Showing papers on "Centroid published in 1993"

An X-ray method for detecting substructure in galaxy clusters - Application to Perseus, A2256, Centaurus, Coma, and Sersic 40/6

Abstract: We use the moments of the X-ray surface brightness distribution to constrain the dynamical state of a galaxy cluster. Using X-ray observations from the Einstein Observatory IPC, we measure the first moment FM, the ellipsoidal orientation angle, and the axial ratio at a sequence of radii in the cluster. We argue that a significant variation in the image centroid FM as a function of radius is evidence for a nonequilibrium feature in the intracluster medium (ICM) density distribution. In simple terms, centroid shifts indicate that the center of mass of the ICM varies with radius. This variation is a tracer of continuing dynamical evolution. For each cluster, we evaluate the significance of variations in the centroid of the IPC image by computing the same statistics on an ensemble of simulated cluster images. In producing these simulated images we include X-ray point source emission, telescope vignetting, Poisson noise, and characteristics of the IPC. Application of this new method to five Abell clusters reveals that the core of each one has significant substructure. In addition, we find significant variations in the orientation angle and the axial ratio for several of the clusters.

A rapid tree-based method for vector quantization

Abstract: A fast vector quantization (VQ) method and apparatus is based on a binary tree search in which the branching decision of each node is made by a simple comparison of a pre-selected element of the candidate vector with a stored threshold resulting in a binary decision for reaching the next lower level. Each node has a preassigned element and threshold value. Conventional centroid distance training techniques (such as LBG and k-means) are used to establish code-book indices corresponding to a set of VQ centroids. The set of training vectors are used a second time to select a vector element and threshold value at each node that approximately splits the data evenly. After processing the training vectors through the binary tree using threshold decisions, a histogram is generated for each code-book index that represents the number of times a training vector belonging to a given index set appeared at each index. The final quantization is accomplished by processing and then selecting the nearest centroid belonging to that histogram. Accuracy comparable to that achieved by conventional binary tree VQ is realized but with almost a full magnitude increase in processing speed.

Method for segmenting features in an image

Abstract: A dual echo magnetic resonance imaging system produces two registered images of a patient in which the images have different contrast relationships between different tissue types. A two dimensional feature space histogram of the two images is produced and a separate centroid is located in the feature space histogram for each one of a pair of tissue types. A Cartesian coordinate system is defined in the feature space so that one axis of the system passes through the two centroids. Vector decomposition is employed to project each image element data point in the feature space onto a point on the one axis. The fractional quantity of each tissue type present in the image element is determined based upon the Euclidean distances from that axis point to the respective centroids. The fractional quantity is calculated for each element in the original images to form a pair of tissue images. The elements of a tissue image are processed to measure the amount of that tissue type in the imaged portion of the patient.

Particle displacement tracking technique and Cramer-Rao lower bound error in centroid estimates from CCD imagery

Abstract: An efficient video based, multi-frame particle displacement tracking technique is presented. The technique is demonstrated on a thermocapillary flow. The Cramer-Rao lower bound centroid measurement uncertainty is derived for Gaussian particle images with Poisson noise recorded on a CCD array. The optimal particle image diameter is determined to be approximately 11/2 pixels. The centroid error increases for particle image diameters larger or smaller than the optimal value. The particle centroid results are carried over to the case of a cross-correlation peak centroid estimate. Particle tracking techniques are shown to have higher accuracy than auto or cross-correlation techniques when the individual velocity measurements are averaged over a comparable correlation subregion.

Flare Plasma Dynamics Observed with the YOHKOH Bragg Crystal Spectrometer. I. Properties of the CA XIX Resonance Line

Abstract: Using data from the Bragg crystal spectrometer on the Yohkoh spacecraft we have computed measures of the total intensity, centroid position, and line width for the resonance line of Ca XIX during the rise phase and after maximum for 219 solar flares. The difference between the centroid positions early and late in each flare yields a measure of the line-of-sight velocity shift of the line centroid. We find a trend in the average value of the centroid shift with distance from Sun center suggesting radial mass motions with a characteristic velocity of 58 km s −1 . There is a correlation between the rise-phase line widths and the centroid shift

