Abstract: A method and structure for clustering documents in datasets which include clustering first documents and a first dataset to produce first document classes, creating centroid seeds based on the first document classes, and clustering second documents in a second dataset using the centroid seeds, wherein the first dataset and the second dataset are related. The clustering of the first documents in the first dataset forms a first dictionary of most common words in the first dataset and generates a first vector space model by counting, for each word in the first dictionary, a number of the first documents in which the word occurs, and clusters the first documents in the first dataset based on the first vector space model, and further generates a second vector space model by counting, for each word in the first dictionary, a number of the second documents in which the word occurs. Creation of the centroid seeds includes classifying second vector space model using the first document classes to produce a classified second vector space model and determining a mean of vectors in each class in the classified second vector space model, the mean includes the centroid seeds.

Abstract: An edge preserving image compression algorithm based on an unsupervised competitive neural network is proposed. The proposed neural network, the called weighted centroid neural network (WCNN), utilizes the characteristics of image blocks from edge areas. The mean/residual vector quantization (M/RVQ) scheme is utilized in this proposed approach as the framework of the proposed algorithm. The edge strength of image block data is utilized as a tool to allocate the proper code vectors in the proposed WCNN. The WCNN successfully allocates more code vectors to the image block data from edge area while it allocates less code vectors to the image black data from shade or non-edge area when compared to conventional neural networks based on VQ algorithm. As a result, a simple application of WCNN to an image compression problem gives improved edge characteristics in reconstructed images over conventional neural network based on VQ algorithms such as self-organizing map (SOM) and adaptive SOM.

Abstract: According to one aspect of the invention, a method is provided in which a set of probabilistic attributes in an N-gram language model is classified into a plurality of classes. Each resultant class is clustered into a plurality of segments to build a code-book for the respective class using a modified K-means clustering process which dynamically adjusts the size and centroid of each segment during each iteration in the modified K-means clustering process. A probabilistic attribute in each class is then represented by the centroid of the corresponding segment to which the respective probabilistic attribute belongs.

Abstract: The centroid decomposition, an approximation for the singular value decomposition (SVD), has a long history among the statistics/psychometrics community for factor analysis research. We revisit the centroid method in its original context of factor analysis and then adapt it to other than a covariance matrix. The centroid method can be cast as an ${\cal O}(n)$-step ascent method on a hypercube. It is shown empirically that the centroid decomposition provides a measurement of second order statistical information of the original data in the direction of the corresponding left centroid vectors. One major purpose of this work is to show fundamental relationships between the singular value, centroid, and semidiscrete decompositions. This unifies an entire class of truncated SVD approximations. Applications include semantic indexing in information retrieval.

Abstract: In this paper we present a partitioning method capable to manage transactions, namelyt uples of variable size of categorical data. We adapt the standard definition of mathematical distance used in the K- Means algorithm to represent dissimilarityam ong transactions, and redefine the notion of cluster centroid. The cluster centroid is used as the representative of the common properties of cluster elements. We show that using our concept of cluster centroid together with Jaccard distance we obtain results that are comparable in qualityw ith the most used transactional clustering approaches, but substantial improve their efficiency.

Abstract: A method and corresponding apparatus for calculating the centroid of a fragment to be rendered is disclosed. The method calls for moving the sampling point of a pixel from its initial center point to the center of the fragment containing a portion of an image to be rendered. The method comprises the steps of receiving a coverage mask containing at least one sample point of the pixel fragment under consideration; determining which of the sample points are within the fragment; determining a value representative of the number of sample points that are within the fragment; determining offset values of the fragment centroid based on the number of sample points within the fragment; and determining the barycentric coordinates of the centroid of the fragment. The centroid of the fragment is where sampling of the primitive will occur. By sampling at the centroid of the fragment, rendered image quality is improved due to the reduced anti-aliasing effects at the edges of the primitive.

