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Circular targets on a plane are often utilized in photogrammetry, particularly in close range photogrammetry, while spherical targetsare sometimes utilized in industrial applications. Both a circle and a sphere are projected as an ellipse onto an image. There is aneccentricity 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 highlyaccurate measurement. This paper shows a process to derive general formulae to calculate an eccentricity of a circle and a sphereusing the size and the location of a circle or a sphere, and the focal length, the position and the attitude of a camera. Furthermore thepaper shows methods to estimate the eccentricity of a circle and a sphere from the equation of the projected ellipse of a circle or asphere on an image

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