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Showing papers in "IEEE Transactions on Pattern Analysis and Machine Intelligence in 1991"


Journal ArticleDOI
TL;DR: A fast and flexible algorithm for computing watersheds in digital gray-scale images is introduced, based on an immersion process analogy, which is reported to be faster than any other watershed algorithm.
Abstract: A fast and flexible algorithm for computing watersheds in digital gray-scale images is introduced. A review of watersheds and related motion is first presented, and the major methods to determine watersheds are discussed. The algorithm is based on an immersion process analogy, in which the flooding of the water in the picture is efficiently simulated using of queue of pixel. It is described in detail provided in a pseudo C language. The accuracy of this algorithm is proven to be superior to that of the existing implementations, and it is shown that its adaptation to any kind of digital grid and its generalization to n-dimensional images (and even to graphs) are straightforward. The algorithm is reported to be faster than any other watershed algorithm. Applications of this algorithm with regard to picture segmentation are presented for magnetic resonance (MR) imagery and for digital elevation models. An example of 3-D watershed is also provided. >

4,983 citations


Journal ArticleDOI
TL;DR: The authors present an efficient architecture to synthesize filters of arbitrary orientations from linear combinations of basis filters, allowing one to adaptively steer a filter to any orientation, and to determine analytically the filter output as a function of orientation.
Abstract: The authors present an efficient architecture to synthesize filters of arbitrary orientations from linear combinations of basis filters, allowing one to adaptively steer a filter to any orientation, and to determine analytically the filter output as a function of orientation. Steerable filters may be designed in quadrature pairs to allow adaptive control over phase as well as orientation. The authors show how to design and steer the filters and present examples of their use in the analysis of orientation and phase, angularly adaptive filtering, edge detection, and shape from shading. One can also build a self-similar steerable pyramid representation. The same concepts can be generalized to the design of 3-D steerable filters. >

3,365 citations


Journal ArticleDOI
TL;DR: The authors present a fuzzy validity criterion based on a validity function which identifies compact and separate fuzzy c-partitions without assumptions as to the number of substructures inherent in the data.
Abstract: The authors present a fuzzy validity criterion based on a validity function which identifies compact and separate fuzzy c-partitions without assumptions as to the number of substructures inherent in the data. This function depends on the data set, geometric distance measure, distance between cluster centroids and more importantly on the fuzzy partition generated by any fuzzy algorithm used. The function is mathematically justified via its relationship to a well-defined hard clustering validity function, the separation index for which the condition of uniqueness has already been established. The performance of this validity function compares favorably to that of several others. The application of this validity function to color image segmentation in a computer color vision system for recognition of IC wafer defects which are otherwise impossible to detect using gray-scale image processing is discussed. >

3,237 citations


Journal ArticleDOI
TL;DR: The proposed theorem is a strict solution of the problem, and it always gives the correct transformation parameters even when the data is corrupted.
Abstract: In many applications of computer vision, the following problem is encountered. Two point patterns (sets of points) (x/sub i/) and (x/sub i/); i=1, 2, . . ., n are given in m-dimensional space, and the similarity transformation parameters (rotation, translation, and scaling) that give the least mean squared error between these point patterns are needed. Recently, K.S. Arun et al. (1987) and B.K.P. Horn et al. (1987) presented a solution of this problem. Their solution, however, sometimes fails to give a correct rotation matrix and gives a reflection instead when the data is severely corrupted. The proposed theorem is a strict solution of the problem, and it always gives the correct transformation parameters even when the data is corrupted. >

2,123 citations


Journal ArticleDOI
TL;DR: The effects of sample size on feature selection and error estimation for several types of classifiers are discussed and an emphasis is placed on giving practical advice to designers and users of statistical pattern recognition systems.
Abstract: The effects of sample size on feature selection and error estimation for several types of classifiers are discussed. The focus is on the two-class problem. Classifier design in the context of small design sample size is explored. The estimation of error rates under small test sample size is given. Sample size effects in feature selection are discussed. Recommendations for the choice of learning and test sample sizes are given. In addition to surveying prior work in this area, an emphasis is placed on giving practical advice to designers and users of statistical pattern recognition systems. >

