Abstract: A wavefront aberration of an eye is determined, e.g., in real time. The eye is illuminated, and the light reflected from the retina is converted into spots with a device such as a Hartmann-Shack detector. The displacement of each spot from where it would be in the absence of aberration allows calculation of the aberration. Each spot is located by an iterative technique in which a corresponding centroid is located in a box drawn on the image data, a smaller box is defined around the centroid, the centroid is located in the smaller box, and so on. The wavefront aberration is calculated from the centroid locations by using a matrix in which unusable data can be eliminated simply by eliminating rows of the matrix. Aberrations for different pupil sizes are handled in data taken for a single pupil size by renormalization.

Abstract: This paper investigates the use of the Space Carving algorithm with outdoor image sequences, using a lambertian lighting model. A new consistency function is proposed that uses a statistical comparison instead of the voxel centroid sampling that was initially proposed. This is important when there is more detail in the images than can be stored in a voxel representation. The new function is evaluated using synthetic data and real image sequences.

Abstract: The conventional way of measuring the average slope of the phase of a wave front is from the centroid of the image formed at the focal plane. We show the limitations of using the centroid and present an optimal estimator along with the derivation of its lower error bound for a diffraction-limited image. The method is extended to slope estimation in the case of a random aberration introduced by atmospheric turbulence. It was found that the variance of the error of the slope estimator can be improved significantly at low turbulence levels by using the minimum mean-square-error estimator instead of the centroid.

Abstract: A real-time adaptive segmentation method based on new distance features is proposed for the centroid tracker. These novel features are distances from the center point of a predicted target to each pixel by a tracking filter in extraction of a moving target. The proposed method restricts clutters with target-like intensity from entering the tracking window with low computational complexity for real- time applications compared with other complex feature-based methods. Comparative experiments show that the proposed method is superior to the other segmentation methods based on the intensity feature only in target detection and tracking.

Abstract: A real-time adaptive segmentation method based on new distance features is proposed for the centroid tracker. These novel features are distances from the center point of a predicted target to each pixel by a tracking filter in extraction of a moving target. The proposed method restricts clutters with target-like intensity from entering the tracking window with low computational complexity for real- time applications compared with other complex feature-based methods. Comparative experiments show that the proposed method is superior to the other segmentation methods based on the intensity feature only in target detection and tracking.

Abstract: A system is provided for determining an eccentricity vector ⊂ which defines the magnitude and direction of an initial placement displaced from a desired location of a centroid O of a right quadrilateral semiconductor wafer (22) which may be clear or opaque. With an initial point for reference desirable established on its peripheral edge (108) for detection by an edge sensor, the wafer is rotated about a point P and a curve defining the profile of the peripheral edge (108) is obtained. The eccentricity vector is computed from the sensed positions of the corners of the wafer and has a magnitude representative of the spatial dislocation of the centroid O relative to the point P and having an orientation Ζ representative of the angle subtended by a first line connecting the point P and the centroid O relative to a second line connecting opposite corners of the wafer. As processing proceeds, the wafer (96) is inserted into an aligner station, then repositioned from an initial position to a desired position, then advanced seriatim into a plurality of processing station (96) while maintaining the desired position previously attained.

Abstract: The present invention provides a method and an apparatus for detecting a position of a light spot in a light distribution that can include stray light components (e.g. from other lasers, ambient lighting etc.). The apparatus includes a continuous response position sensitive detector (CRPSD, e.g. lateral effect photo-diode) for determining a first centroid of the light distribution and a discrete response position sensitive detector (DRPSD, e.g. multiplexed array) for determining a second centroid of the light distribution within a reading window defined about the first centroid and within the light distribution. The second centroid represents the position of the light spot in the light distribution. This multiple stage approach exploits the high resolution and speed offered by traditional CRPSDs together with the accuracy under variable lighting conditions offered by traditional DRPSDs.