Abstract: It is usual to preprocess data before reduction, but it is not so common to study how this operation affects the final results. Determination of the centroid is a relevant task for many optical measurement devices, and the centroid is very often calculated over thresholded data. The influence of preprocessing thresholding algorithms on the statistical properties of intensity data affected by additive Gaussian noise is described as a different effective additive signal perturbation. Theoretical, simulated, and experimental analyses of the model of the effective noise were performed, and good agreement among the analyses was obtained. Direct extension of the analyses from the influence of preprocessing to centroid determination is also presented.

Abstract: A new neural model for direct classification, DC, is introduced for acoustic/pictorial data compression. It is based on the Adaptive Resonance Theorem and Kohonen Self Organizing Feature Map neural models. In the adaptive training of the DC model, an input data file is vectorized into a domain of same size vector subunits. The result of the training (step 10 to 34 ) is to cluster the input vector domain into classes of similar subunits, and develop a center of mass called a centroid for each class to be stored in a codebook (CB) table. In the compression process, which is parallel to the training (step 33 ), for each input subunit, we obtain the index of the closest centroid in the CB. All indices and the CB will form the compressed file, CF. In the decompression phase (steps 42 to 52 ), for each index in the CF, a lookup process is performed into the CB to obtain the centroid representative of the original subunit. The obtained centroid is placed in the decompressed file. The compression is realized because the size of the input subunit ((8 or 24)*n 2 bits) is an order of magnitude larger than its encoding index log 2 [size of CB] bits. In order to achieve a better compression ratio, LZW is performed on CF (step 38 ) before storing (or transmitting) it.

Abstract: In non-monopulse mechanically scanned surveillance radars, each target can be detected multiple times as the beam is scanned across the target. To prevent redundant reports of the object, a centroid processing algorithm is used to associate and cluster the multiple detections, called primitives, into a single object measurement. This paper reviews several techniques for centroid processing, and presents a new center of mass algorithm that is implemented with the recursive least squares algorithm. The new algorithm has a unique gating process to enable the primitive measurement association. Simulation results of the new algorithm are reported. Multiple object merged measurement handling issues within the centroid processing context are discussed.

Abstract: A range of a wavefront sensor is extended by focusing collimated light onto a lenslet array, an output creating a grid formed by edges of the lenslets and a reference spot in the members of the grid. Each reference spot has a known relationship to the grid member and a centroid. A relationship between the reference centroids is determined. Next a wavefront emanating from an eye is focused onto the lenslet array, with the output from the lenslet array forming the grid and aberrated eye spots thereon, each eye spot having a centroid. A relationship between the eye spot centroids is determined. One known relationship between one reference centroid and the centroid of one eye spot is identified. Finally, at least some of the remaining relationships between the reference centroids and the eye spot centroids are determined. The determined relationships provide a measure indicative of the eye aberration.

Abstract: This paper describes a novel technique for determining a useful dimension for a time-delay embedding of an arbitrary time series, along with the individual time delays for each dimension. A binary-string genetic algorithm is designed to search for a variable number of time delays that minimize the standard deviation of the distance between each embedded data point and the centroid of the set of all data points, relative to the mean distance between each data point and the centroid. The geometric transformations of rotation and scaling are added to the algorithm to allow it to identify attractors that are not aligned with the data axes. Several artificial and real-world attractors and time series are analyzed to describe the types of attractors favorable to the use of this technique.

Abstract: This paper presents a new method for edge level detection. Edge level detection is related to how much attention a person needs to use to detect an edge. The new edge level method is based on the analysis of gradient information of images that is considered as fuzzy information. This fuzzy gradient information is used to determine fuzzy class centroids that define the edge levels. The centroids are obtained with the fuzzy C means algorithm. Once the centroids are defined the gradient information is classified through a distance metric based on the centroids into different edge levels. Results show that this method provides a well-defined methodology to obtain information about edge levels in images that may be used for image analysis purposes. The algorithm also corrects the problems of lost edges and edge level change generated by another edge level algorithm reviewed in this paper.