Tracking moving objects

Abstract: A method of tracking an object in a sequence of picture frames comprises inputting motion vectors (100) and segmenting the picture into areas of uniform motion (101). For the initial frame (1027) the object is located (103) either automatically or manually and its centroid and motion vector are calculated (104). For each subsequent frame (105) motion vectors (100) are input and the frame is segmented into areas of uniform motion (101). The forward motion vector of the object is calculated (120) and used to project the centroid of the object from the previous frame onto the present frame (106). The object is then grown round the projected centroid (107) by allocating areas similar to areas of the object in the previous frame and which together produce a centroid close to the projected centroid to a set of areas which define the object. A rectangle may then be drawn around the object (109) which may be used in a coding arrangement to define areas of different resolution. Backward motion vectors of the areas within the set are then calculated (110) and used to determine the similarity of areas in the next frame. Apparatus for performing the method is disclosed particularly in relation to tracking a head for videophone communications.

Effects of window size and shape on accuracy of subpixel centroid estimation of target images

Abstract: A new algorithm is presented for increasing the accuracy of subpixel centroid estimation of (nearly) point target images in cases where the signal-to-noise ratio is low and the signal amplitude and shape vary from frame to frame. In the algorithm, the centroid is calculated over a data window that is matched in width to the image distribution. Fourier analysis is used to explain the dependency of the centroid estimate on the size of the data window, and simulation and experimental results are presented which demonstrate the effects of window size for two different noise models. The effects of window shape were also investigated for uniform and Gaussian-shaped windows. The new algorithm was developed to improve the dynamic range of a close-range photogrammetric tracking system that provides feedback for control of a large gap magnetic suspension system (LGMSS).

Triangle Centers as Functions

Abstract: We consider a kind of problem that appears to be new to Euclidean geometry, since it depends on an understanding of a point as a function rather than a position in a two-dimensional plane. Certain special points we call centers, including the centroid, incenter, circumcenter, and orthocenter. For example, the centroid, as a function of the class of triangles with sidelengths in the ratio a1 : a2 : a3, is given by the formula 1/a1 : 1/a2 : 1/a3. The kind of problem introduced here leads to functional equations whose solutions are centers.

Clustering and associate processor

Abstract: A clustering and assignment processor (40) for correlating set (12) of two-dimensional data points (14). Clustering is performed by treating each data point (14) as a mass subject to gravitational attraction by other data points (14). The data points (14) are permitted to move in data space until all data points (14) in particular regions (16) of the data set (12) fall into a single point, or centroid (18). Individual data points (14) and correlated regions (16) of successive data sets (12) are then correlated by means of a resonant descent technique, which determines the distance and direction of individual data points (14) from a chosen data point (108). The processor (40) then matches a pair of two data points (12) with the chosen data point (108) which are equidistant and collinear with the chosen data point (108).

A ρ‐θ technique for treatment verification in radiotherapy and its clinical applications

Abstract: A new technique based on a ρ‐θ coordinate system for determining differences in patient position between portal and simulator images is presented. Unlike the conventional point matching method, which requires the fiducial points to be labeled in pairs before the registration, the ρ‐θ technique avoids this manual procedure. It accomplishes the treatment verification in two major steps; image alignment and field displacement analysis. For the same number of fiducial points in the simulator and portal images, it first finds the corresponding paired points if the points are not distributed symmetrically about their centroid. This is followed by alignment of these paired points using the least squares matching method to find the optimal two‐dimensional rigid body transformation parameters (shift, rotation, and scaling factor). The transformation parameters are then used to transform the portal field edge into the simulator image, so that the portal field can be compared with the prescribed field on the simulator image. A number of parameters were explored to describe the field displacement errors, including treatment field size, under/over irradiated size, the shift in center of gravity of the field, the field edge shift, and rotation of the field. The ρ‐θ technique as implemented is both fast and accurate. Experiments on the registration of radiological phantom portal images acquired with an on‐line portal imagingsystem mounted on a linear accelerator indicate an accuracy on the order of 1 mm in detecting the shift of the field’s center of gravity and approximately 1° in detecting the field rotation. The results of a clinical trial are also presented. The technique appears well suited as an integral part of an automated on‐line portal imaging treatment verification system.

