Showing papers in "IEEE Transactions on Pattern Analysis and Machine Intelligence in 1995"
TL;DR: Mean shift, a simple interactive procedure that shifts each data point to the average of data points in its neighborhood is generalized and analyzed and makes some k-means like clustering algorithms its special cases.
Abstract: Mean shift, a simple interactive procedure that shifts each data point to the average of data points in its neighborhood is generalized and analyzed in the paper. This generalization makes some k-means like clustering algorithms its special cases. It is shown that mean shift is a mode-seeking process on the surface constructed with a "shadow" kernal. For Gaussian kernels, mean shift is a gradient mapping. Convergence is studied for mean shift iterations. Cluster analysis if treated as a deterministic problem of finding a fixed point of mean shift that characterizes the data. Applications in clustering and Hough transform are demonstrated. Mean shift is also considered as an evolutionary strategy that performs multistart global optimization. >
3,924 citations
TL;DR: In this article, the authors proposed a shape model based on the Hamilton-Jacobi approach to shape modeling, which retains some of the attractive features of existing methods and overcomes some of their limitations.
Abstract: Shape modeling is an important constituent of computer vision as well as computer graphics research. Shape models aid the tasks of object representation and recognition. This paper presents a new approach to shape modeling which retains some of the attractive features of existing methods and overcomes some of their limitations. The authors' techniques can be applied to model arbitrarily complex shapes, which include shapes with significant protrusions, and to situations where no a priori assumption about the object's topology is made. A single instance of the authors' model, when presented with an image having more than one object of interest, has the ability to split freely to represent each object. This method is based on the ideas developed by Osher and Sethian (1988) to model propagating solid/liquid interfaces with curvature-dependent speeds. The interface (front) is a closed, nonintersecting, hypersurface flowing along its gradient field with constant speed or a speed that depends on the curvature. It is moved by solving a "Hamilton-Jacobi" type equation written for a function in which the interface is a particular level set. A speed term synthesized from the image is used to stop the interface in the vicinity of object boundaries. The resulting equation of motion is solved by employing entropy-satisfying upwind finite difference schemes. The authors present a variety of ways of computing the evolving front, including narrow bands, reinitializations, and different stopping criteria. The efficacy of the scheme is demonstrated with numerical experiments on some synthesized images and some low contrast medical images. >
3,039 citations
IBM1
TL;DR: In this paper, the authors proposed the use of low-dimensional, simple to compute distance measures between the color distributions, and showed that these are lower bounds on the histogram distance measure.
Abstract: In image retrieval based on color, the weighted distance between color histograms of two images, represented as a quadratic form, may be defined as a match measure. However, this distance measure is computationally expensive and it operates on high dimensional features (O(N)). We propose the use of low-dimensional, simple to compute distance measures between the color distributions, and show that these are lower bounds on the histogram distance measure. Results on color histogram matching in large image databases show that prefiltering with the simpler distance measures leads to significantly less time complexity because the quadratic histogram distance is now computed on a smaller set of images. The low-dimensional distance measure can also be used for indexing into the database. >
822 citations
TL;DR: This paper presents a methodology for evaluation of low-level image analysis methods, using binarization (two-level thresholding) as an example, and defines the performance of the character recognition module as the objective measure.
Abstract: This paper presents a methodology for evaluation of low-level image analysis methods, using binarization (two-level thresholding) as an example. Binarization of scanned gray scale images is the first step in most document image analysis systems. Selection of an appropriate binarization method for an input image domain is a difficult problem. Typically, a human expert evaluates the binarized images according to his/her visual criteria. However, to conduct an objective evaluation, one needs to investigate how well the subsequent image analysis steps will perform on the binarized image. We call this approach goal-directed evaluation, and it can be used to evaluate other low-level image processing methods as well. Our evaluation of binarization methods is in the context of digit recognition, so we define the performance of the character recognition module as the objective measure. Eleven different locally adaptive binarization methods were evaluated, and Niblack's method gave the best performance.
700 citations
TL;DR: Results of tests with the new color-constant-color-indexing algorithm show that it works very well even when the illumination varies spatially in its intensity and color, which circumvents the need for color constancy preprocessing.
