustering system in this paper the fully automatic clustering system facs is presented it is a technique for clustering and vector quantization whose objective is the automatic calculation of the codebook of the right dimension the desired error or target being fixed at each iteration facs tries to improve the setting of the existing codewords and if necessary some elements are removed from or added to the codebook in order to save on the number of computations per iteration greedy techniques are adopted it has been demonstrated from a heuristic point of view that the number of the codewords determined by facs is very low and that the algorithm quickly converges toward the final solution

on the characterizations of cofinite complexes over affine curves and hypersurfaces abstract let a be a homomorphic image of a gorenstein ring of finite krull dimension j an ideal of a of dimension one and n a bounded below complex of a modules suppose that a is complete with respect to a j adic topology in this paper we prove that n is a j cofinite complex if and only if h i n is a j cofinite module for all i the same result is also proved for principal ideals j consequently for the fourth question given by r hartshorne cf 6 fourth question p 149 we obtain an answer over the ring on affine curves and hypersurfaces

cofiniteness of local cohomology modules for ideals of small dimension abstract let r be a commutative noetherian ring and let m be a non zero finitely generated r module let i be an ideal of r and t a non negative integer such that dim supp h i i m 1 for all i t it is shown that the r modules h i 0 m h i 1 m h i t 1 m are i cofinite and the r module hom r r i h i t m is finitely generated this immediately implies that if i has dimension one i e dim r i 1 then h i i m is i cofinite for all i 0 this is a generalization of the main results of delfino and marley d delfino t marley cofinite modules and local cohomology j pure appl algebra 121 1997 45 52 and yoshida k i yoshida cofiniteness of local cohomology modules for ideals of dimension one nagoya math j 147 1997 179 191 for an arbitrary noetherian ring r also we prove that if r is local and dim supp h i i m 2 for all i t then the r modules ext r j r i h i i m and hom r r i h i t m are weakly laskerian for all i t and all j 0 as a consequence it follows that the set of associated primes of h i i m is finite for all i 0 whenever dim r i 2

range image segmentation based on differential geometry a hybrid approach the authors describe a hybrid approach to the problem of image segmentation in range data analysis where hybrid refers to a combination of both region and edge based considerations the range image of 3 d objects is divided into surface primitives which are homogeneous in their intrinsic differential geometric properties and do not contain discontinuities in either depth of surface orientation the method is based on the computation of partial derivatives obtained by a selective local biquadratic surface fit then by computing the gaussian and mean curvatures an initial region gased segmentation is obtained in the form of a curvature sign map two additional initial edge based segmentations are also computed from the partial derivatives and depth values namely jump and roof edge maps the three image maps are then combined to produce the final segmentation experimental results obtained for both synthetic and real range data of polyhedral and curved objects are given

real time and automatic two class clustering by analytical formulas several feature preserving two class clustering methods are investigated in this paper by preserving certain features of the input data some formulas useful in calculating the two class representatives and population percentages are derived the derived formulas are expressed in general forms suitable for any dimensionality higher than two the complexities of the investigated methods are all of order n if the data size is n and hence are much faster than any other clustering method which uses n x n dissimilarity matrix additionally all investigated methods use no initial guesses experimental results are included to make a comparison among the four investigated methods so that only two methods are recommended further comparisons with the k means method and hierarchical clustering methods also are included the proposed feature preserving approach was found to be fast automatic and suitable for any field requiring fast high dimensional two class clustering

segmentation through variable order surface fitting the solution of the segmentation problem requires a mechanism for partitioning the image array into low level entities based on a model of the underlying image structure a piecewise smooth surface model for image data that possesses surface coherence properties is used to develop an algorithm that simultaneously segments a large class of images into regions of arbitrary shape and approximates image data with bivariate functions so that it is possible to compute a complete noiseless image reconstruction based on the extracted functions and regions surface curvature sign labeling provides an initial coarse image segmentation which is refined by an iterative region growing method based on variable order surface fitting experimental results show the algorithm s performance on six range images and three intensity images

geometric primitive extraction using a genetic algorithm extracting geometric primitives from geometric sensor data is an important problem in model based vision a minimal subset is the smallest number of points necessary to define a unique instance of a geometric primitive a genetic algorithm based on a minimal subset representation is used to perform primitive extraction it is shown that the genetic approach is an improvement over random search and is capable of extracting more complex primitives than the hough transform