Abstract: Object recognition is a very important task in industrial applications. In this paper, a new feature (the reciprocal of compactness of the triangles formed by two adjacent dominant points and the centroid of the object) is proposed for two-dimensional object recognition. A string matching technique is introduced to find the best matches. The experimental results indicate that using this new feature gives better recognition rates and more consistent performance than using conventional features. Another advantage of using the proposed feature is that no parameter needs to be set in the recognition process.

Abstract: The centroid body. Recall that the support function of a compact convex set K is denned to be hK(u) = maxxΣk: { }. The support function hK is positive homogeneous and convex, and any function with these properties is the support function of some compact convex set (see the illuminating paper of Berger [2], or the classic [5] by Bonnesen and Fenchel).

Abstract: Object of the present invention is to generate highly reliable three-dimensional data. The invention provides a method and an apparatus for measuring a three dimensional position of a point on an object by calculating a centroid of a temporal distribution or a spatial distribution of a light reception amount based on a set of light reception data indicating light reception intensity of a light reflected at the object. The three-dimensional measurement apparatus comprises a calculator for calculating a centroid based on the light reception data exceeding a threshold value, a setting section capable of varying the threshold value and a judgment section for determining a difference between a centroid based on the light reception data exceeding a threshold value and a centroid based on the light reception data exceeding another threshold value and judging if the centroids are correct or not based on the difference.

Abstract: In accordance with one aspect of the present invention, a system for tracking a target is provided that includes an image sensor mounted to a gimbal for acquiring an image, wherein the image includes a plurality of pixels representing the target and a background. The system further includes a motor for rotating the gimbal and an autotracker electrically coupled to the image sensor and the motor. The autotracker includes a probability map generator for computing a probability that each of the plurality of pixels having a particular intensity is either a portion of the target or a portion of the background, a pixel processor in communicative relation with the probability map generator for calculating a centroid of the target based upon the probabilities computed by the probability map generator, and a controller in communicative relation with the pixel processor for generating commands to the motor based upon the centroid.

Abstract: A new concept of approximation for rigid point sets is suggested. As a necessary condition of optimality, the principle of the conjoint centroid is proved: to achieve a best approximation, certain co-sets must conjoin their centroids. The practical use of the centroid principle, and how it opens up a non-classical method of modelling various aspects of orientational disorder in crystals, is demonstrated. The principle is applied to the interpretation of density data, to the prediction of high-pressure conformations through qualitative simulations, and to the prediction and computation of disordered sets of possible reorientation pathways which explain the shape of the electron-density distribution reconstructed from diffraction experiments. It is also demonstrated how an inversion of the centroid principle can be used to model forces between the parts of the disordered structures.

Abstract: While a first generation of video coding techniques proposed to remove the redundancies in and between image frames to get smaller bitstreams, second generation schemes like MPEG-4 and MPEG-7 aim at doing content-based coding and interactivity. To reach this goal, tools for the extraction and description of semantic objects need to be developed. In this work, we propose an algorithm for the extraction and tracking of semantic objects and an MPEG-7 compliant descriptor set for generic objects; together, they can be seen like a smart camera for automatic scene description. Some parts of the proposed system will be tested by software. The tracking algorithm has been laid out so as to follow generic objects in scenes including partial occlusions and merging. To do this, we first localize each moving object of the scene using a change-detection mask. Then, a certain number of representative points called centroids is given to the objects by a fuzzy C-means algorithm. For each centroid of some current frame, we try to find the closest centroid in the previous frame. Once we found these pairs, each object can be labelled according to its corresponding previous centroids. The description structure is a subset of the DDL language used in MPEG-7. The main concern was to find a simple, but flexible descriptor set for generic objects. A corresponding C-structure for software implementations is also proposed and partially tested.

Abstract: The integration of photo-detectors onto a standard CMOS integrated circuit is presented. This device provides the optical front end for a real time centroid detection system to be used as part of a larger system for implementing a Shack- Hartmann wavefront sensor. A hardware emulation system containing a Field Programmable Gate Array is used to prototype suitable algorithms prior to IC fabrication. Data is presented on the performance of photodetectors and the ability to extract in real time a centroid coordinate.