Abstract: Objects can be recognized on the basis of their color alone by color indexing, a technique developed by Swain-Ballard (1991) which involves matching color-space histograms. Color indexing fails, however, when the incident illumination varies either spatially or spectrally. Although this limitation might be overcome by preprocessing with a color constancy algorithm, we instead propose histogramming color ratios. Since the ratios of color RGB triples from neighboring locations are relatively insensitive to changes in the incident illumination, this circumvents the need for color constancy preprocessing. Results of tests with the new color-constant-color-indexing algorithm on synthetic and real images show that it works very well even when the illumination varies spatially in its intensity and color. >
670 citations
TL;DR: A novel technique for the integration of multiple classifiers at an hybrid rank/measurement level is introduced using HyperBF networks and two different methods for the rejection of an unknown person are introduced.
Abstract: This paper presents a person identification system based on acoustic and visual features. The system is organized as a set of non-homogeneous classifiers whose outputs are integrated after a normalization step. In particular, two classifiers based on acoustic features and three based on visual ones provide data for an integration module whose performance is evaluated. A novel technique for the integration of multiple classifiers at an hybrid rank/measurement level is introduced using HyperBF networks. Two different methods for the rejection of an unknown person are introduced. The performance of the integrated system is shown to be superior to that of the acoustic and visual subsystems. The resulting identification system can be used to log personal access and, with minor modifications, as an identity verification system. >
663 citations
TL;DR: A modified box-counting approach is proposed to estimate the FD, in combination with feature smoothing in order to reduce spurious regions and to segment a scene into the desired number of classes, an unsupervised K-means like clustering approach is used.
Abstract: This paper deals with the problem of recognizing and segmenting textures in images. For this purpose the authors employ a technique based on the fractal dimension (FD) and the multi-fractal concept. Six FD features are based on the original image, the above average/high gray level image, the below average/low gray level image, the horizontally smoothed image, the vertically smoothed image, and the multi-fractal dimension of order two. A modified box-counting approach is proposed to estimate the FD, in combination with feature smoothing in order to reduce spurious regions. To segment a scene into the desired number of classes, an unsupervised K-means like clustering approach is used. Mosaics of various natural textures from the Brodatz album as well as microphotographs of thin sections of natural rocks are considered, and the segmentation results to show the efficiency of the technique. Supervised techniques such as minimum-distance and k-nearest neighbor classification are also considered. The results are compared with other techniques. >
650 citations
TL;DR: A method was developed which can aggregate the decisions obtained from individual classifiers and derive the best final decisions from the statistical point of view, and outperforms voting, Bayesian, and Dempster-Shafer approaches.
Abstract: For pattern recognition, when a single classifier cannot provide a decision which is 100 percent correct, multiple classifiers should be able to achieve higher accuracy. This is because group decisions are generally better than any individual's. Based on this concept, a method called the "Behavior-Knowledge Space Method" was developed, which can aggregate the decisions obtained from individual classifiers and derive the best final decisions from the statistical point of view. Experiments on 46451 samples of unconstrained handwritten numerals have shown that this method achieves very promising performances and outperforms voting, Bayesian, and Dempster-Shafer approaches. >
604 citations
TL;DR: Presents a formulation for recursive recovery of motion, pointwise structure, and focal length from feature correspondences tracked through an image sequence, yielding a stable and accurate estimation framework which applies uniformly to both true perspective and orthographic projection.
Abstract: Presents a formulation for recursive recovery of motion, pointwise structure, and focal length from feature correspondences tracked through an image sequence. In addition to adding focal length to the state vector, several representational improvements are made over earlier structure from motion formulations, yielding a stable and accurate estimation framework which applies uniformly to both true perspective and orthographic projection. Results on synthetic and real imagery illustrate the performance of the estimator. >
561 citations
TL;DR: The theory of probabilistic relaxation for matching features extracted from 2D images is developed, derive as limiting cases the various heuristic formulae used by researchers in matching problems, and state the conditions under which they apply.
Abstract: In this paper, we develop the theory of probabilistic relaxation for matching features extracted from 2D images, derive as limiting cases the various heuristic formulae used by researchers in matching problems, and state the conditions under which they apply, We successfully apply our theory to the problem of matching and recognizing aerial road network images based on road network models and to the problem of edge matching in a stereo pair. For this purpose, each line network is represented by an attributed relational graph where each node is a straight line segment characterized by certain attributes and related with every other node via a set of binary relations. >
545 citations
TL;DR: Improved formulation of modal matching utilizes a new type of finite element formulation that allows for an object's eigenmodes to be computed directly from available image information, and is applicable to data of any dimensionality.