on a characterization of cofinite complexes theorem 1 let a be a ring which is a homomorphic image of a gorenstein ring of finite krull dimension j an ideal of a suppose that a is complete with respect to a jadic topology let n be a complex of a modules in d a where d a is the derived category consisting of complexes bounded below if the ideal j is of dimension one then the complex n is j cofinite if and only if h i n is in m a j cof for all i where m a j cof is the category of j cofinite modules see definition 3 below theorem 2 let a and n be as in theorem 1 let j be an ideal of a if j is principal up to radical then the complex n is j cofinite if and only if h i n is in m a j cof for all i

a similarity based robust clustering method this paper presents an alternating optimization clustering procedure called a similarity based clustering method scm it is an effective and robust approach to clustering on the basis of a total similarity objective function related to the approximate density shape estimation we show that the data points in scm can self organize local optimal cluster number and volumes without using cluster validity functions or a variance covariance matrix the proposed clustering method is also robust to noise and outliers based on the influence function and gross error sensitivity analysis therefore scm exhibits three robust clustering characteristics 1 robust to the initialization cluster number and initial guesses 2 robust to cluster volumes ability to detect different volumes of clusters and 3 robust to noise and outliers several numerical data sets and actual data are used in the scm to show these good aspects the computational complexity of scm is also analyzed some experimental results of comparing the proposed scm with the existing methods show the superiority of the scm method

hierarchical image segmentation by multi dimensional clustering and orientation adaptive boundary refinement in this paper we present a new multi dimensional segmentation algorithm we propose an orientation adaptive boundary estimation process embedded in a multiresolution pyramidal structure that allows the use of different clustering procedures without spatial connectivity constraints the presence of noise in the feature space mainly produced by modeling errors causes a class overlap which can be reduced in a multiresolution pyramid at the coarsest resolution level the separation between the different classes is increased and the within class variance reduced thus at this level the classes can be obtained with different multi dimensional clustering algorithms without connectivity constraints small and scattered classes as well as isolated class labels are reassigned to their neighborhood by a process which guarantees the spatial connectivity the resolution is then increased by projecting down the class labels at each level the borders are improved by reassigning the boundary pixels to their spatially closest class however the class uncertainty astride the borders has first to be reduced and we propose to do this by means of orientation adaptive butterfly shaped filters this refinement process further eliminates spatially misclassified pixels produced by the unconstrained clustering experimental results show that similarly accurate boundaries are obtained with different clustering algorithms for various test images

template matching of binary targets in grey scale images a nonparametric approach this paper introduces a nonparametric similarity measure based on the kolmogorov smirnov ks statistic to be used in template matching problems where a target of binary characteristics is to be located in a grey scale image ks statistic yields the best expected value for a binary domain similarity measure if the threshold selection to binarize the image had been optimized to take into account the geometric constraints of the template there is however no need to actually binarize the image some good properties of a ks based similarity measure are exposed and compared with the corresponding properties of normalized correlation a practical algorithm to implement a template matching procedure based on the ks statistic is shown and its computing time is compared with normalized correlation a ks based similarity measure proves to be usually much faster computationally that normalized correlation finally some experimental results are shown

a novel scale invariant dynamic method for hierarchical clustering of data affected by measurement uncertainty abstract an enhanced technique for hierarchical agglomerative clustering is presented classical clusterings suffer from non uniqueness resulting from the adopted scaling of data and from the arbitrary choice of the function to measure the proximity between elements moreover most classical methods cannot account for the effect of measurement uncertainty on initial data when present to overcome these limitations the definition of a weighted asymmetric function is introduced to quantify the proximity between any two elements the data weighting depends dynamically on the degree of advancement of the clustering procedure the novel proximity measure is derived from a geometric approach to the clustering and it allows to both disengage the result from the data scaling and to indicate the robustness of a clustering against the measurement uncertainty of initial data the method applies to both flat and hierarchical clustering maintaining the computational cost of the classical methods