Abstract: A method and corresponding apparatus for determining the centroid (V c ) of a waveform signal being sampled at a set of parameter values (V i , i=1, . . . , n) yielding a corresponding set of sampled amplitudes (A i , i=1, . . . , n), each parameter value and corresponding amplitude forming a sampled point (V i , A i ), the method including the steps of: selecting an amplitude at which to create an interpolated point; interpolating a first parameter value corresponding to the amplitude selected in the step of selecting an amplitude; and performing a centroid calculation using only the sampled points with an amplitude greater than a predetermined threshold. The waveform is sometimes sampled in the presence of background noise, and the method sometimes also includes: estimating the background (B i ) for each value in the set of parameter values at which sampling is performed; and reducing the amplitude (A i ) of each sampled amplitude by the background (B i ) so estimated.

Abstract: This paper develops a systematic approach to track the centroid of a maneuvering target in image sequences based on the concept of Track while Detect The statistical performance of centroid estimation with a strong Gauss noise background is studied The authors clearly present the dilemma between performance of bias and variance when only binary transform or intensity bandpass processing is used The suggested way for overcoming the difficulty is image pre-processing by spatial matched filtering when the shape is obtained A simple and experimental method is found to predict the statistical performance of centroid estimation after matched filtering and segmentation A new adaptive IMM algorithm called ATIMM is employed as the tracking filter and proved to satisfy the need of track while detect in a simulated low SNR image sequence, while the combination of matched filter, binary transform plus clustering, and ATIMM can achieve the best tracking performance

Abstract: PROBLEM TO BE SOLVED: To identify with which one of objects estimated beforehand a measurement object matches by a simple processing without accompanying three-dimensional coordinate transformation for a position/posture of the measurement object. SOLUTION: Three-dimensional image data 1 of the object are inputted and the three- dimensional image data 1 are projected on a first two-dimensional projection plane determined by being specified by an operator or selected beforehand in a projection part 2. The centroid of a projection image is obtained in a centroid calculation part 3 and a straight line passing through the centroid and matching with the longest direction of the projection image is obtained in an inertia principal axis calculation part 4. The three-dimensional image data of the object are cut off by a second two-dimensional plane passing through the major axis of the inertia principal axis and orthogonally crossing the first two-dimensional plane and then, a cut-off cross section shape is obtained as a vertical cross section image in a vertical cross section image generation part 5. For the vertical cross section image, the contour is extracted in a contour curve extraction part 6 and all or a part of the area, peripheral length and roundness of the extracted contour and the aspect ratio of a rectangle including a contour curve is obtained as an identification parameter 8 in an identification parameter extraction part 7.

Abstract: The metric sample space of Frcurves (Fr´ 1934, 1951, 1961) is based on a generalization ofregular curves that covers continuous curves in f ull generality. This makes it possible to deal with both smooth and non-smooth, even non-rectifiable geometric curves in statistical analysis. In the present paper this sample space is further extended in two directions that are relevant in practice: to incorporate information on landmark points in the curves and to impose invariance with respect to an arbitrary group ofisometric spatial transf ormations. Properties ofthe introduced sample spaces ofcurves are studied, specially those concerning to the generation and representation of random curves by random functions. In order to provide measures of central tendency and dispersion ofrandom curves, centroids and restricted centroids ofrandom curves are defined in a general metric framework, and methods for their consistent estimation are derived.

Abstract: This shpae of fruit is one of the most important features in classification. Various mathematical methods for describing the shape of irregular fruits were investigated. It was not suitable to adopt curve fitting to describe the pear shape in the course of fruit classification. The new method to calulate centroid coordinates and to describe the shape of the object only based on the boundary information was put forward. It was greatly efficient to describe the shape using Fourier descriptor, which uses boundary radius and its Fourier transform to spectrum domain. It appeared that the change patterns of first 4 harmonics were sufficient for representing the main shape features of fruit, and more accuracy in the reconstruction, especially at the calyx pole, was obtained with first 15 harmonics. Besides, they allow the reconstruction of the pear shape. Furthermore, the Fourier descriptors can made in variant to translation, rotation, and scale, this feature is very important for "on-line" grading objectives. It was found that the identification accuracy reached 90% by applying the Fourier descriptor in combination with artificial neural networks. This method also could be used to identify the shape of other fruits if suitable training set is found.

