Showing papers on "Centroid published in 1985"

On Symmetry Detection

Abstract: A straight line is an axis ofsymmetry of a planar figure if the figure is invariant to reflection with respect to that line The purpose of this correspondence is to describe an O( n log n) time algorithm for enumerating all the axes of symmetry of a planar figure which is made up of (possibly intersecting) segments, circles, points, etc The solution involves a reduction of the problem to a combinatorial question on words Our algorithm is optimal since we can establish an Ω(n log n) time lower bound for this problem

An algorithm to construct continuous area cartograms

Abstract: Continuous area cartograms distort planimetric maps to produce a desired set of areas while preserving the topology of the original map. We present a computer algorithm which achieves the result iteratively with high accuracy. The approach uses a model of forces exerted from each polygon centroid, acting on coordinates in inverse proportion to distance. This algorithm can handle more realistic descriptions of polygon boundaries than previous algorithms and manual methods, thus enhancing visual recognition.

Learned part system

Abstract: A system for learning a characterization of an object and thereafter identifying the presence and orientation of the object is capable of controlling a robotic system for grasping the object. In an off-line learning mode, a television camera produces a video signal from the object and a preprocessor develops a segmented line outline of the object in digital form. A computer is programmed to generate a mathematical "rubber band" or convex hull around the object outline formed from segmented lines and to store the x-y coordinates of the lines. The centroid of the hull is calculated and an R(.0.) function as the radius from the centroid to the hull with the maxima thereof is calculated for characterizing the orientation of the object. A truncated Fourier series of the R(.0.) function is generated and the coefficients stored. In an on-line characterization mode, the apparatus generates a characterization of an unknown object and compares it with the learned and stored values of R(.0.) and Fourier coefficients. Upon identification of the object, the orientation is calculated by comparing the shift in .0. from the stored reference values.

Method for spatial measurement of holes

Abstract: The three-dimensional position of a hole through a workpiece is determined using back lighting or front lighting (feature lighting) to determine the centroid of the hole's image in two-dimensional computer memory image space. The centroid determines a line of sight between the center of the hole's image and the actual center of the hole in real space. Next a crosshair lighting pattern (structured lighting) is projected onto the plane of the workpiece in the neighborhood of the hole. From the reflected crosshair pattern an equation representing the plane containing the hole is determined in image space. The intersection of the plane equation and the line of sight is computed and the three-dimensional, real space position of the hole is determined for comparision with an ideal position established during calibration.

Line of sight of an aberrated optical system

Abstract: The line of sight of an aberrated optical system is defined in terms of the centroid of its point-spread function (PSF). It is also expressed in terms of its optical transfer function as well as its pupil function. Whereas the PSF’s obtained according to wave-diffraction optics and ray geometrical optics are quite different from each other, they have the same centroid. Although different amplitude distributions across an aberration-free pupil give the same centroid location, in the case of an aberrated pupil not only the phase but also the amplitude distribution affects the centroid location. If the amplitude across a pupil is uniform, then the centroid may be obtained from the aberration only along the perimeter of the pupil, without regard for the aberration across its interior irrespective of its shape. Next, an optical system with aberrated but uniformly illuminated annular pupil is considered. The aberration function is expanded in terms of Zernike annular polynomials. It is shown that only those aberrations that vary with angle as cos θ or sin θ contribute to the line of sight. A simple expression is obtained for the line of sight in terms of the Zernike aberration coefficients. Similar results are obtained for annular pupils with radially symmetric illumination. Finally, as numerical examples, some specific results are discussed for annular pupils aberrated by classical primary and secondary coma. As an example of a radially symmetric illumination, we obtain numerical results for Gaussian illumination of aberrated annular pupils. It is emphasized that the centroid and the peak of the PSF’s aberrated by coma are not coincident. Moreover, as the amount of the aberration increases, the separation of the centroid and peak locations also increases.

