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Analysis for center deviation of circular target under perspective projection

Yu Sun (College of Computer Science and Technology, Xi’an University of Science and Technology, Xi’an, China)

Engineering Computations

ISSN: 0264-4401

Article publication date: 19 July 2019

Issue publication date: 12 September 2019




Accurate feature localization is a fundamental problem in computer vision and visual measurement. In a perspective projection model of the camera, the projected center of a spatial circle and the center of the projection ellipse are not identical. This paper aims to show how to locate the real projection center precisely in the perspective projection of a space circle target.


By analyzing the center deviation caused by projection transformation, a novel method is presented to precisely locate the real projection center of a space circle using projective geometry. Solution distribution of the center deviation is analyzed, and the quadratic equation for determining the deviation is derived by locating vanishing points. Finally, the actual projected center of the circular target is achieved by solving the deviation quadratic equations.


The procedures of the author’s method are simple and easy to implement. Experimental data calculated that maximum deviation occurs at approximately between 3π/10 and 2π/5 of the angle between the projection surface and the space target plane. The absolute reduction in error is about 0.03 pixels; hence, it is very significant for a high-accuracy solution of the position of the space circle target by minimizing systematic measurement error of the perspective projection.


The center deviation caused by the space circle projection transformation is analyzed, and the detailed algorithm steps to locate the real projection center precisely are described.



This work is supported by the Scientific and Technology Program funded by Xi’an City (Program 2017079CG/RC042(XAKD003)).


Sun, Y. (2019), "Analysis for center deviation of circular target under perspective projection", Engineering Computations, Vol. 36 No. 7, pp. 2403-2413.



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