Showing papers on "Centroid published in 1981"

Evaluation Of Peak Location Algorithms With Subpixel Accuracy For Mosaic Focal Planes

Abstract: The ability to achieve subpixel peak location accuracy for point source taraets in the cross-scan direction for scanning sensors and in both directions for staring sensors is examined systematically by means of Monte Carlo experiments. The performance of three peak location algorithms (simple centroid, extended centroid, polynomial least squares fit) is tested for sensitivity to system signal-to-noise ratio, detector deadspace, and blur spot size relative to detector size. A symmetrical, gaussian intensity profile of the blur spot is used in all cases. Computational efficiency, in terms of the number of multiplies and adds required, was considered in selecting the algorithms to be compared. Overall, we found that the simple centroid algorithm provides the optimum performance, giving %1/10 pixel accuracy for S/N=10 and no deadspace. In addition, performance improves for the centroid algorithms and degrades for the least squares fit algorithm as the blur spot size increases. Increasing deadspace markedly degrades the performance of the centroid algo-rithms.

X-ray digital image treating apparatus

Abstract: An image processor which can accurately and promptly obtain information about a ventricle of a living body, such as the boundary diagram, the volume, the centroid movement view and a three-dimensional view. An X-ray projection of a part to be diagnosed is quantized. The boundary and centroid of the part are obtained from the optimal ternary data using the variance of the gray-level of the image and the separation degree of a histogram. The volume and three-dimensional view of the part are obtained from this data using the gray-level method.

Feature Extraction and Selection for Pattern Recognition of Two-Dimensional Hydrometeor Images

Abstract: New feature extraction techniques are developed for two-dimensional binary images of ice particles and raindrops. These features are employed in the statistical classification of these patterns into one of seven basic hydrometeor shapes. These images have been recorded by an airborne two-dimensional probe in order to provide information leading to an understanding of important physical processes in clouds. Minimum average probability of classification error is employed as the performance criterion with informal minimization of computing time. A synthetic image set was generated to develop feature extraction techniques. Moment normalization and rotation normalization are employed to convert all images to a common size and orientation. Ten time domain features are explored including a new development (circular deficiency) and a new application (cross correlation). Three frequency domain features are investigated including a new Fourier descriptor (centroid distance). An original method of reducing ...

FixedJ spectral distribution in large shell model spaces

Abstract: A method is develloped to exactly calculate the fixedJ configuration centroid energies and widths. The resulting approximate level densities for204Pb and020Pb show large departures with respect to the gaussian approximate level densities. The goodness of the polynomial expansion of fixedJ configuration moments is studied and a simple improvement to this approximation is proposed which gives very good results.

Detector for centroid position

Abstract: PURPOSE:To enable accurate finding of a centroid position without being affected by a structure and properties, by a method wherein a plane centroid of an object to be measured is found in a manner to position a stand in a horizontal state, and then, the height of the centroid is found through inclination of the stand. CONSTITUTION:A stand 1, whereon an object to be measured is placed, is supported at fulcrums 2a-2c, and a hydraulic cylinder 5 for inclining the stand 1 is mounted between the fulcrum 2a and the stand 1. A support force, exerted by the fulcrums 2a-2c, is detected by load detectors 4a-4c, and an inclining angle detector 6 is located on the upper surface of the stand 1. A support 7 is mounted to the stand 1, and a camera head 8, being of a non-contact displacement detector, is secured thereto. A plane centroid G is found under a condition to position the stand in a horizontal state. The hydraulic cylinder 5, the position of the current centroid determined as a G', and a support force exerted by the fulcrums 2a-2c are detected by the load detectors 4a-4c. From the values the centroid position G' is computed. A fall angle is detected from a visual field caught by the camera head 8. A real position of a centroid is computed from the plane centroid positions G and G' and the fall angle.

Detecting device for picture shift component

Abstract: PURPOSE:To ensure an accurate detection for the velocity vector of the shifting picture data, by obtaining both the direction and the shift extent of the straight line connecting the centroids of both the front and back edge images each which are proportional to the shift velocity. CONSTITUTION:The data D (ji) having the address (i,j) is grouped into D (i,j) and D (i,j) according to the front and back edge images, and the X and Y coordinates corresponding to the address (i,j) are defined as X(i,j) and Y(i,j) each. Then all data of the picture memory 1 are supplied to the centroid operation circuit 2 to obtain the centroid coordinates GF(XG , YG ) and GA(XG , YG ) of the front and back edge images each. Then the angle formed by the straight line connecting each centroid and the coordinate axis, i.e., the shift direction theta is obtained by the angle operation circuit 3. Furthermore, the shift extent V is obtained by the coordinate rotation operation circuit 4 and the deflection operation circuit 5 each. In such way, an automatic and accurate detection is secured for the velocity vector of the shifting picture data.