Abstract: This paper describes the development of a system for the segmentation of small vessels and objects present in a maritime environment. The system assumes no a priori knowledge of the sea, but uses statistical analysis within variable size image windows to determine a characteristic vector that represents the current sea state. A space of characteristic vectors is searched and a main group of characteristic vectors and its centroid found automatically by using a new method of iterative reclustering. This method is an extension and improvement of the work described in [9]. A Mahalanobis distance measure from the centroid is calculated for each characteristic vector and is used to determine inhomogenities in the sea caused by the presence of a rigid object. The system has been tested using several input image sequences of static small objects such as buoys and small and large maritime vessels moving into and out of a harbour scene and the system successfully segmented these objects.

Abstract: The authors studied the problem of finding an optimal rigid-body transformation that maps one configuration of points to a corresponding configuration when the alignment errors are anisotropically weighted. Such a problem arises in point-to-point registration, in particular when an optical device (e.g. microscope or video camera) is involved, as in image-guided surgery. The authors review the existing literature and algorithms and study the mathematical difficulties. After stating a symmetry condition for critical points, they use it to establish some results. In particular, they show that the starting configuration and weight matrices can have a special form (orthogonal columns), they show that the rotational part can be computed from configurations translated so that their centroids lie at the origin, and they give an estimate for the total number of critical points. The authors then compare the 2 existing algorithms, studying carefully their dependence on the different parameters, and propose an independent technique in order to validate them. This technique reduces the problem to the problem of finding the roots of a system of 3 polynomials in 3 variables.

Abstract: In this work, we study the problem of finding an optimal rigid-body transformation that maps one configuration of points to a corresponding configuration when the alignment errors are anisotropically weighted. Such a problem arises in point-to-point registration, in particular when an optical device (e.g., microscope or video camera) is involved, as in image-guided surgery.We review the existing literature and algorithms and study the mathematical difficulties. After stating a symmetry condition for critical points, we use it to establish some results. In particular, we show that the starting configuration and weight matrices can have a special form (orthogonal columns), we show that the rotational part can be computed from configurations translated so that their centroids lie at the origin, and we give an estimate for the total number of critical points. We then compare the two existing algorithms, studying carefully their dependence on the different parameters, and propose an independent technique in order to validate them. This technique reduces the problem to the problem of finding the roots of a system of three polynomials in three variables.

Abstract: In this paper we present a novel approach to shape similarity estimation The target application is content-based indexing and retrieval over large image databases The technique is based on wavelet decomposition and uses polygon approximation over several scales This technique uses simple features (aspect ratio, angles, distances from the centroid, distance ratios and relative positions) extracted at high curvature points These points are detected at each level of the wavelet decomposition as wavelet transform modulus maxima The experimental results and comparisons show the performance of the proposed technique This technique is also suitable to be extended to the retrieval of 3-D objects

Abstract: First and second codeword are selected from respective first and second codebooks having an equal number of codewords and wherein the first and second codewords represent unequal numbers of elements of respective first and second sub-vectors. A codebook populating method for a split vector quantizer relies on comparing centroid calculations for the first codebook. The calculations are performed on eligible pairs of codewords. Eligible codewords are limited to those which satisfy and ordered property based on Line Spectrum Frequencies (LSF). The results of the centroid pair codeword calculations are used to populate the second codebook.

Abstract: Modeling of image content based on chromatic arrangement includes representation of the spatial relationship between complex sets of pixels. We propose a model of spatial directional relationship between extended sets. This involves the same computational and programming complexity as that of conventional representations based on centroids, but it is able to account for the overall sets of pixels without reducing them to a single representative point or to a bounding rectangle. The gain in effectiveness is evaluated in a user-based comparison with a representation based on mutual centroid orientation.

Abstract: The radiation detector used in typical gamma cameras and NaI-based positron emission tomography (PET) scanners effectively positions events over most of its crystal area, but the spatial resolution begins to suffer at the edges. One reason is that the measured light distribution is truncated or otherwise asymmetric, and the centroid positioning algorithm no longer optimally weights the photomultiplier tube (PMT) signals in this case. As a result, events less than a certain distance from the edge must be rejected, reducing geometric efficiency and complicating image reconstruction for PET systems with multiple fixed detectors. Short of discarding the centroid algorithm altogether, a computationally simple way to improve the positioning is to define a strip of physically nonexistent, or virtual, PMTs around the actual PMTs and to assign realistic signal values to them event by event based on the signals of nearby real PMTs. If the centroid algorithm now also includes the virtual PMTs, improved spatial resolution is obtained due to better weighting of the PMT signals. With minimal modification to the detector, the virtual PMT method was implemented and tested on an ADAC UGM C-PET detector and found to significantly improve spatial resolution near the detector edges.