1,323 citations


Journal ArticleDOI
Gabriel Taubin1
TL;DR: It is shown how this unified representation can be used for object recognition, object position estimation, and segmentation of objects into meaningful subobjects, that is, the detection of 'interest regions' that are more complex than high curvature regions and, hence, more useful as features for object Recognition.
Abstract: The author addresses the problem of parametric representation and estimation of complex planar curves in 2-D surfaces in 3-D, and nonplanar space curves in 3-D. Curves and surfaces can be defined either parametrically or implicitly, with the latter representation used here. A planar curve is the set of zeros of a smooth function of two variables x-y, a surface is the set of zeros of a smooth function of three variables x-y-z, and a space curve is the intersection of two surfaces, which are the set of zeros of two linearly independent smooth functions of three variables x-y-z For example, the surface of a complex object in 3-D can be represented as a subset of a single implicit surface, with similar results for planar and space curves. It is shown how this unified representation can be used for object recognition, object position estimation, and segmentation of objects into meaningful subobjects, that is, the detection of 'interest regions' that are more complex than high curvature regions and, hence, more useful as features for object recognition. >

1,155 citations


Journal ArticleDOI
TL;DR: Current methods of parameter solving are extended to handle objects with arbitrary curved surfaces and with any number of internal parameters representing articulation, variable dimensions, or surface deformations to allow model-based vision to be used for a much wider class of problems than was possible with previous methods.
Abstract: Model-based recognition and motion tracking depend upon the ability to solve for projection and model parameters that will best fit a 3-D model to matching 2-D image features. The author extends current methods of parameter solving to handle objects with arbitrary curved surfaces and with any number of internal parameters representing articulation, variable dimensions, or surface deformations. Numerical stabilization methods are developed that take account of inherent inaccuracies in the image measurements and allow useful solutions to be determined even when there are fewer matches than unknown parameters. The Levenberg-Marquardt method is used to always ensure convergence of the solution. These techniques allow model-based vision to be used for a much wider class of problems than was possible with previous methods. Their application is demonstrated for tracking the motion of curved, parameterized objects. >

1,000 citations


Journal ArticleDOI
TL;DR: An approach to visual object recognition in which a 3D object is represented by the linear combination of 2D images of the object is proposed and it is shown that for objects with sharp edges as well as with smooth bounding contours, the set of possible images of a given object is embedded in a linear space spanned by a small number of views.
Abstract: An approach to visual object recognition in which a 3D object is represented by the linear combination of 2D images of the object is proposed. It is shown that for objects with sharp edges as well as with smooth bounding contours, the set of possible images of a given object is embedded in a linear space spanned by a small number of views. For objects with sharp edges, the linear combination representation is exact. For objects with smooth boundaries, it is an approximation that often holds over a wide range of viewing angles. Rigid transformations (with or without scaling) can be distinguished from more general linear transformations of the object by testing certain constraints placed on the coefficients of the linear combinations. Three alternative methods of determining the transformation that matches a model to a given image are proposed. >

900 citations


Journal ArticleDOI
TL;DR: The authors formulate the deformable superquadrics which incorporate the global shape parameters of a conventional superellipsoid with the local degrees of freedom of a spline to form a novel class of dynamic models that can deform both locally and globally.
Abstract: The authors present a physically based approach to fitting complex three-dimensional shapes using a novel class of dynamic models that can deform both locally and globally. They formulate the deformable superquadrics which incorporate the global shape parameters of a conventional superellipsoid with the local degrees of freedom of a spline. The model's six global deformational degrees of freedom capture gross shape features from visual data and provide salient part descriptors for efficient indexing into a database of stored models. The local deformation parameters reconstruct the details of complex shapes that the global abstraction misses. The equations of motion which govern the behavior of deformable superquadrics make them responsive to externally applied forces. The authors fit models to visual data by transforming the data into forces and simulating the equations of motion through time to adjust the translational, rotational, and deformational degrees of freedom of the models. Model fitting experiments involving 2D monocular image data and 3D range data are presented. >