unsupervised fuzzy clustering with multi center clusters a new unsupervised fuzzy clustering algorithm is provided in this paper to cluster the data patterns without a priori information about the number of clusters the initial guesses of the locations of the cluster centers or the initial guesses of the membership values are not necessary with the minimization of a new objective function cluster centers are generated one by one related centers are defined to belong to the same cluster multi centers are adopted to represent the non spherical shape of clusters thus the clustering algorithm with multi center clusters can handle non traditional curved clusters the proposed algorithm is tested on different data sets with a variety of cluster shapes cluster densities and number of points in each cluster also the results are compared with some other clustering algorithms to show the effectiveness of the algorithm moreover the designed unsupervised fuzzy clustering algorithm is applied to cluster the pixels in a color image to show the efficiency of the algorithm

dynamic quantization two adaptive data structures for multidimensional spaces two new data structures are defined for use in multidimensional histogramming their purpose is to cover a parameter space with a limited number of histogram bins so that fine precision is maintained where it is needed the original motivation for these data structures was to implement hough like transforms in high dimensional parameter spaces the two data structures share the ability to adapt to distributions that change with time

a swarm inspired projection algorithm in this paper a new data projection algorithm which was inspired by the foraging behaviors of doves is proposed we name the new data projection the swarm inspired projection sip algorithm the algorithm allows us to visually estimate the number of clusters existing in a data set based on the projection result we may then partition the data set into the corresponding number of clusters the sip algorithm regards each data pattern in a data set as a piece of crumb which will be sequentially tossed to a flock of doves on the ground the doves will adjust their physical positions to compete for crumbs gradually the flock of doves will be divided into several groups according to the distributions of the crumbs the formed groups will naturally correspond to the underlying data structures in the data set by viewing the scatter plot of the final positions of the doves we can estimate the number of clusters existing in the data set several data sets were used to demonstrate the effectiveness of the proposed sip algorithm

gaussian mixture density modeling decomposition and applications we present a new approach to the modeling and decomposition of gaussian mixtures by using robust statistical methods the mixture distribution is viewed as a contaminated gaussian density using this model and the model fitting mf estimator we propose a recursive algorithm called the gaussian mixture density decomposition gmdd algorithm for successively identifying each gaussian component in the mixture the proposed decomposition scheme has advantages that are desirable but lacking in most existing techniques in the gmdd algorithm the number of components does not need to be specified a priori the proportion of noisy data in the mixture can be large the parameter estimation of each component is virtually initial independent and the variability in the shape and size of the component densities in the mixture is taken into account gaussian mixture density modeling and decomposition has been widely applied in a variety of disciplines that require signal or waveform characterization for classification and recognition we apply the proposed gmdd algorithm to the identification and extraction of clusters and the estimation of unknown probability densities probability density estimation by identifying a decomposition using the gmdd algorithm that is a superposition of normal distributions is successfully applied to automated cell classification computer experiments using both real data and simulated data demonstrate the validity and power of the gmdd algorithm for various models and different noise assumptions

fuzzy and possibilistic shell clustering algorithms and their application to boundary detection and surface approximation ii shell clustering algorithms are ideally suited for computer vision tasks such as boundary detection and surface approximation particularly when the boundaries have jagged or scattered edges and when the range data is sparse this is because shell clustering is insensitive to local aberrations it can be performed directly in image space and unlike traditional approaches it does assume dense data and does not use additional features such as curvatures and surface normals the shell clustering algorithms introduced in part i of this paper assume that the number of clusters is known however which is not the case in many boundary detection and surface approximation applications this problem can be overcome by considering cluster validity we introduce a validity measure called surface density which is explicitly meant for the type of applications considered in this paper we show through theoretical derivations that surface density is relatively invariant to size and partiality incompleteness of the clusters we describe unsupervised clustering algorithms that use the surface density measure and other measures to determine the optimum number of shell clusters automatically and illustrate the application of the proposed algorithms to boundary detection in the case of intensity images and to surface approximation in the case of range images