A centroid based switching strategy for active power filters

Abstract: A novel switching strategy for current-fed active power filter applications based on the notion of equal area criteria is presented. In addition, the centroids of both the injected current pulses and the corresponding areas of the continuous harmonic current reference waveform are constrained to occupy the same position in the time domain. In essence the method is a nonuniform sampling technique. The proposed approach provides better performance in terms of improved distortion factor characteristics than equal sampling techniques. From a computational point of view, the centroid-based technique is also far less demanding, by a factor of five, compared to previously published work. >

Method for locating eye points on objects subject to size variations

Abstract: A novel method for locating eye point features on patterns or objects whose size varies between the reference object and the find object includes generating a set of reference vectors that define the location of the reference eye point. The set of vectors is modified and separated equidistant from each other. A centroid of the object area is calculated. When a fixed object is to be located, an area of certainty is established which contains a plurality of candidate eye points one of which is the proper find eye point of the object to be located. Sets of find vectors are generated for each candidate eye point which are compared with the set vectors for the reference eye point. Centroids of the find objects having the best comparison are calculated and compared with the centroid of the reference object. The candidate eye point having a best vector correlation match and the best centroid comparison is selected as the eye point of the find object.

Computer simulation of super-resolution point source image detection

Abstract: We present a computer simulation of the analysis of an "infocus" two-dimensional (2-D) Airy disk. Two competing methods are used to calculate the coordinates of the center of this point spread function image. The first one is the classical technique that relies on the 2-D "centroid" of the image, and the second one is a more original method that uses the frequency dependence of the argument of the Fourier transform. Comparative simulations show that the latter technique [Fourier phase shift (FPS)] allows us to obtain a very good precision of better than 1% of a pixel spacing after quantization. Perturbations such as dc offset reduction, quantization noise, and additive Gaussian noise are introduced in the simulation. The results show that there is an improved perturbation immunity for the FPS method

Video recorder for long time

Abstract: PURPOSE:To video-record the state of a specified cell in the observing image of a microscope for a long time by providing an area setting part, a centroid calculating part and a moving discrimination control part. CONSTITUTION:This recorder is provided with the area setting part setting a processing area including an object for video-recording object to operate the centroid in the observing image from an image pickup device (CCD camera) 6, the centroid calculating part calculating the centroid of the object for video- recording from the binarized image of the area set by the area setting part and the moving discriminating control part controlling the stage driving part 11 of the microscope 1 to prevent the centroid of the object for video-recording from moving on a screen. Consequently, if the cell to be a first video-recording object, etc., is set at the central part of the screen, the position of the centroid of the cell set as the object of video-recording is operated and a stage is automatically moved to allow the object of video-recording to always position at the center of the monitoring screen. Thus, even the object which moves or grows can certainly be video-recorded for a long time.

The Centroid Method in Inequalities

Abstract: The concept of the centroid, introduced most likely by Archimedes, can be applied in solving various Mathematical problems. We mention, for example, the papers of K. F. Gauss [1] and L. Fejer [2]. Here we shall give a chronological account of the use of the centroid in developing inequalities, pointing to some priorities which are neglected in the literature.

Model of visual localization.

Abstract: The position of an object in the visual field is a global characteristic of the object which must be determined shortly after its appearance. This characteristic is useful for organizing actions towards the object or for its better examination. A model of visual localization based on the concept of "image function" is proposed. It predicts that the centroid of a visual object determines its position. The centroid could be easily extracted from the maximum in the image function under certain conditions. Symmetry and size may influence the accuracy (absolute and relative) in locating visual objects.

Variation of anatomical and centroid points in the human fetal skull.

Abstract: To overcome the problem of variation of reference points in cephalometric analysis two methods have been used: 1) fixed relations between consistently recognizable anatomical points and 2) centers of gravity. The linear distance between each point and every other point was calculated from their coordinates measured on radiographs of 60 fetuses (49-212 mm crown-rump length). For each distance between every permutation of points the variance was calculated for the series of 60 fetuses. The sum of the variances for each individual point against all other points was added together and the mean variance for each point derived by dividing by the total number of points. On the basis of mean variance the centroid of the total skull outline showed least variation and was therefore the most stable point measured. This was closely followed by the origin of the coordinate reference grid based on fixed relations theory. All the centroid points showed less variation than the anatomical points upon which the origin of the grid was based.

