Volume III-5
ISPRS Ann. Photogramm. Remote Sens. Spatial Inf. Sci., III-5, 19-26, 2016
https://doi.org/10.5194/isprs-annals-III-5-19-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
ISPRS Ann. Photogramm. Remote Sens. Spatial Inf. Sci., III-5, 19-26, 2016
https://doi.org/10.5194/isprs-annals-III-5-19-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.

  06 Jun 2016

06 Jun 2016

ECCENTRICITY ON AN IMAGE CAUSED BY PROJECTION OF A CIRCLE AND A SPHERE

R. Matsuoka and S. Maruyama R. Matsuoka and S. Maruyama
  • Geospatial Technology Department, Kokusai Kogyo Co., Ltd., 2-24-1 Harumi-cho, Fuchu, Tokyo 183-0057, Japan

Keywords: Eccentricity, Projection, Circle, Sphere, Ellipse, Formula

Abstract. Circular targets on a plane are often utilized in photogrammetry, particularly in close range photogrammetry, while spherical targets are sometimes utilized in industrial applications. Both a circle and a sphere are projected as an ellipse onto an image. There is an eccentricity on an image between the centre of the projected ellipse and the projected location of the centre of a circle or a sphere. Since only the centre of the projected ellipse is measured, the correction of the eccentricity is considered to be necessary for highly accurate measurement. This paper shows a process to derive general formulae to calculate an eccentricity of a circle and a sphere using the size and the location of a circle or a sphere, and the focal length, the position and the attitude of a camera. Furthermore the paper shows methods to estimate the eccentricity of a circle and a sphere from the equation of the projected ellipse of a circle or a sphere on an image.