unsupervised clustering and feature weighting based on generalized dirichlet mixture modeling abstract we propose a possibilistic approach for generalized dirichlet mixture parameter estimation data clustering and feature weighting the proposed algorithm called robust and unsupervised learning of finite generalized dirichlet mixture models rule gdm exploits a property of the generalized dirichlet distributions that transforms the data to make the features independent and follow beta distributions then it learns optimal relevance weights for each feature within each cluster this property makes rule gdm suitable for noisy and high dimensional feature spaces in addition rule gdm associates two types of memberships with each data sample the first one is the posterior probability and indicates how well a sample fits each estimated distribution the second membership represents the degree of typicality and is used to identify and discard noise points and outliers rule gdm minimizes one objective function which combines learning the two membership functions distribution parameters and the relevance weights for each feature within each distribution we also extend our algorithm to find the optimal number of clusters in an unsupervised and efficient way by exploiting some properties of the possibilistic membership function the performance of rule gdm is illustrated and compared to similar algorithms we use synthetic data to illustrate its robustness to noisy and high dimensional features we also compare our approach to other relevant algorithms using several standard data sets

cofiniteness of extension functors of cofinite modules abstract let r be a commutative noetherian ring i an ideal of r and let m and n be non zero r modules it is shown that the r modules ext r i n m are i cofinite for all i 0 whenever m is i cofinite and n is finitely generated of dimension d 2 also we prove that the r modules ext r i n m are i cofinite for all i 0 whenever n is finitely generated and m is i cofinite of dimension d 1 this immediately implies that if i has dimension one i e dim r i 1 then ext r i n h i i m is i cofinite for all i 0 and all finitely generated r modules m and n also we prove that if r is local then the r modules ext r i n m are i weakly cofinite for all i 0 whenever m is i cofinite and n is finitely generated of dimension d 3 finally it is shown that the r modules ext r i n m are i weakly cofinite for all i 0 whenever r is local n is finitely generated and m is i cofinite of dimension d 2

spectral and scattering theory for symbolic potentials of order zero the spectral and scattering theory is investigated for a generalization to scattering metrics on two dimensional compact manifolds with boundary of the class of smooth potentials on r2 which are homogeneous of degree zero near infinity the most complete results require the additional assumption that the restriction of the potential to the circle s at infinity be morse generalized eigenfunctions associated to the essential spectrum at non critical energies are shown to originate both at minima and maxima although the latter are not germane to the l2 spectral theory asymptotic completeness is shown both in the traditional l2 sense and in the sense of tempered distributions this leads to a definition of the scattering matrix the structure of which will be described in a future publication

mir an approach to robust clustering application to range image segmentation this paper describes an unsupervised region merging technique based on a novel robust statistical test the merging decision is derived from the mutual inlier ratio mir of adjacent regions this ratio is computed using robust regression techniques and a novel method to estimate the robust scale of the gaussian distribution a discrimination value to recognize identical gaussian distributions with the mir is derived theoretically as a function of the sizes of the compared sets the presented method to test distributions is compared with the established kolmogorov smirnov test and implemented into a segmentation algorithm for planar range images the iterative region growing technique is evaluated using an established framework for range image segmentation comparison involving 60 real range images the evaluation incorporates a comparison with four state of the art algorithms and gives an experimental demonstration of the need for robust methods capable of handling noisy data in real applications

asymptotics of reweighted estimators of multivariate location and scatter we investigate the asymptotic behavior ofa weighted sample mean and covariance where the weights are determined by the mahalanobis distances with respect to initial robust estimators we derive an explicit expansion for the weighted estimators from this expansion it can be seen that reweighting does not improve the rate ofconvergence ofthe initial estimators we also show that ifone uses smooth s estimators to determine the weights the weighted estimators are asymptotically normal finally we will compare the efficiency and local robustness of the reweighted s estimators with two other improvements of s estimators estimators and constrained m estimators

robust clustering methods a unified view clustering methods need to be robust if they are to be useful in practice in this paper we analyze several popular robust clustering methods and show that they have much in common we also establish a connection between fuzzy set theory and robust statistics and point out the similarities between robust clustering methods and statistical methods such as the weighted least squares technique the m estimator the minimum volume ellipsoid algorithm cooperative robust estimation minimization of probability of randomness and the epsilon contamination model by gleaning the common principles upon which the methods proposed in the literature are based we arrive at a unified view of robust clustering methods we define several general concepts that are useful in robust clustering state the robust clustering problem in terms of the defined concepts and propose generic algorithms and guidelines for clustering noisy data we also discuss why the generalized hough transform is a suboptimal solution to the robust clustering problem