Method and apparatus for determining measured quantities with a centroid detecting encoder

Abstract: A plurality of marks are carried on a movable member, the position of which represents a measured quantity. An image of a mark is projected onto a surface having a large number of detectors. The output signals of the detectors are fed into an evaluation circuit, which sequentially determines the intensity distribution on the detector and, thereby, the position of the mark by means of comparison of fixed threshold values with each of the detector signals and determines the centroid of the thus obtained intensity value distribution. The position of the centroid is a measure of the quantity to be measured.

Sloping angle detector for character string

Abstract: PURPOSE:To detect the sloping angle of a character string to a horizontal scan line in a short time and to recognize characters of the character string, by obtaining the centroid point of the character string and the sloping angle of an inertia main axis in case the character string has an inclination in an optional direction when viewed from the upper surface of a cylindrical matter. CONSTITUTION:The video signal of a camera 1 is binary coded 4 and sampled in a proper interval to be supplied to a memory 5. A circle segmenting circuit 13 and a character string segmenting circuit 14 segments an upper surface 19 of a matter 12 and the part of a character string 3 on the memory 5. The segmented train 3 is considered as a graphic, and the centroid point of this graphic is calculated by a centroid point calculating circuit 15. While the inertia main axis of the graphic is calculated by an inertia main axis calculating circuit 16. A coordinate conversion circuit 25 turns said graphic round the centroid point to set a bit pattern of the train 3 horizontal to the scan line of the camera 1. This character string pattern is temporarily stored to a memory 5a. Using these data, a character recognizing circuit 26 recognizes characters.

Pick and place

Abstract: PURPOSE:To highly accurately incorporate built-in parts in a camera by allowing a vision to execute silhouette processing under a state that a TV camera is arranged just above the built-in parts. CONSTITUTION:The camera 3 is moved to the upper part of the built-in parts 4 to detect the silhouette of the parts 4, the vision calculates the centroid position and inclined angle of the silhouette and a robot arm 1 is moved so that the XY coordinates of the center of the camera 3 are positioned just above the centroid of the parts 4. Then, the TV camera 3 picks up the silhouette of the parts 4 again as a silhouette image and the vision calculates the centroid position and inclined angle of the silhouette from the silhouette image and transmits the calculated results to the robot. Consequently, the centroid coordinates and the inclined angle of the silhouette of the built-in parts 4 can be obtained without generating an error and highly accurate incorporation can be attained.

Point target location using hexagonal detector arrays

Abstract: For staring sensors, improved performance in the location of point targets can be achieved by using an array of hexagonal detectors instead of the usual array of square or rectangular detectors. This fact is demonstrated by calculating the accuracy of the centroid algorithm as a function of signal to noise ratio and blur spot size for both types of detector arrays. The probability density function for the centroid random variable is derived and is used to perform all noise analysis. The analysis indicates that the algorithm error is reduced by as much as a factor of three, the sensitivity to noise is reduced by 17 percent, the computational load is decreased by 23 percent, and the data storage requirement is reduced by 22 percent. The clutter induced noise, as measured by the clutter equivalent target, is essentially identical for square and hexagonal detectors of the same area.

Robot measurement system

Abstract: PURPOSE:To measure an accurate distance between a work and a handling reference point by obtaining the tilt of a visual coordinate system to a robot coordinate system and converting both coordinates into the same quadrant. CONSTITUTION:A work 8 is shifted by a robot 1 within the viewfields (9a-9c) of a visual device 7, and the centroid coordinates of the work 8 are measured at 2 teaching points. At the same time, the robot movement amount is obtained at each teaching point of a robot coordinate at that time point. Then either one of the obtained robot coordinate system and visual coordinate system is converted, and both coordinates are converted into the same quadrant. Then the relative relation is obtained between both coordinate systems. Based on this relation, the movement amount of the robot 1 is measured in a working mode.