Abstract: Modal matching is a new method for establishing correspondences and computing canonical descriptions. The method is based on the idea of describing objects in terms of generalized symmetries, as defined by each object's eigenmodes. The resulting modal description is used for object recognition and categorization, where shape similarities are expressed as the amounts of modal deformation energy needed to align the two objects. In general, modes provide a global-to-local ordering of shape deformation and thus allow for selecting which types of deformations are used in object alignment and comparison. In contrast to previous techniques, which required correspondence to be computed with an initial or prototype shape, modal matching utilizes a new type of finite element formulation that allows for an object's eigenmodes to be computed directly from available image information. This improved formulation provides greater generality and accuracy, and is applicable to data of any dimensionality. Correspondence results with 2D contour and point feature data are shown, and recognition experiments with 2D images of hand tools and airplanes are described. >
TL;DR: The information provided by the user's selected points is explored and an optimal method to detect contours which allows a segmentation of the image is applied, based on dynamic programming (DP), and applies to a wide variety of shapes.
Abstract: The problem of segmenting an image into separate regions and tracking them over time is one of the most significant problems in vision. Terzopoulos et al. (1987) proposed an approach to detect the contour regions of complex shapes, assuming a user selected initial contour not very far from the desired solution. We propose to further explore the information provided by the user's selected points and apply an optimal method to detect contours which allows a segmentation of the image. The method is based on dynamic programming (DP), and applies to a wide variety of shapes. It is exact and not iterative. We also consider a multiscale approach capable of speeding up the algorithm by a factor of 20, although at the expense of losing the guaranteed optimality characteristic. The problem of tracking and matching these contours is addressed. For tracking, the final contour obtained at one frame is sampled and used as initial points for the next frame. Then, the same DP process is applied. For matching, a novel strategy is proposed where the solution is a smooth displacement field in which unmatched regions are allowed while cross vectors are not. The algorithm is again based on DP and the optimal solution is guaranteed. We have demonstrated the algorithms on natural objects in a large spectrum of applications, including interactive segmentation and automatic tracking of the regions of interest in medical images. >
TL;DR: The effectiveness with which registration of range images can be accomplished makes this method attractive for many practical applications where surface models of 3D objects must be constructed.
Abstract: Concerns the problem of range image registration for the purpose of building surface models of 3D objects. The registration task involves finding the translation and rotation parameters which properly align overlapping views of the object so as to reconstruct from these partial surfaces, an integrated surface representation of the object. The registration task is expressed as an optimization problem. We define a function which measures the quality of the alignment between the partial surfaces contained in two range images as produced by a set of motion parameters. This function computes a sum of Euclidean distances from control points on one surfaces to corresponding points on the other. The strength of this approach is in the method used to determine point correspondences. It reverses the rangefinder calibration process, resulting in equations which can be used to directly compute the location of a point in a range image corresponding to an arbitrary point in 3D space. A stochastic optimization technique, very fast simulated reannealing (VFSR), is used to minimize the cost function. Dual-view registration experiments yielded excellent results in very reasonable time. A multiview registration experiment took a long time. A complete surface model was then constructed from the integration of multiple partial views. The effectiveness with which registration of range images can be accomplished makes this method attractive for many practical applications where surface models of 3D objects must be constructed. >
TL;DR: An unsupervised segmentation algorithm which uses Markov random field models for color textures which characterize a texture in terms of spatial interaction within each color plane and interaction between different color planes is presented.
Abstract: We present an unsupervised segmentation algorithm which uses Markov random field models for color textures. These models characterize a texture in terms of spatial interaction within each color plane and interaction between different color planes. The models are used by a segmentation algorithm based on agglomerative hierarchical clustering. At the heart of agglomerative clustering is a stepwise optimal merging process that at each iteration maximizes a global performance functional based on the conditional pseudolikelihood of the image. A test for stopping the clustering is applied based on rapid changes in the pseudolikelihood. We provide experimental results that illustrate the advantages of using color texture models and that demonstrate the performance of the segmentation algorithm on color images of natural scenes. Most of the processing during segmentation is local making the algorithm amenable to high performance parallel implementation. >
TL;DR: Two linear time algorithms for computing the Euclidean distance transform of a two-dimensional binary image are presented based on the construction and regular sampling of the Voronoi diagram whose sites consist of the unit pixels in the image.