Abstract: PROBLEM TO BE SOLVED: To execute more accurate rotation correction and to realize a high collation rate even if a part of a fingerprint picture lacks and is inclined by obtaining the inclination of an input picture by a neural network(NN) method and correcting data by the inclination quantity. SOLUTION: When picture data are inputted from a picture input device 1, data of an original picture (292×524 pixels, for example) are compressed and new picture data (18×32 pixels, for example) are generated. Then, the centroid coordinate (XG, YG) of an input picture and the inclination θ (the inclination of a center line passing through a centroid) of the input picture are calculated by an NN method. When the obtained inclination θ is not in a correction unnecessary range, data on the picture (rotated correction picture) obtained by rotating the original by the inclination θwith know affine transformation around the obtained centroid coordinate (XG, YG) so that the inclination is cancelled, are generated.

Abstract: PROBLEM TO BE SOLVED: To provide an image recognizing device capable of speedy recognition, even objective rotation information while executing target tracking speedily. SOLUTION: This image recognizing device consists of a centroid calculating means 11 for calculating the centroid of a fetched objective image, an edge extracting means 12 for preparing the edge extraction image of an image from an original image, a Hough conversion means 13 for preparing a Hough converted image from the edge-extracted image and an actuator part 14 for driving the direction of an image fetching means to coincide with the direction of the object, based on the centroid calculating result of the image. A sampling time for detecting the rotation of the object is sharply reduced by target- tracking the object and optically executing Hough conversion using such a constitution.

Abstract: This paper considers a clustering problem where distorted images are allocated into a specific number of clusters such that each cluster is composed of images that are similar. Similarity is determined by summing the mean squared error of each image of a cluster with the centroid of that cluster. A genetic algorithm guided by a descent algorithm is presented to minimise this error. Tabu search is also employed to maintain genetic diversity and improve efficiency. Experiments use monochrome, greyscale and colour images.

Abstract: A system and method which substantially eliminates systematic error in a centroid determination of reconstructed waveforms from images generated by an image sensor. A predetermined wavefront error is added to an input wavefront and the wavefront is detected. The input wavefront is passed through a random phase plate. The phase plate is an optical window in which the thickness in a z-axis varies randomly over an X/Y plane. The random phase plate acts as a low pass filter and the output of the phase plate is an aberrated wavefront. That is, the nonuniform thickness of the phase plate generates random spatial phase errors in the optical wavefront. The autocorrelation function of the phase plate is such that random phase errors in the optical wavefront will filter out spatial frequencies higher than one cycle per pixel. Hence, the systematic centroiding error is reduced. Software running on the microprocessor computes the position of the image centroid on the CCD using the digitized pixel data in a conventional manner.

Abstract: PROBLEM TO BE SOLVED: To provide a scientific and uniform skill learning device which is capable of effectively providing discrete learners with the guidance and learning of special skills of calligraphy, plasterers, etc., for which there are heretofore no choices but to depend on the ability of directors which make judgment by viewing the action of the discrete learners and the result thereof. SOLUTION: The special skills of the calligraphy, plasterers, etc., may be scientifically and uniformly processed by the force (weighting) that the learner exerts on a flat planar object and the movements (bearing, velocity, etc.), on the flat planar object. This skill learning device has a learning board supported at four points, a four-point weighting detecting means, a calculating means for calculating the centroid position and total weighting of the weighting, a memory means for storing the results of the calculation and a display means for displaying the images of the movements of the centroid position while displaying the total weighting by the sizes of graphics.