792 citations


Journal ArticleDOI
TL;DR: In this paper, the effect of surface roughness on the three primary components of a reflectance model is analyzed in detail, and the conditions that determine the validity of the model are clearly stated.
Abstract: Reflectance models based on physical optics and geometrical optics are studied. Specifically, the authors consider the Beckmann-Spizzichino (physical optics) model and the Torrance-Sparrow (geometrical optics) model. These two models were chosen because they have been reported to fit experimental data well. Each model is described in detail, and the conditions that determine the validity of the model are clearly stated. By studying reflectance curves predicted by the two models, the authors propose a reflectance framework comprising three components: the diffuse lobe, the specular lobe, and the specular spike. The effects of surface roughness on the three primary components are analyzed in detail. >

737 citations


Journal ArticleDOI
TL;DR: A method for comparing polygons that is a metric, invariant under translation, rotation, and change of scale, reasonably easy to compute, and intuitive is presented.
Abstract: A method for comparing polygons that is a metric, invariant under translation, rotation, and change of scale, reasonably easy to compute, and intuitive is presented. The method is based on the L/sub 2/ distance between the turning functions of the two polygons. It works for both convex and nonconvex polygons and runs in time O(mn log mn), where m is the number of vertices in one polygon and n is the number of vertices in the other. Some examples showing that the method produces answers that are intuitively reasonable are presented. >

Journal ArticleDOI
TL;DR: The theory is developed for the case when orientation computations are necessary at all local neighborhoods of the n-dimensional Euclidean space and a certainty measure, based on the error of the fit, is proposed.
Abstract: The problem of detection of orientation in finite dimensional Euclidean spaces is solved in the least squares sense. The theory is developed for the case when such orientation computations are necessary at all local neighborhoods of the n-dimensional Euclidean space. Detection of orientation is shown to correspond to fitting an axis or a plane to the Fourier transform of an n-dimensional structure. The solution of this problem is related to the solution of a well-known matrix eigenvalue problem. The computations can be performed in the spatial domain without actually doing a Fourier transformation. Along with the orientation estimate, a certainty measure, based on the error of the fit, is proposed. Two applications in image analysis are considered: texture segmentation and optical flow. The theory is verified by experiments which confirm accurate orientation estimates and reliable certainty measures in the presence of noise. The comparative results indicate that the theory produces algorithms computing robust texture features as well as optical flow. >

Journal ArticleDOI
TL;DR: In this article, an efficient algorithm for the continuous representation of a discrete signal in terms of B-splines and for interpolative signal reconstruction with an expansion factor m are described.
Abstract: Efficient algorithms for the continuous representation of a discrete signal in terms of B-splines (direct B-spline transform) and for interpolative signal reconstruction (indirect B-spline transform) with an expansion factor m are described. Expressions for the z-transforms of the sampled B-spline functions are determined and a convolution property of these kernels is established. It is shown that both the direct and indirect spline transforms involve linear operators that are space invariant and are implemented efficiently by linear filtering. Fast computational algorithms based on the recursive implementations of these filters are proposed. A B-spline interpolator can also be characterized in terms of its transfer function and its global impulse response (cardinal spline of order n). The case of the cubic spline is treated in greater detail. The present approach is compared with previous methods that are reexamined from a critical point of view. It is concluded that B-spline interpolation correctly applied does not result in a loss of image resolution and that this type of interpolation can be performed in a very efficient manner. >