Abstract: Two linear time (and hence asymptotically optimal) algorithms for computing the Euclidean distance transform of a two-dimensional binary image are presented. The algorithms are based on the construction and regular sampling of the Voronoi diagram whose sites consist of the unit (feature) pixels in the image. The first algorithm, which is of primarily theoretical interest, constructs the complete Voronoi diagram. The second, more practical, algorithm constructs the Voronoi diagram where it intersects the horizontal lines passing through the image pixel centers. Extensions to higher dimensional images and to other distance functions are also discussed. >
TL;DR: This paper presents an evaluation of eleven locally adaptive binarization methods for gray scale images with low contrast, variable background intensity and noise and Niblack's method with the addition of the postprocessing step of Yanowitz and Bruckstein's method (1989) performed the best and was also one of the fastest binarized methods.
Abstract: This paper presents an evaluation of eleven locally adaptive binarization methods for gray scale images with low contrast, variable background intensity and noise. Niblack's method (1986) with the addition of the postprocessing step of Yanowitz and Bruckstein's method (1989) added performed the best and was also one of the fastest binarization methods. >
TL;DR: An experimental comparison of shape classification methods based on autoregressive modeling and Fourier descriptors of closed contours shows better performance of Fourier-based methods, especially for images containing noise.
Abstract: An experimental comparison of shape classification methods based on autoregressive modeling and Fourier descriptors of closed contours is carried out. The performance is evaluated using two independent sets of data: images of letters and airplanes. Silhouette contours are extracted from non-occluded 2D objects rotated, scaled, and translated in 3D space. Several versions of both types of methods are implemented and tested systematically. The comparison clearly shows better performance of Fourier-based methods, especially for images containing noise. >
TL;DR: The authors consider grayscale images as 3D shapes, and use the symmetry distance to find the orientation of symmetric objects from their images, and to find locally symmetric regions in images.
Abstract: Symmetry is treated as a continuous feature and a continuous measure of distance from symmetry in shapes is defined. The symmetry distance (SD) of a shape is defined to be the minimum mean squared distance required to move points of the original shape in order to obtain a symmetrical shape. This general definition of a symmetry measure enables a comparison of the "amount" of symmetry of different shapes and the "amount" of different symmetries of a single shape. This measure is applicable to any type of symmetry in any dimension. The symmetry distance gives rise to a method of reconstructing symmetry of occluded shapes. The authors extend the method to deal with symmetries of noisy and fuzzy data. Finally, the authors consider grayscale images as 3D shapes, and use the symmetry distance to find the orientation of symmetric objects from their images, and to find locally symmetric regions in images.
TL;DR: A new method for recovering the three dimensional structure of a scene composed of straight line segments using the image data obtained from a moving camera using an objective function which measures the total squared distance in the image plane between the observed edge segments and the projections (perspective) of the reconstructed lines.
Abstract: This paper presents a new method for recovering the three dimensional structure of a scene composed of straight line segments using the image data obtained from a moving camera. The recovery algorithm is formulated in terms of an objective function which measures the total squared distance in the image plane between the observed edge segments and the projections (perspective) of the reconstructed lines. This objective function is minimized with respect to the line parameters and the camera positions to obtain an estimate for the structure of the scene. The effectiveness of this approach is demonstrated quantitatively through extensive simulations and qualitatively with actual image sequences. The implementation is being made publicly available. >
TL;DR: The trilinearity result is shown to be of much practical use in visual recognition by alignment-yielding a direct reprojection method that cuts through the computations of camera transformation, scene structure and epipolar geometry.
Abstract: In the general case, a trilinear relationship between three perspective views is shown to exist. The trilinearity result is shown to be of much practical use in visual recognition by alignment-yielding a direct reprojection method that cuts through the computations of camera transformation, scene structure and epipolar geometry. Moreover, the direct method is linear and sets a new lower theoretical bound on the minimal number of points that are required for a linear solution for the task of reprojection. The proof of the central result may be of further interest as it demonstrates certain regularities across homographics of the plane and introduces new view invariants. Experiments on simulated and real image data were conducted, including a comparative analysis with epipolar intersection and the linear combination methods, with results indicating a greater degree of robustness in practice and a higher level of performance in reprojection tasks. >
TL;DR: The feature-based optic flow field is segmented into clusters with affine internal motion which are tracked over time and runs in real-time, and is accurate and reliable.
Abstract: This paper describes a system for detecting and tracking moving objects in a moving world. The feature-based optic flow field is segmented into clusters with affine internal motion which are tracked over time. The system runs in real-time, and is accurate and reliable. >
TL;DR: In this paper, a least squares minimization of the energy necessary to bring the set of the camera-contour projection lines tangent to the surface is proposed to solve the 3D/2D matching problem.