Stroke identification system

Abstract: PURPOSE:To decide whether a character to be written is being written in the correct order of making strokes or not by identifying strokes in response to an appreciation value outputted from a stroke centroid moving direction appreciating means and an appreciation value of a stroke shape which is found by a stroke shape appreciating means in accordance with a feature point found from a coordinate system and a dictionary feature point of a dictionary. CONSTITUTION:A representative point extracting circuit 2 converts the coordinate system of a character stroke inputted from a tablet 1 into feature points. In response to the feature points from the circuit 2 and a ten plate (dictionary feature points) from a dictionary 4, the inter-stroke distance (ds) (appreciation value for the stroke shape) between both the feature points is found out by a stroke shape appreciation circuit 3. Then, an input stroke centroid moving vector is calculated by a stroke centroid moving direction appreciating circuit 5 on the basis of the feature point from the circuit 2 to find out the distance (appreciation value) (dg) between the vector and the ten plate (dictionary stroke centroid moving vector) from the dictionary 4. A decision circuit 6 decides whether a correct shape stroke is inputted in the correct order of making strokes or not on the basis of the distance (dg) found out by said procedure.

Device for detecting positional shear of pattern

Abstract: PURPOSE:To detect maximum frequency and to detect positional shear precisely by executing the thick or thin processing of a pattern to be matched, finding out the centroid coordinates of the remaining part and comparing said centroid coordinates with reference centroid coordinates which have been previously registered. CONSTITUTION:A picture inputted from a picture input device 10 of a pattern positional shear detector is accumulated in the 1st storage device 20, a thickening processing circuit 30 and a thinning processing circuit 40 executes the thickening and thinning processing of the accumulated picture respectively. The centroid coordinates of plural partial patterns surrounded by a background part including in the picture processed by the circuits 30, 40 are detected by a centroid detecting circuit 50. A prescribed processing for a picture previously inputted to a reference file 80 is executed and the centroid coordinates are found out and registered. The reference centroil coordinates registered in a file 80 are compared with the centroid coordinate of an input picture found out by the circuit 50 by a rotational shear detecting circuit 60 and a parallel shear detecting circuit 70 to detect the positional shear precisely.

Method for extracting inner point of polygon

Abstract: PURPOSE:To extract an inner point rapidly and exactly by using the phenomenon that a triangle having the centroid to be an inner point of any polygon is included in a triangle formed by three continuous vertexes of the polygon. CONSTITUTION:A triangular surface determining circuit 23 determines three continuous vertexes in accordance with polygonal surface model data received from a surface model circuit 21. A triangular centroid calculating circuit 24 finds out the centroid of the determined triangle to fix the centroid as a candidate inner point. Then, an inside/outside deciding circuit 25 decides whether the candidate inner point exists in an area determined by the polygonal surface model data or outside the area. If the candidate inner point is decided as an outer point, the processing is transferred to the circuit 23, and in case of an inner point, a surface normal determining circuit 22 determines the surface normal.

Application Of An Algotecture For Invariant Feature Extraction In Machine Vision

Abstract: The exponential non-uniform to uniform hardwired spatial coordinate transformation inherently imbeds an algorithm in the hardware architecture and has thus been called an algotecture. It has been suggested that the algotecture described may be more sensitive to centroid pointing errors than conventional cartesian grid structures. Simulation results for crosscorrelation template matching in the algotecture space, as opposed to standard rectilinear coordinate space, is presented for the case of annulii images with various centroid mismatch. These simulations support the claim that the algotecture mapping is less sensitive to centroid mismatch. The use of template matching on an algotecture mapped grey scale image shows the feasibility of using this technique on more complex images. Since crosscorrelation is a relatively time consuming operation, a sliding window differencing similarity measure is proposed to accomplish fast detection in the algotecture mapped space directly at the sensor level. Coupling this idea with the classification of objects via the formation of orthogonal feature vectors contained in separate spatial frequency channels which are constrained by human visual system physiological data provides a fast method of object classification which exploits the fact that different features occur in different spatial frequency bands. Finally, the use of a three spatial frequency bandpass feature extraction filter system useful for an intra-class, inter-class, and membership identification classification scheme is discussed.