robust clustering using outlier sparsity regularization notwithstanding the popularity of conventional clustering algorithms such as k means and probabilistic clustering their clustering results are sensitive to the presence of outliers in the data even a few outliers can compromise the ability of these algorithms to identify meaningful hidden structures rendering their outcome unreliable this paper develops robust clustering algorithms that not only aim to cluster the data but also to identify the outliers the novel approaches rely on the infrequent presence of outliers in the data which translates to sparsity in a judiciously chosen domain leveraging sparsity in the outlier domain outlier aware robust k means and probabilistic clustering approaches are proposed their novelty lies on identifying outliers while effecting sparsity in the outlier domain through carefully chosen regularization a block coordinate descent approach is developed to obtain iterative algorithms with convergence guarantees and small excess computational complexity with respect to their non robust counterparts kernelized versions of the robust clustering algorithms are also developed to efficiently handle high dimensional data identify nonlinearly separable clusters or even cluster objects that are not represented by vectors numerical tests on both synthetic and real datasets validate the performance and applicability of the novel algorithms

a bayesian segmentation methodology for parametric image models region based image segmentation methods require some criterion for determining when to merge regions this paper presents a novel approach by introducing a bayesian probability of homogeneity in a general statistical context the authors approach does not require parameter estimation and is therefore particularly beneficial for cases in which estimation based methods are most prone to error when little information is contained in some of the regions and therefore parameter estimates are unreliable the authors apply this formulation to three distinct parametric model families that have been used in past segmentation schemes implicit polynomial surfaces parametric polynomial surfaces and gaussian markov random fields the authors present results on a variety of real range and intensity images

color image segmentation an innovative approach in this paper we describe a color image segmentation system that performs color clustering in a color space and then color region segmentation in the image domain for color segmentation we developed a fuzzy clustering algorithm that iteratively generates color clusters using a uniquely defined fuzzy membership function and an objective function for clustering optimization the fuzzy membership function represents belief value of a color belonging to a color cluster and the mutual interference of neighboring clusters the region segmentation algorithm merges clusters in the image domain based on color similarity and spatial adjacency we developed three different methods for merging regions in the image domain unlike many existing clustering algorithms the image segmentation system does not require the knowledge about the number of the color clusters to be generated at each stage and the resolution of the color regions can be controlled by one single parameter the radius of a cluster the color image segmentation system has been implemented and tested on a variety of color images including satellite images car and face images the experiment results are presented and the performance of each algorithm in the segmentation system is analyzed the system has shown to be both effective and efficient

robust linear clustering structures are not well represented by points we present a method that searches for linear groups in the presence of outliers the method is based on the idea of impartial trimming we search for the best subsample containing a proportion 1 a of the data and the best k affine subspaces fitting to those non discarded observations by measuring discrepancies through orthogonal distances the population version of the sample problem is also considered we prove the existence of solutions for the sample and population problems together with their consistency a feasible algorithm for solving the sample problem is described as well finally some examples showing how the method proposed works in practice are provided

comparison of texture features based on gabor filters texture features that are based on the local power spectrum obtained by a bank of gabor filters are compared the features differ in the type of nonlinear post processing which is applied to the local power spectrum the following features are considered gabor energy complex moments and grating cell operator features the capability of the corresponding operators to produce distinct feature vector clusters for different textures is compared using two methods the fisher 1923 criterion and the classification result comparison both methods give consistent results the grating cell operator gives the best discrimination and segmentation results the texture detection capabilities of the operators and their robustness to nontexture features are also compared the grating cell operator is the only one that selectively responds only to texture and does not give false response to nontexture features such as object contours

robust line fitting in a noisy image by the method of moments the standard least squared distance method of fitting a line to a set of data points is known to be unreliable when the random noise in the input is significant compared with the data correlated to the line itself here we present a new statistical clustering method based on legendre moment theory and maximum entropy principle for line fitting in a noisy image we propose a new approach for estimating the underlying probability density function p d f of the data set the p d f is expanded in terms of legendre polynomials by means of the legendre moments the order of the expansion is selected according to the maximum entropy principle then the points corresponding to the maxima of the p d f will be the true points of the line to be extracted by a chaining algorithm this approach is directly generalized to multidimensional data the proposed algorithm was successfully applied to real and simulated noisy line images with comparison to some well known methods