Journal ArticleDOI
TL;DR: Deterministic approximations to Markov random field (MRF) models are derived and one of the models is shown to give in a natural way the graduated nonconvexity (GNC) algorithm proposed by A. Blake and A. Zisserman (1987).
Abstract: Deterministic approximations to Markov random field (MRF) models are derived. One of the models is shown to give in a natural way the graduated nonconvexity (GNC) algorithm proposed by A. Blake and A. Zisserman (1987). This model can be applied to smooth a field preserving its discontinuities. A class of more complex models is then proposed in order to deal with a variety of vision problems. All the theoretical results are obtained in the framework of statistical mechanics and mean field techniques. A parallel, iterative algorithm to solve the deterministic equations of the two models is presented, together with some experiments on synthetic and real images. >

Journal ArticleDOI
TL;DR: The authors present a closed-form, physically based solution for recovering a three-dimensional (3-D) solid model from collections of 3-D surface measurements that is overconstrained and unique except for rotational symmetries.
Abstract: The authors present a closed-form, physically based solution for recovering a three-dimensional (3-D) solid model from collections of 3-D surface measurements. Given a sufficient number of independent measurements, the solution is overconstrained and unique except for rotational symmetries. The proposed approach is based on the finite element method (FEM) and parametric solid modeling using implicit functions. This approach provides both the convenience of parametric modeling and the expressiveness of the physically based mesh formulation and, in addition, can provide great accuracy at physical simulation. A physically based object-recognition method that allows simple, closed-form comparisons of recovered 3-D solid models is presented. The performance of these methods is evaluated using both synthetic range data with various signal-to-noise ratios and using laser rangefinder data. >

Journal ArticleDOI
TL;DR: A model-based vision system that recognizes curved plane objects irrespective of their pose is demonstrated and the stability of a range of invariant descriptors to measurement error is treated in detail.
Abstract: Invariant descriptors are shape descriptors that are unaffected by object pose, by perspective projection, or by the intrinsic parameters of the camera. These descriptors can be constructed using the methods of invariant theory, which are briefly surveyed. A range of applications of invariant descriptors in 3D model-based vision is demonstrated. First, a model-based vision system that recognizes curved plane objects irrespective of their pose is demonstrated. Curves are not reduced to polyhedral approximations but are handled as objects in their own right. Models are generated directly from image data. Once objects have been recognized, their pose can be computed. Invariant descriptors for 3D objects with plane faces are described. All these ideas are demonstrated using images of real scenes. The stability of a range of invariant descriptors to measurement error is treated in detail. >

Journal ArticleDOI
TL;DR: The authors present a polarization reflectance model that uses the Fresnel reflection coefficients, which accurately predicts the magnitudes of polarization components of reflected light, and all the polarization-based methods presented follow from this model.
Abstract: The authors present a polarization reflectance model that uses the Fresnel reflection coefficients. This reflectance model accurately predicts the magnitudes of polarization components of reflected light, and all the polarization-based methods presented follow from this model. The authors demonstrate the capability of polarization-based methods to segment material surfaces according to varying levels of relative electrical conductivity, in particular distinguishing dielectrics, which are nonconducting, and metals, which are highly conductive. Polarization-based methods can provide cues for distinguishing different intensity-edge types arising from intrinsic light-dark or color variations, intensity edges caused by specularities, and intensity edges caused by occluding contours where the viewing direction becomes nearly orthogonal to surface normals. Analysis of reflected polarization components is also shown to enable the separation of diffuse and specular components of reflection, unobscuring intrinsic surface detail saturated by specular glare. Polarization-based methods used for constraining surface normals are discussed. >

Journal ArticleDOI
TL;DR: Different implementations of adaptive smoothing are presented, first on a serial machine, for which a multigrid algorithm is proposed to speed up the smoothing effect, then on a single instruction multiple data (SIMD) parallel machine such as the Connection Machine.
Abstract: A method to smooth a signal while preserving discontinuities is presented. This is achieved by repeatedly convolving the signal with a very small averaging mask weighted by a measure of the signal continuity at each point. Edge detection can be performed after a few iterations, and features extracted from the smoothed signal are correctly localized (hence, no tracking is needed). This last property allows the derivation of a scale-space representation of a signal using the adaptive smoothing parameter k as the scale dimension. The relation of this process to anisotropic diffusion is shown. A scheme to preserve higher-order discontinuities and results on range images is proposed. Different implementations of adaptive smoothing are presented, first on a serial machine, for which a multigrid algorithm is proposed to speed up the smoothing effect, then on a single instruction multiple data (SIMD) parallel machine such as the Connection Machine. Various applications of adaptive smoothing such as edge detection, range image feature extraction, corner detection, and stereo matching are discussed. >

