Ellipse

Algorithm

Center (category theory)

Economics

Computer science

Orthographic projection

Projection (relational algebra)

Mathematics

Position (finance)

Mathematical analysis

Geometry

Planar projection

Crystallography

Chemistry

Finance

Computer vision

Engineering Computations

Purpose 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. Design/methodology/approach 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. Findings 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. Originality/value 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.

Analysis for center deviation of circular target under perspective projection