Related Experiment Video
Updated: Jun 27, 2026

Precision Measurements and Parametric Models of Vertebral Endplates
Published on: September 17, 2019
Curve parametrization by moments
Irina Popovici1, William Douglas Withers
1United States Naval Academy, Annapolis, MD 21402-5002, USA. popovici@usna.edu
Abstract:
We present a method for deriving a parametric description of a conic section (quadratic curve) in an image from the moments of the image with respect to several specially-constructed kernel functions. In contrast to Hough-transform-type methods, the moment approach requires no large accumulator array. Judicious implementation allows the parameters to be determined using five multiplication operations and six addition operations per pixel. The use of moments renders the calculation robust in the presence of high-frequency noise or texture and resistant to small-scale irregularities in the edge. Our method is generalizable to more complex classes of curves with more parameters as well as to surfaces in higher dimensions.
Related Concept Videos
Curves Defined by Parametric Equations
Parametric Surfaces
Centroid for the Paraboloid of Revolution
The centroid for the paraboloid of revolution is the point where all the mass of the paraboloid is concentrated. This centroid is important for engineering applications, as it determines how forces are...
Calculus with Parametric Curves: Tangents and Areas
Tangent Planes to a Parametric Surface
Calculus with Parametric Curves: Surface Areas