Journal ArticleDOI
TL;DR: The results of the adaptive segmentation algorithm of Lakshamanan and Derin are compared with a simple nearest-neighbor classification scheme to show that if enough information is available, simple techniques could be used as alternatives to computationally expensive schemes.
Abstract: The problem of unsupervised segmentation of textured images is considered. The only explicit assumption made is that the intensity data can be modeled by a Gauss Markov random field (GMRF). The image is divided into a number of nonoverlapping regions and the GMRF parameters are computed from each of these regions. A simple clustering method is used to merge these regions. The parameters of the model estimated from the clustered segments are then used in two different schemes, one being all approximation to the maximum a posterior estimate of the labels and the other minimizing the percentage misclassification error. The proposed approach is contrasted with the algorithm of S. Lakshamanan and H. Derin (1989), which uses a simultaneous parameter estimation and segmentation scheme. The results of the adaptive segmentation algorithm of Lakshamanan and Derin are compared with a simple nearest-neighbor classification scheme to show that if enough information is available, simple techniques could be used as alternatives to computationally expensive schemes. >

Journal ArticleDOI
TL;DR: A multiple resolution algorithm is presented for segmenting images into regions with differing statistical behavior and an algorithm is developed for determining the number of statistically distinct regions in an image and estimating the parameters of those regions.
Abstract: A multiple resolution algorithm is presented for segmenting images into regions with differing statistical behavior. In addition, an algorithm is developed for determining the number of statistically distinct regions in an image and estimating the parameters of those regions. Both algorithms use a causal Gaussian autoregressive model to describe the mean, variance, and spatial correlation of the image textures. Together, the algorithms can be used to perform unsupervised texture segmentation. The multiple resolution segmentation algorithm first segments images at coarse resolution and then progresses to finer resolutions until individual pixels are classified. This method results in accurate segmentations and requires significantly less computation than some previously known methods. The field containing the classification of each pixel in the image is modeled as a Markov random field. Segmentation at each resolution is then performed by maximizing the a posteriori probability of this field subject to the resolution constraint. At each resolution, the a posteriori probability is maximized by a deterministic greedy algorithm which iteratively chooses the classification of individual pixels or pixel blocks. The unsupervised parameter estimation algorithm determines both the number of textures and their parameters by minimizing a global criterion based on the AIC information criterion. Clusters corresponding to the individual textures are formed by alternately estimating the cluster parameters and repartitioning the data into those clusters. Concurrently, the number of distinct textures is estimated by combining clusters until a minimum of the criterion is reached. >

Journal ArticleDOI
TL;DR: This model is based on the finite element method, but decouples the degrees of freedom by breaking down object motion into rigid and nonrigid vibration or deformation modes, resulting in an accurate representation for both rigid andnonrigid motion that has greatly reduced dimensionality.
Abstract: The authors introduce a physically correct model of elastic nonrigid motion. This model is based on the finite element method, but decouples the degrees of freedom by breaking down object motion into rigid and nonrigid vibration or deformation modes. The result is an accurate representation for both rigid and nonrigid motion that has greatly reduced dimensionality, capturing the intuition that nonrigid motion is normally coherent and not chaotic. Because of the small number of parameters involved, this representation is used to obtain accurate overstrained estimates of both rigid and nonrigid global motion. It is also shown that these estimates can be integrated over time by use of an extended Kalman filter, resulting in stable and accurate estimates of both three-dimensional shape and three-dimensional velocity. The formulation is then extended to include constrained nonrigid motion. Examples of tracking single nonrigid objects and multiple constrained objects are presented. >