Abstract: PROBLEM TO BE SOLVED: To quickly detect the direction of an object in a simple constitution by calculating the sizes and an area ratio of the 1st and 2nd areas which are extracted from the image data of the object and calculating the direction of the object from these calculation results. SOLUTION: The image data of an object that is picked up by a video camera are inputted to an arithmetic unit, which extracts both the hair and face areas of the object from the image data. In this example, the hair area is extracted as the black pixels and the face area is extracted as the skin color pixels. Then the continuous range areas are calculated for both black and skin colors, respectively, and a ratio is also calculated between both areas. The calculated ratio is compared with the reference value that is previously set to calculate the angle of an object (e.g. the face of an attendant of a video conference). The arithmetic unit also calculates the centroid of the x coordinate direction for each of black and skin color areas, and the x coordinates of the centroid GB of the hair area is set at the right of the x coordinates of the centroid GS of the face area when the object person turns to the left (A).

Abstract: An eigenspace based human face detection method is proposed. The distribution of human face patterns in image space is modeled by means of the Mahalanobis-based clustering method. The eigenspace decomposition approach for conditional probability density estimation includes both the distance measure between the sample and eigenspace and the measure of sample projection and cluster centroid which is more robust than the traditional probability density estimation method where only the latter distance is considered. Thus it can achieve better human face detection result.

Abstract: A new method for pattern recognition that is invariant under changes of position, orientation, intensity, and scale is presented. The centroids of objects provide unique points that are related to the energy distribution. For obtaining more such unique points a conformal transform can be used to rearrange the energy distribution of the object. By means of the conformal transform many different centroids can be produced from the same object. A useful pattern-recognition and object-registration method that yields a position-, rotation-, intensity-, and scale-invariant feature vector based on these centroids can be created.

Abstract: Individual objects are located according to a coordinate system in time-successive patterns and correlated between patterns. The objects are correlated by assigning identifiers to each in both patterns. The locations are transformed by reorientation to their centroid. The average of the transformed coordinate differences is used to adjust the centroid of the objects in a subsequent pattern and the transformed coordinate differences adjusted for the centroid displacement. A figure of merit is taken as the root-mean-square of the adjusted differences and used to determine which possible combination of correlated objects between two patterns is most likely.

Abstract: The orthocentroidal circle of a nonequilateral triangle has diameter GH, joining the centroid to the orthocenter. We show that the incenters of triangles with a given Euler line simply cover the interior of the orthocentroidal circle, and that their Fermat points also lie within this circle.

Abstract: PROBLEM TO BE SOLVED: To provide an image classifying device for judging whether or not inputted image data are document images, especially business card images. SOLUTION: Multilevel image data inputted from an image input device 51 are recorded in memories 5231 and 5232 as the multilevel image data and the binarized binary image data. Only valid connection components in the binary image data are left, the number of them is obtained and centroid points are extracted. The respective centroid points and the nearest centroid points are obtained and the direction is recorded in a frequency histogram memory 5236. Gradation images are differentiated, a density projection histogram is prepared from the differential images and it is differentiated and stored. Whether or not an input image is a business card is judged by whether or not the number of the valid connection components is equal to or less than a threshold, whether or not the frequency of the direction from the centroid point to the nearest centroid point is equal to or more than the threshold and whether or not an average value of the derivation of the histogram is equal to or less than the threshold, a keyword is supplied to the input image and it is recorded in an image data base device 53.

Abstract: The CMD is a powerful technique to simulate the real-time semi-classical dynamics of quantum many-body systems.1) Recently, we extended the original Boltzmanntype CMD method to include Bose/Fermi statistics. In the present paper, we focus on the practical technique of the Bose/Fermi CMD, and propose a set of Newtonian equations of motion to be solved with superior efficiency in computational time.