Abstract: The accurate matching of 3D anatomical surfaces with sensory data such as 2D X-ray projections is a basic problem in computer and robot assisted surgery, In model-based vision, this problem can be formulated as the estimation of the spatial pose (position and orientation) of a 3D smooth object from 2D video images The authors present a new method for determining the rigid body transformation that describes this match The authors' method performs a least squares minimization of the energy necessary to bring the set of the camera-contour projection lines tangent to the surface To correctly deal with projection lines that penetrate the surface, the authors consider the minimum signed distance to the surface along each line (ie, distances inside the object are negative) To quickly and accurately compute distances to the surface, the authors introduce a precomputed distance map represented using an octree spline whose resolution increases near the surface This octree structure allows the authors to quickly find the minimum distance along each line using best-first search Experimental results for 3D surface to 2D projection matching are presented for both simulated and real data The combination of the authors' problem formulation in 3D, their computation of line to surface distances with the octree-spline distance map, and their simple minimization technique based on the Levenberg-Marquardt algorithm results in a method that solves the 3D/2D matching problem for arbitrary smooth shapes accurately and quickly >
TL;DR: The shape of the FIS is determined by searching for a shape which maximizes a focus measure, which results in more accurate shape recovery than the traditional methods.
Abstract: A new shape-from-focus method is described which is based on a new concept, named focused image surface (FIS). FIS of an object is defined as the surface formed by the set of points at which the object points are focused by a camera lens. According to paraxial-geometric optics, there is a one-to-one correspondence between the shape of an object and the shape of its FIS. Therefore, the problem of shape recovery can be posed as the problem of determining the shape of the FIS. From the shape of FIS the shape of the object is easily obtained. In this paper the shape of the FIS is determined by searching for a shape which maximizes a focus measure. In contrast to previous literature where the focus measure is computed over the planar image detector of the camera, here the focus measure is computed over the FIS. This results in more accurate shape recovery than the traditional methods. Also, using FIS, a more accurate focused image can be reconstructed from a sequence of images than is possible with traditional methods. The new method has been implemented on an actual camera system, and the results of shape recovery and focused image reconstruction are presented. >
TL;DR: Experimental results show that the integration technique can be used to build connected surface models of free-form objects and not impose constraints on the topology of the observed surfaces, the position of the viewpoints, or the number of views that can be merged.
Abstract: This paper presents a new and general solution to the problem of range view integration. The integration problem consists in computing a connected surface model from a set of registered range images acquired from different viewpoints. The proposed method does not impose constraints on the topology of the observed surfaces, the position of the viewpoints, or the number of views that can be merged. The integrated surface model is piecewise estimated by a set of triangulations modeling each canonical subset of the Venn diagram of the set of range views. The connection of these local models by constrained Delaunay triangulations yields g non-redundant surface triangulation describing all surface elements sampled by the set of range views. Experimental results show that the integration technique can be used to build connected surface models of free-form objects. No integrated models built from objects of such complexity have yet been reported in the literature, It is assumed that accurate range views are available and that frame transformations between all pairs of views can be reliably computed. >
TL;DR: A new algorithm for determining minimal length paths between two regions on a three dimensional surface based on finding equal geodesic distance contours from a given area is presented.
Abstract: We present a new algorithm for determining minimal length paths between two regions on a three dimensional surface. The numerical implementation is based on finding equal geodesic distance contours from a given area. These contours are calculated as zero sets of a bivariate function designed to evolve so as to track the equal distance curves on the given surface. The algorithm produces all paths of minimal length between the source and destination areas on the surface given as height values on a rectangular grid. >
TL;DR: Computational support for the limb-based and neck-based parts is presented by showing that they are invariant, robust, stable and yield a hierarchy of parts.
Abstract: Underlying recognition is an organization of objects and their parts into classes and hierarchies. A representation of parts for recognition requires that they be invariant to rigid transformations, robust in the presence of occlusions, stable with changes in viewing geometry, and be arranged in a hierarchy. These constraints are captured in a general framework using notions of a PART-LINE and a PARTITIONING SCHEME. A proposed general principle of "form from function" motivates a particular partitioning scheme involving two types of parts, neck-based and limb-based. Neck-based parts arise from narrowings in shape, or the local minima in distance between two points on the boundary, while limb-based parts arise from a pair of negative curvature minima which have "co-circular" tangents. In this paper, we present computational support for the limb-based and neck-based parts by showing that they are invariant, robust, stable and yield a hierarchy of parts. Examples illustrate that the resulting decompositions are robust in the presence of occlusion and clutter for a range of man-made and natural objects, and lead to natural and intuitive parts which can be used for recognition. >
TL;DR: A technique is presented that allows: 1) computing the best approximation of a given family using linear combinations of a small number of 'basis' functions; and 2) describing all finite-dimensional families, i.e., the families of filters for which a finite dimensional representation is possible with no error.