Journal ArticleDOI
TL;DR: A robust approach to the recovery of shape from shading information is presented, and the algorithm is data driven, stable, updates the surface slope and height maps simultaneously, and significantly reduces the residual errors in irradiance and integrability terms.
Abstract: A robust approach to the recovery of shape from shading information is presented. Assuming uniform albedo and Lambertian surface for the imaging model, two methods for estimating the azimuth of the illuminant are presented. One is based on local estimates on smooth patches, and the other method uses shading information along image contours. The elevation of the illuminant and surface albedo are estimated from image statistics, taking into consideration the effect of self-shadowing. With the estimated reflectance map parameters, the authors then compute the surface shape using a procedure that implements the smoothness constraint by requiring the gradients of reconstructed density to be close to the gradients of the input image. The algorithm is data driven, stable, updates the surface slope and height maps simultaneously, and significantly reduces the residual errors in irradiance and integrability terms. A hierarchical implementation of the algorithm is presented. Typical results on synthetic and images are given to illustrate the usefulness of the approach. >

Journal ArticleDOI
TL;DR: The method of regularization is portrayed as providing a compromise between fidelity to the data and smoothness, with the tradeoff being determined by a scalar smoothing parameter.
Abstract: The method of regularization is portrayed as providing a compromise between fidelity to the data and smoothness, with the tradeoff being determined by a scalar smoothing parameter. Various ways of choosing this parameter are discussed in the case of quadratic regularization criteria. They are compared algebraically, and their statistical properties are comparatively assessed from the results of all extensive simulation study based on simple images. >

Journal ArticleDOI
TL;DR: The authors use the Gaussian Markov random field to model the texture image of nondefective fabric and generalize the test when the model parameters of the fabric are assumed to be unknown.
Abstract: The authors discuss the problem of textile fabric inspection using the visual textural properties of the fabric. The problem is to detect and locate the various kinds of defects that might be present in a given fabric sample based on an image of the fabric. Stochastic models are used to model the visual fabric texture. The authors use the Gaussian Markov random field to model the texture image of nondefective fabric. The inspection problem is cast as a statistical hypothesis testing problem on statistics derived from the model. The image of the fabric patch to be inspected is partitioned into nonoverlapping windows of size N*N where each window is classified as defective or nondefective based on a likelihood ratio test of size alpha . The test is recast in terms of the sufficient statistics associated with the model parameters. The sufficient statistics are easily computable for any sample. The authors generalize the test when the model parameters of the fabric are assumed to be unknown. >

Journal ArticleDOI
TL;DR: A modified Bayes decision rule is used to classify a given test image into one of C possible texture classes and the classification power of the method is demonstrated through experimental results on natural textures from the Brodatz album.
Abstract: Consideration is given to the problem of classifying a test textured image that is obtained from one of C possible parent texture classes, after possibly applying unknown rotation and scale changes to the parent texture. The training texture images (parent classes) are modeled by Gaussian Markov random fields (GMRFs). To classify a rotated and scaled test texture, the rotation and scale changes are incorporated in the texture model through an appropriate transformation of the power spectral density of the GMRF. For the rotated and scaled image, a bona fide likelihood function that shows the explicit dependence of the likelihood function on the GMRF parameters, as well as on the rotation and scale parameters, is derived. Although, in general, the scaled and/or rotated texture does not correspond to a finite-order GMRF, it is possible nonetheless to write down a likelihood function for the image data. The likelihood function of the discrete Fourier transform of the image data corresponds to that of a white nonstationary Gaussian random field, with the variance at each pixel (i,j) being a known function of the rotation, the scale, the GMRF model parameters, and (i,j). The variance is an explicit function of the appropriately sampled power spectral density of the GMRF. The estimation of the rotation and scale parameters is performed in the frequency domain by maximizing the likelihood function associated with the discrete Fourier transform of the image data. Cramer-Rao error bounds on the scale and rotation estimates are easily computed. A modified Bayes decision rule is used to classify a given test image into one of C possible texture classes. The classification power of the method is demonstrated through experimental results on natural textures from the Brodatz album. >