object classification in 3 d images using alpha trimmed mean radial basis function network we propose a pattern classification based approach for simultaneous three dimensional 3 d object modeling and segmentation in image volumes the 3 d objects are described as a set of overlapping ellipsoids the segmentation relies on the geometrical model and graylevel statistics the characteristic parameters of the ellipsoids and of the graylevel statistics are embedded in a radial basis function rbf network and they are found by means of unsupervised training a new robust training algorithm for rbf networks based on spl alpha trimmed mean statistics is employed in this study the extension of the hough transform algorithm in the 3 d space by employing a spherical coordinate system is used for ellipsoidal center estimation we study the performance of the proposed algorithm and we present results when segmenting a stack of microscopy images

unmasking multivariate outliers and leverage points abstract detecting outliers in a multivariate point cloud is not trivial especially when there are several outliers the classical identification method does not always find them because it is based on the sample mean and covariance matrix which are themselves affected by the outliers that is how the outliers get masked to avoid the masking effect we propose to compute distances based on very robust estimates of location and covariance these robust distances are better suited to expose the outliers in the case of regression data the classical least squares approach masks outliers in a similar way also here the outliers may be unmasked by using a highly robust regression method finally a new display is proposed in which the robust regression residuals are plotted versus the robust distances this plot classifies the data into regular observations vertical outliers good leverage points and bad leverage points several examples are discussed

rederivation of the fuzzypossibilistic clustering objective function through bayesian inference unsupervised clustering of a set of datums into homogeneous groups is a primitive operation required in many signal and image processing applications in fact different incarnations and hybrids of fuzzy c means fcm and possibilistic c means pcm have been suggested which address additional requirements such as accepting weighted sets and being robust to the presence of outliers nevertheless arriving at a general framework which is independent of the datum model and the notion of homogeneity of a particular problem class is a challenge however this process has not been followed organically and clustering algorithms are generally based on exogenous objective functions which are heuristically engineered and are believed to lead to the satisfaction of a required behavior these techniques also commonly depend on regularization coefficients which are to be set prudently by the user or through separate processes in contrast in this work we utilize bayesian inference and derive a robustified objective function for a fuzzypossibilistic clustering algorithm by assuming a generic datum model and a generic notion of cluster homogeneity we utilize this model for the purpose of cluster validity assessment as well we emphasize the epistemological importance of the theoretical basis on which the developed methodology rests at the end of this paper we present experimental results to exhibit the utilization of the developed framework in the context of four different problem classes

two stage clustering via neural networks this paper presents a two stage approach that is effective for performing fast clustering first a competitive neural network cnn that can harmonize mean squared error and information entropy criteria is employed to exploit the substructure in the input data by identifying the local density centers a gravitation neural network gnn then takes the locations of these centers as initial weight vectors and undergoes an unsupervised update process to group the centers into clusters each node called gravi node in the gnn is associated with a finite attraction radius and would be attracted to a nearby centroid simultaneously during the update process creating the gravitation like behavior without incurring complicated computations this update process iterates until convergence and the converged centroid corresponds to a cluster compared to other clustering methods the proposed clustering scheme is free of initialization problem and does not need to pre specify the number of clusters the two stage approach is computationally efficient and has great flexibility in implementation a fully parallel hardware implementation is very possible

cofiniteness and associated primes of local cohomology modules abstract let r be a d dimensional regular local ring i an ideal of r and m a finitely generated r module of dimension n we prove that the set of associated primes of ext r i r i h i j m is finite for all i and j in the following cases a dim m 3 b dim r 4 c dim m im 2 and m satisfies serre s condition s n 3 d dim m im 3 ann r m 0 r is unramified and m satisfies s n 3 in these cases we also prove that h i i m p is i p cofinite for all but finitely many primes p of r additionally we show that if dim r i 2 and spec r i m i is disconnected then h i d 1 r is not i cofinite generalizing a result due to huneke and koh