Abstract: Early vision algorithms often have a first stage of linear-filtering that 'extracts' from the image information at multiple scales of resolution and multiple orientations. A common difficulty in the design and implementation of such schemes is that one feels compelled to discretize coarsely the space of scales and orientations in order to reduce computation and storage costs. A technique is presented that allows: 1) computing the best approximation of a given family using linear combinations of a small number of 'basis' functions; and 2) describing all finite-dimensional families, i.e., the families of filters for which a finite dimensional representation is possible with no error. The technique is based on singular value decomposition and may be applied to generating filters in arbitrary dimensions and subject to arbitrary deformations. The relevant functional analysis results are reviewed and precise conditions for the decomposition to be feasible are stated. Experimental results are presented that demonstrate the applicability of the technique to generating multiorientation multi-scale 2D edge-detection kernels. The implementation issues are also discussed. >
TL;DR: A complete, fast and practical isolated object recognition system has been developed which is very robust with respect to scale, position and orientation changes of the objects as well as noise and local deformations of shape (due to perspective projection, segmentation errors and non-rigid material used in some objects).
Abstract: A complete, fast and practical isolated object recognition system has been developed which is very robust with respect to scale, position and orientation changes of the objects as well as noise and local deformations of shape (due to perspective projection, segmentation errors and non-rigid material used in some objects). The system has been tested on a wide variety of three-dimensional objects with different shapes and material and surface properties. A light-box setup is used to obtain silhouette images which are segmented to obtain the physical boundaries of the objects which are classified as either convex or concave. Convex curves are recognized using their four high-scale curvature extrema points. Curvature scale space (CSS) representations are computed for concave curves. The CSS representation is a multi-scale organization of the natural, invariant features of a curve (curvature zero-crossings or extrema) and useful for very reliable recognition of the correct model since it places no constraints on the shape of objects. A three-stage, coarse-to-fine matching algorithm prunes the search space in stage one by applying the CSS aspect ratio test. The maxima of contours in CSS representations of the surviving models are used for fast CSS matching in stage two. Finally, stage three verifies the best match and resolves any ambiguities by determining the distance between the image and model curves. Transformation parameter optimization is then used to find the best fit of the input object to the correct model. >
TL;DR: A new information theoretic discretization method optimized for supervised learning is proposed and described that seeks to maximize the mutual dependence as measured by the interdependence redundancy between the discrete intervals and the class labels, and can automatically determine the most preferred number of intervals for an inductive learning application.
Abstract: Inductive learning systems can be effectively used to acquire classification knowledge from examples. Many existing symbolic learning algorithms can be applied in domains with continuous attributes when integrated with a discretization algorithm to transform the continuous attributes into ordered discrete ones. In this paper, a new information theoretic discretization method optimized for supervised learning is proposed and described. This approach seeks to maximize the mutual dependence as measured by the interdependence redundancy between the discrete intervals and the class labels, and can automatically determine the most preferred number of intervals for an inductive learning application. The method has been tested in a number of inductive learning examples to show that the class-dependent discretizer can significantly improve the classification performance of many existing learning algorithms in domains containing numeric attributes. >
TL;DR: Analytically, it is demonstrated that MINPRAN distinguished good fits to random data andMINPRAN finds accurate fits and nearly the correct number of inliers, regardless of the percentage of true inLiers.
Abstract: MINPRAN is a new robust estimator capable of finding good fits in data sets containing more than 50% outliers. Unlike other techniques that handle large outlier percentages, MINPRAN does not rely on a known error bound for the good data. Instead, it assumes the bad data are randomly distributed within the dynamic range of the sensor. Based on this, MINPRAN uses random sampling to search for the fit and the inliers to the fit that are least likely to have occurred randomly. It runs in time O(N/sup 2/+SN log N), where S is the number of random samples and N is the number of data points. We demonstrate analytically that MINPRAN distinguished good fits to random data and MINPRAN finds accurate fits and nearly the correct number of inliers, regardless of the percentage of true inliers. We confirm MINPRAN's properties experimentally on synthetic data and show it compares favorably to least median of squares. Finally, we apply MINPRAN to fitting planar surface patches and eliminating outliers in range data taken from complicated scenes. >