Three Edge-point Estimation Schemes For Tracking Airborne Targets

Abstract: This paper presents three schemes which can be used to determine the radar centroid of a tar­ get inpace. These estimator schemes employ an edge-polnt estimate of position based on a scan­ determined threshold. A fourth method based on amplitude weighting is used as a comparison. Er­ ror of estimate graphs and hi stograms form the basis for comparison of the relative accuracy of the techniques.

The simplex method for minimisation of a general function

Abstract: The simplex method is a reasonably fast and efficient procedure for minimising a general function of any number of variables. It operates with function values at a number of points and so can more easily avoid local minima than other methods. It works by constructing a polyhedron and reflecting the point with the highest function value in the centroid of the others. If this results in a lower value, the exploration continues in the same direction; if not the highest point or its reflection is moved towards the centroid. The polyhedron thus moves gradually to lower values until it settles into a minimum. The simplex method contains procedures to deal with special cases and refinements to speed up the process. The report gives the full mathematical statement of the procedure, and the appendix describes a computer program to implement it. The method was developed as part of a research study of long term trends in transport: it is published as a contribution which may find a wider application in the field of mathematical techniques. (Author/TRRL)

Method of aligning position through charged beam

Abstract: PURPOSE:To improve the aligning accuracy of a charged beam with a reference mark with the product of the detected position and the intensity of the reflected electrons obtained upon scanning of the electron beam on the reference mark as divided by the sum of the intensity as a reference position by sampling and storing the intensity of the reflecting electrons and obtaining the product of the detected position and the intensity of the reflected electrons. CONSTITUTION:When scanning an electron beam in a direction X, the intensity of the signal at the position X(i) is represented by Ex(i), the sum of the Ex(i)X(i) is obtained, and is divided by the sum of the Ex(9). Then, there can be obtained the reference point of the reference mark as the centroid of the rotating profile. The same calculation can be executed in a direction Y. Accordingly, the position of the centroid can be determined irrespective of the change such as roundness or the like of the edge of the reference mark. Therefore, when this position of centroid is used as a reference point, the alignment of the position can be accurately executed.