Fuzzy control method

Abstract: PURPOSE:To obtain a fuzzy control method which does not give unpleasant feeling to a user by smoothingly changing output to a controlled object. CONSTITUTION:In a fuzzy controller 1 to which the fuzzy control method is applied, the extracted membership functions of the respective conclusion parts of a fuzzy rule are respectively corrected as membership functions MS1 and L1. On the other hand, a membership function OM having a centroid value which agrees with a previous centroid value G stored in a memory is generated. Composite membership function including all the membership functions MS1, L1 and OM are synthesized and a centroid value G is obtained. Since the centroid value G is approximated to the previous letroid value G1 compared to a centroid value G2 obtained by the synthesis only of the membership functions MS1 and L1, change from previous output becomes smooth in output for a motor, which is decided based on the centroid value G.

Extraction of symmetry properties using correlation with rotated and reflected images

Abstract: The symmetrical properties of an image or a figure are important in visual psychology and computer vision. This paper proposes a new method to extract the properties of rotational symmetry and reflectional symmetry from planar two-dimensional images. In the detection of the rotational symmetry, first, the original image for a quantized range of angles of rotation is rotated. The rotated results are convolved with the image using directional features. Then a set of affine transformations is applied to the parameter space to obtain the correlation results using each pixel as the center of rotation. The periodicity of the correlation along the rotation angle for each point is evaluated. Finally, the local maximum correlation is determined that indicates the center and the number of folds of the rotational symmetry. In the detection of the reflectional symmetry, the image for the lines in the possible quantized directions is reflected. Then the correlation between the resulting images and the original image is calculated. The transformation that maximizes the correlation directly indicates the direction of the axis of the reflectional symmetry and the translation amount of the glide symmetry. This method does not require any segmentation nor knowledge of the centroid position. The method in this paper evaluates the transformation that matches the images even though the match is a partial one; thus, it can extract the symmetrical property that exists only partially. Although a large amount of computation and storage capacity is required, the method is fundamental, versatile, and suited to the parallel computation.

Accurate Polygon Centroid Computation Using ARC/INFO GIS

Abstract: Version 5.0 of the ARC/INFO geographic information system (GIS) does not support a single command to correctly determine the centroid of a polygon. The CREATELABELS command, which is intended to center a polygon label, was used previously to estimate drainage‐basin centroid locations for hydrologic modeling. The use of the polygon CREATELABELS command resulted in an average error of 22% when used to estimate the centroid location of an equilateral triangle. A relatively simple procedure is suggested to compute accurately centroid locations.

Burglar camera device

Abstract: PURPOSE:To prevent the misdispatch of a guardian and to reduce line capacity by finding out the height of the centroid of a moving object, and only at the time of judging that the moving object is a human body based upon the height of the centroid, transmitting an image to a central monitoring center. CONSTITUTION:An image processing part 6 takes in a background image through a camera 1, and when a change is generated in the image, regards the change as the appearance of a moving object and removes the background. Then the many-valued image of only the moving object is binarized and labeling processing is applied to the binary image to find out the area of the moving object. When a difference between the obtained area value and the area value of an image obtained immediately after is less than a prescribed value, the existence of the moving object in a monitoring area is judged and its centroid is calculated. Only when the height of the centroid is included within a fixed range corresponding to the height of the centroid of a human body, an alarm and an image of an invader are sent from a transmitting equipment to the monitoring center through a communication line 9. Consequently the generation of a misalarm due to a non-organism, an inanimate object a small animal, or the like can be prevented.

Frequency-multiplexed multiple-beam optical position detector using phase detection

Abstract: The `smartness' of the optical position sensitive detector (PSD) lies in its capability to read the centroid position of the incident optical intensity distribution, independent of total intensity. Most measurands of interest to the smart structures community can be made to appear as changes in spatial distributions of optical intensity, such as interference pattern shifts, motion of reflected spots from moving or deforming objects, or changes in relative intensity among two or more light sources. In this work we demonstrate a technique to make a PSD smarter, in this case capable of reading centroid positions of multiple light intensity distributions which are modulated at different frequencies. This capability can be exploited in multi-degree-of- freedom position sensors as well as for multiplexing outputs from sensors distributed over a smart structure or skin. In this novel operating mode, the PSD behaves as a transmission line with detectors at either end and a current source at the centroid. Measurements of phase difference versus spot position for different modulation frequencies show good agreement with a superposition-based numerical model. Multiple light distributions incident on the same PSD can be frequency multiplexed. Spatial resolution increases with modulation frequency for positions near the center of the working range.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.