To Measure the Perimeter of an Ellipse Using Image Processing and Mathematical Reasoning (original) (raw)
2017
Image processing and mathematical reasoning are two powerful techniques to solve some of the complex problems. Since the perimeter of ellipse is not determined accurately as well as the existing perimeter equations are too complex, researchers attempt to find proper solutions for this issue. This paper proposes a novel approach to measure the perimeter of an ellipse by using image processing and mathematical reasoning. This approach consists of two stages. In the first stage, value of a pixel is calculated via a pixel-by-pixel image processing based on the perimeter of several circles having different radii. In the second stage, the perimeter of an ellipse is defined by the pixels of various ellipses having different diameters and the value of a pixel through a mathematical reasoning. Simulation results show that P = 1.14167p (a + b) is the suggested perimeter of an ellipse according to the considered simulation scenarios.
Related papers
DERIVING THE EXACT FORMULA FOR PERIMETER OF AN ELLIPSE USING COORDINATE TRANSFORMATION
Alifmatika: Jurnal Pendidikan dan Pembelajaran Matematika, 2022
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.
Measuring Curvature Method for the Exact Value of the Ellipse Perimeter
Eurasian Journal of Physics, Chemistry and Mathematics, 2023
An ellipse is a curve formed by a plane, that intersects a cone at an angle with respect to the base. The perimeter of an ellipse is the total distance run by its outer boundary. Each of the two fixed points is called a focus. Unfortunately, there is no easy technique to determine the perimeter of the ellipse by using elementary functions of a and b, instead it requires complicated functions beyond trigonometric, exponential, and
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.