robust clustering with applications in computer vision a clustering algorithm based on the minimum volume ellipsoid mve robust estimator is proposed the mve estimator identifies the least volume region containing h percent of the data points the clustering algorithm iteratively partitions the space into clusters without prior information about their number at each iteration the mve estimator is applied several times with values of h decreasing from 0 5 a cluster is hypothesized for each ellipsoid the shapes of these clusters are compared with shapes corresponding to a known unimodal distribution by the kolmogorov smirnov test the best fitting cluster is then removed from the space and a new iteration starts constrained random sampling keeps the computation low the clustering algorithm was successfully applied to several computer vision problems formulated in the feature space paradigm multithresholding of gray level images analysis of the hough space and range image segmentation

robust estimation for range image segmentation and reconstruction this correspondence presents a segmentation and fitting method using a new robust estimation technique we present a robust estimation method with high breakdown point which can tolerate more than 80 of outliers the method randomly samples appropriate range image points in the current processing region and solves equations determined by these points for parameters of selected primitive type from k samples we choose one set of sample points that determines a best fit equation for the largest homogeneous surface patch in the region this choice is made by measuring a residual consensus resc using a compressed histogram method which is effective at various noise levels after we get the best fit surface parameters the surface patch can be segmented from the region and the process is repeated until no pixel left the method segments the range image into planar and quadratic surfaces the resc method is a substantial improvement over the least median squares method by using histogram approach to inferring residual consensus a genetic algorithm is also incorporated to accelerate the random search

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

robust adaptive segmentation of range images we propose a novel image segmentation technique using the robust adaptive least kth order squares alks estimator which minimizes the kth order statistics of the squares of residuals the optimal value of k is determined from the data and the procedure detects the homogeneous surface patch representing the relative majority of the pixels the alks shows a better tolerance to structured outliers than other recently proposed similar techniques the performance of the new fully autonomous range image segmentation algorithm is compared to several other methods

a robust competitive clustering algorithm with applications in computer vision this paper addresses three major issues associated with conventional partitional clustering namely sensitivity to initialization difficulty in determining the number of clusters and sensitivity to noise and outliers the proposed robust competitive agglomeration rca algorithm starts with a large number of clusters to reduce the sensitivity to initialization and determines the actual number of clusters by a process of competitive agglomeration noise immunity is achieved by incorporating concepts from robust statistics into the algorithm rca assigns two different sets of weights for each data point the first set of constrained weights represents degrees of sharing and is used to create a competitive environment and to generate a fuzzy partition of the data set the second set corresponds to robust weights and is used to obtain robust estimates of the cluster prototypes by choosing an appropriate distance measure in the objective function rca can be used to find an unknown number of clusters of various shapes in noisy data sets as well as to fit an unknown number of parametric models simultaneously several examples such as clustering mixture decomposition line plane fitting segmentation of range images and estimation of motion parameters of multiple objects are shown

self organization of pulse coupled oscillators with application to clustering we introduce an efficient synchronization model that organizes a population of integrate and fire oscillators into stable and structured groups each oscillator fires synchronously with all the others within its group but the groups themselves fire with a constant phase difference the structure of the synchronized groups depends on the choice of the coupling function we show that by defining the interaction between oscillators according to the relative distance between them our model can be used as a general clustering algorithm unlike existing models our model incorporates techniques from relational and prototype based clustering methods and results in a clustering algorithm that is simple efficient robust unbiased by the size of the clusters and that can find an arbitrary number of clusters in addition to helping the model self organize into stable groups the synergy between clustering and synchronization reduces the computational complexity significantly the resulting clustering algorithm has several advantages over conventional clustering techniques in particular it can generate a nested sequence of partitions and it can determine the optimum number of clusters in an efficient manner moreover since our approach does not involve optimizing an objective function it is not sensitive to initialization and it can incorporate nonmetric similarity measures we illustrate the performance of our algorithms with several synthetic and real data sets

unmasking multivariate outliers and leverage points comment detecting outliers in a multivariate point cloud is not trivial especially when there are several outliers the classical identification method does not always find them because it is based on the sample mean and covariance matrix which are themselves affected by the outliers to avoid this masking effect we propose to compute distances based on very robust estimates of location and covariance in the case of regression data the outliers also may be unmasked by using a highly robust regression method a new display is proposed in which the robust regression residuals are plotted versus the robust distances