A real-time and precise ellipse detector via edge screening and aggregation
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Ellipse
SummaryThe tangent to an ellipse at a point P can be constructed as the exterior angle bisector of the angle that the point P makes with the two foci of the ellipse. Typically this fact is proved by showing that the exterior angle bisector cannot meet the ellipse in a second point, and therefore must be the tangent. This note gives an alternative proof that is more in line with the notion of tangent as a limit of secants.
Ellipse
Tangent vector
Line (geometry)
Tangent cone
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In this paper, we address the fundamental problem of tangent estimation for digital curves encountered in digital image processing. We propose a simple, geometry based tangent estimation method for digital curves. The geometrical proof of the method and the maximum error analysis for digital curves are presented as the theoretical backbone of the method. Numerical results have been tested for digital ellipses of various eccentricities (circle to very sharp ellipses) and the maximum error of the proposed method is bounded and is less than 5.5 degrees for reasonably large ellipses. The proposed tangent estimator is applied to a practical application which analyzes the error in a geometric ellipse detection method. The ellipse detection method is greatly benefited by the proposed tangent estimator, as the maximum error in geometrical ellipse detection is no more critically dependent upon the tangent estimation (due to the reduced error in tangent estimation). The proposed tangent estimator also increases the reliability and precision of the ellipse detection method.
Ellipse
Tangent vector
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Design a process of drawing an ellipse using Visual Basic , it is convenient and quick to draw an ellipse at any position by this process , solved the problem that the ellipse cant be drawn at any position by the Circle-Method in VB.
Ellipse
Position (finance)
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The ellipse can be transformed into a circle by dilating the coordinates of the ellipse relative to the x-axis and y-axis. Therefore, this study aimed to derive the formula for the equation of the perimeter of an ellipse by using the transformation of an ellipse to a circle. This transformation was arranged so that the perimeter of the ellipse was equal to the perimeter of the circle. The type of research was in the review of books, articles, and relevant research reports. The results showed that the ellipse can be transformed into a circle while maintaining its perimeter. So, the perimeter of the ellipse was the same as the perimeter of the circle.
Ellipse
Perimeter
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A new algorithm on Ellipse detection in color image was proposed in this paper.Firstly the geometry of ellipse was analyzed in this paper.Then an ideal ellipse of a similar ellipse region can reason out by the help of the concept of inertial square.This algorithm decreased computation greatly.If the center of an ellipse can work out,an ideal ellipse of a region can be figured out soon.After getting the ideal ellipse,by fitting the edge of the region to the ideal ellipse,whether the region is an ellipse region will be verified.The algorithm can be well applied to ellipse detection.
Ellipse
Square (algebra)
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Based on the basic geometrical fact that the sum length of the two tangents from a point outside a circularity to it is larger than the arc between the tangents, we can draw the same conclusion if we replace the arc with a protruding slick curve.
Arc length
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A new ellipse detect method is presented based on major axis of the ellipse,which uses major axis of the ellipse to calculate four ellipse parameters and accumulates the length information for minor axis of the ellipse.Using dual points method to validate whether this is a major axis of the ellipse.Experimental results demonstrate that this method is faster than the former method based on major axis of the ellipse.
Ellipse
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We propose a pattern recognition method that identifies the common tangent lines of a set of ellipses. The detection of the tangent lines is attained by applying the Legendre transform on a given set of ellipses. As context, we consider a hypothetical detector made out of layers of chambers, each of which returns an ellipse as an output signal. The common tangent of these ellipses represents the trajectory of a charged particle crossing the detector. The proposed method is evaluated using ellipses constructed from Monte Carlo generated tracks.
Ellipse
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483. [L1. 4. c.] The tangents to an ellipse at Q and R intersect at a point P on a coaxial ellipse whose axes are respectively n times those of the former curve. Find the locus of the centroid of the triangle PQR - Volume 3 Issue 45
Ellipse
Coaxial
Centroid
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Ellipse detection is a widely used technology.Since there are many objects are similar to ellipse,so ellipse detection becomes a key technology in image segment and object extraction.The geometry of ellipse is analyzed in this paper.Then an ideal ellipse of a similar ellipse region can reason out in the help of the concept of inertial square.This algorithm decreased computation greatly.If the center of an ellipse can work out,an ideal ellipse of a region can be figured out.After getting the ideal ellipse,by fitting the edge of the region to the ideal ellipse,whether the region is an ellipse region can be verified.
Ellipse
Square (algebra)
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