Imaging terminal guidance seeker

Abstract: A certain guidance seeker is designed to aim at the location of the most vulnerable point of a moving target. The seeker extracts an appropriate feature of the target and continuously tracks it using a tracking algorithm. The performance of the tracker was evaluated in terms of probability of acquisition and positional error. The algorithm was verified using a data base obtained from the flight of an A-7E aircraft. The cockpit of the aircraft was continuously identified by a rectangular gate as the seeker’s aimpoint. INTRODUCTION A certain terminal guidance seeker, aided by an imaging subsystem, acquires targets, selects a target of interest, aims at its most vulnerable point and tracks the aimpoint continuously until the deployment of munitions. The imaging subsystem in the seeker collects the data from the scene through an infrared sensor, uses an appropriate algorithm for target acquisition, classification, and tracking, and generates steering commands to direct the seeker to the target. The seeker uses a scene matching algorithm to track the position of the target in the field of view (FOV). The scene matching algorithm consists of correlating a reference target scene with the incoming scene to find the best matching position. The reference target scene is obtained either from a previous scene or from a priori knowledge of the target. The target extraction process from the FOV is shown in Figure 1. In many practical applications, the reference target data is not available or the correlation with the reference data does not track well because of a noisy environment. Besides, the target size grows from a few pixels to the whole FOV as the vehicle gets close to the target and correlation with the fixed size target data becomes useless. The reference target data are to be extracted in our case from the scene itself through a segmentation process as shown in Figure 2. The segmentation process is usually a variation of the maximum likelihood detection. The initial acquisition of the target can be obtained by using a double gate algorithm. This paper addresses the tracking of targets in real time after initial acquisition. Tracking of the target is performed by using a centroid algorithm initially and later using a correlation algorithm employing updated reference target data extracted from the scene itself. The image registration process is described briefly in Section 2. In Section 3, we discuss the centroid algorithm to locate the position of the target in the FOV and then employ the correlation technique. The cockpit area was chosen as an aimpoint and was used as a reference scene to be correlated with the incoming scene. The best matched area is used as an updated reference for the cockpit area. The performance of the tracker as measured in terms of location error and probability of detection is derived in Section 4. Section 5 deals with the verification of the tracking algorithm. More than 100 frames of data from the A-7E aircraft flight data were used as a data base. Comments are discussed in Section 6. 2. IMAGE REGISTRATION Image registration involves the initial acquisition of the target and location of the target in the FOV. The acquisition of a bright target is done by simply thresholding. In general, the acquisition of a target is done by segmentation. After the target is detected, an appropriate feature of the target is extracted from the current frame of the FOV and is stored as a reference scene. When the next frame of the data is received, the FOV is searched to locate the appropriate feature again. This is done by comparing the current scene with the reference scene. In general, matching techniques for image registration include (a) cross correlation, (b) amplitude ranking method, (c) line feature matching, (d) minimum absolute difference method, and (e) moment methods. In this paper we apply a cross correlation method because of its simplicity in terms of real time implementation in the guidance missile seeker. In a cross correlation method, the reference scene and the current scene images are translated relative to one another until they overlay as indicated by a maximum of the computed correlation coefficient. 3. TRACKING ALGORITHM Initially the seeker determines the presence and size of the entire target and applies a centroid algorithm to locate its position in each incoming scene. The centroid of the target is indicated by a crosshair in the FOV. As the target size increases, a rectangular area containing a specific aimpoint of interest is stored as a reference frame. Tracking the aimpoint only assures the tracking accuracy as well as vulnerability of the target. In the current literature, usually the whole target scene is used for correlation; this has two disadvantages. Firstly, the FOV is not large enough to contain the entire target image until the terminal phase of weapon delivery. Secondly, the FOV may not contain the most vulnerable part of the target. In the feature correlation technique, on the other hand, as each scene is received, a correlation algorithm is applied to search the area containing the aimpoint. For an aircraft target, an appropriate aimpoint is chosen as the cockpit area. The features of the aimpoint are determined and the search area is identified by means of correlation. The area containing the aimpoint is marked by a rectangular gate; the size of the gate is determined by a minimum convex hull of the aimpoint area. The identified area is stored as an updated reference gate. The process of correlating and storing the current aimpoint area is continued until the deployment of munitions, Another advantage of the feature correlation is that only a small section of the target is stored as a reference gate. This results in a significant reduction of the computational load in implementing the correlation algorithm. The computational requirement for correlation is given in Table 1 as a function of gate size. Table 1. Computational Requirement Spatial Size Time Domain (No. of Operation) Frequency Doman (No. of Operation) 4 x 4 8 x 8 16 x 16 32 x 32 64 x 64 128 x 128 256 x 256 400 5,184 73,984 1,115,136 17,305,600 272,646,144 4,328,587,264 392 2,320 12,320 61,504 295,040 1,376,512 6,291,968 The acquisition time depends upon the computing device used in the seeker based on the above operation. (a) Centroid Let x(i,j), 1 # i # P, 1 # j # Q be the value of the picture element at (i,j) position in the FOV. PQ is the size of the reference scene (see Figure 1). The centroid of the target is given by The centroid of the target (x,y) is marked by a crosshair in the target in each frame and the sensor is erected to point towards the crosshair position of the FOV. This is performed in a guidance and command subsystem in the seeker. The guidance subsystem records the spatial position of the target in the FOV. (b) Correlation Computation In Figures 1 and 3, we denote x(i,j) = reference pixel value at i row and,j column i = 1, P, P number of rows of the feature j = 1 , Q, Q number of columns of the feature and y(i,j) = current pixel value at i row and j column i = 1, M, M number of rows of the search area j = 1, N, N number of columns of the search area. The mean of the reference scene is given by The mean of the current is defined as The modified reference scene is ^ x (i,j) = x(i,j) mx i = 1,..,P j = 1,..,Q The modified current scene is ^ y(i,j) = y(i,j) my i = 1,..,P, P 1/2 XX1 (4.4) assuming that the probability of the aimpoint’s presence or absence is equilikely. The detection rule is to cross correlate the incoming data with the reference data and to compare the output with the threshold, half the signal energy. Let there be M1, search vectors, i.e., Y1 Y2...YM, each of dimension N1. The correlation scheme will determine which of the {Yj} contains the reference scene when the reference target is present in the FOV. Let us denote Zj = Yj X, 1 # j # M1 (4.5) Z = max {ZJ}, 1 # j # M1 (4.6) Where Zj is the correlation output of X with the search vector {Yj}. It can be noted that Zj is a Gaussian random with mean and variance F1 = F and the probability density of Zj is given by

Discriminant Analysis of Multivariates Taken from a Single Population

Abstract: The null hypothesis of a one-sample test of multivariate means states that the population centroid is equal to a vector of specified constants. If this hypothesis is rejected, then the distance from the population centroid to the hypothesized centroid is different from zero. The purpose of this paper is to present a linear function (analogous to a discriminant function) which will allow the data analyst to interpret the dimension of the line joining the two centroids. The statistics developed to interpret this dimension are the coefficients of a discriminant function and the correlation of each dependent variable with a discriminant score. A data example is also presented to demonstrate the material and contrast it with conventional methodology.