Abstract: As an efficient method to detect blending of general gravitational microlensing events, it is proposed to measure the shift of source star image centroid caused by microlensing. The conventional method to detect blending by this method is measuring the difference between the positions of the source star image point spread function measured on the images taken before and during the event (the PSF centroid shift, c,PSF). In this paper, we investigate the difference between the centroid positions measured on the reference and the subtracted images obtained by using the difference image analysis method (DIA centroid shift, c.DIA), and evaluate its relative usefulness in detecting blending over the conventional method based on c,PSF measurements. From this investigation, we find that the DIA centroid shift of an event is always larger than the PSF centroid shift. We also find that while c,PSF becomes smaller as the event amplification decreases, c.DIA remains constant regardless of the amplification. In addition, while c,DIA linearly increases with the increasing value of the blended light fraction, c,PSF peaks at a certain value of the blended light fraction and then eventually decreases as the fraction further increases. Therefore, measurements of c,DIA instead of c,PSF will be an even more efficient method to detect the blending effect of especially of highly blended events, for which the uncertainties in the determined time scales are high, as well as of low amplification events, for which the current method is highly inefficient.

Abstract: We propose a randomized method for the detection of symmetry in planar polygons without assuming the predetermination of the centroids of the objects. Using a voting process, which is the main concept of the Hough transform in image processing, we transform the geometric computation for symmetry detection which is usually based on graph theory and combinatorial optimization, to the peak detection problem in a voting space in the context of the Hough transform.

Abstract: This paper describes tree­based classification of character images, comparing two methods of tree formation and two methods of matching: nearest neighbor and nearest centroid. The first method, Preprocess Using Relative Distances (PURD) is a tree­based reorganization of a flat list of patterns, designed to speed up nearest­ neighbor matching. The second method is a variant of agglomerative hierarchical clustering (HCLUS) which aims at finding a hierarchical structure of centroids in the pattern space. Results indicate that the PURD method is a very fast, effective and convenient method for the speedup of 1NN search, from which it is, however, difficult to derive usable character prototypes. HCLUS can be used to obtain very fast search with acceptable classification rate while providing character prototypes, however, at the cost of significant training efforts.

Abstract: PROBLEM TO BE SOLVED: To reduce the number of data of a data base, and to calculate highly accurate table data by preparing a masking matrix by averaging the prescribed number of obtained masking coefficients. SOLUTION: Three basic data are extracted from RGB data, which are the closest to a centroid point RxGxBx in the order of the short distance, and all masking coefficients aij of masking matrixes at the centroid point are within a prescribed range is determined. When all the masking coefficients aij are within the prescribed range, a counter P indicating the number of times of the search of the masking matrix is incremented. Then, a relation between the value of the counter P and a determined value Q is checked, and when P>=Q, the mean value of the obtained masking coefficients aij is calculated. Then, the averaged masking coefficient is converted into the masking matrix at the centroid point, and matrix operation is performed to the centroid point data RxGxBx, so that L*a*b data which is the converted value corresponding to the centroid point can be calculated.

Abstract: PROBLEM TO BE SOLVED: To drastically reduce the labor and the man-hour of a CAD system user without making a CAD system complicated or expensive. SOLUTION: A centroid calculation means 1 calculates the centroid of each of indicated plural face data out of inputted or generated face data, and an offset direction indicating vector calculation means 2 calculates offset direction indicating vectors going to an indicated offset direction point from respective centroids of plural face data, and a normal vector calculation means 3 calculates normal vectors at respective centroids of plural face data. A face data offset means 4 offsets each of plural face data in the direction of the normal vector if the angle formed between the offset direction indicating vector of the face data and the normal vector is 90 deg..

Abstract: An efficient shape recognition scheme based on three new ideas is presented. First, a new method is presented for estimating real-valued boundary points from the integer-valued coordinates and the grey-level values of binary images. Secondly, we can quickly determine all of the feature points with this representation by using an angle calculation formula and the separating technique which are also proposed in this paper. Then, each shape is represented by an array of pairs, where each pair contains the coordinate of a feature point and its distance from the centroid. Thirdly, in the matching process, we also propose a new split-merge technique to assist in the shape matching. The effectiveness of the shape recognition scheme is clearly proven by the good recognition rates of our experiments.