Journal ArticleDOI
TL;DR: A survey is presented of some of the surface reconstruction methods that can be found in the literature; the focus is on a small, recent, and important subset of the published reconstruction techniques.
Abstract: A survey is presented of some of the surface reconstruction methods that can be found in the literature; the focus is on a small, recent, and important subset of the published reconstruction techniques. The techniques are classified based on the surface representation used, implicit versus explicit functions. A study is made of the important aspects of the surface reconstruction techniques. One aspect is the viewpoint invariance of the methods. This is an important property if object recognition is the ultimate objective. The robustness of the various methods is examined. It is determined whether the parameter estimates are biased, and the sensitivity to obscuration is addressed. The latter two aspects are particularly important for fitting functions in the implicit form. A detailed description is given of a parametric reconstruction method for three-dimensional object surfaces that involves numeric grid generation techniques and variational principle formulations. This technique is invariant to rigid motion in dimensional space. >

Journal ArticleDOI
TL;DR: A clustering algorithm based on the minimum volume ellipsoid (MVE) robust estimator is proposed that 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.
Abstract: 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. >

Journal ArticleDOI
TL;DR: A revised fundamental theorem of moment invariants for pattern recognition which corrects the fundamental theorem proposed by M.K. Hu (1962) is presented, which yields three new invariants, which are additionally invariant to changes in the illumination of an image.
Abstract: A revised fundamental theorem of moment invariants for pattern recognition which corrects the fundamental theorem proposed by M.K. Hu (1962), is presented. The correction affects neither similitude (scale) nor rotation invariants derived using the original theorem, but it does affect features invariant to general linear transformations. Four of the latter invariants were presented originally by Hu. These are revised to take the correction to the fundamental theorem into account. Furthermore, these four invariants are combined to yield three new invariants, which are additionally invariant to changes in the illumination of an image. >

Journal ArticleDOI
TL;DR: An iterative algorithm that finds a locally optimal partition for an arbitrary loss function, in time linear in N for each iteration, is presented and it is proven that the globally optimal partition must satisfy a nearest neighbour condition using divergence as the distance measure.
Abstract: An iterative algorithm that finds a locally optimal partition for an arbitrary loss function, in time linear in N for each iteration is presented. The algorithm is a K-means-like clustering algorithm that uses as its distance measure a generalization of Kullback's information divergence. Moreover, it is proven that the globally optimal partition must satisfy a nearest neighbour condition using divergence as the distance measure. These results generalize similar results of L. Breiman et al. (1984) to an arbitrary number of classes or regression variables and to an arbitrary number of bills. Experimental results on a text-to-speech example are provided and additional applications of the algorithm, including the design of variable combinations, surrogate splits, composite nodes, and decision graphs, are suggested. >

Journal ArticleDOI
TL;DR: Numerical results on a waveform recognition problem are presented to support the theory and practical considerations suggest that the iterative free growing and pruning algorithm should perform better and require less computation than other widely used tree growing andPruning algorithms.
Abstract: A critical issue in classification tree design-obtaining right-sized trees, i.e. trees which neither underfit nor overfit the data-is addressed. Instead of stopping rules to halt partitioning, the approach of growing a large tree with pure terminal nodes and selectively pruning it back is used. A new efficient iterative method is proposed to grow and prune classification trees. This method divides the data sample into two subsets and iteratively grows a tree with one subset and prunes it with the other subset, successively interchanging the roles of the two subsets. The convergence and other properties of the algorithm are established. Theoretical and practical considerations suggest that the iterative free growing and pruning algorithm should perform better and require less computation than other widely used tree growing and pruning algorithms. Numerical results on a waveform recognition problem are presented to support this view. >