Circular array targets are widely used in 3D measurement and camera calibration. Under the perspective projection of the camera, the circular marker on the target will degenerate into an ellipse. However, the geometric center of the ellipse is not the central projection of the circular marker on the image plane. Therefore, a fast image point extraction algorithm based on projective geometry is proposed by using the geometric invariance of collinear and common points under projective transformation. Firstly, the general equation is obtained by fitting the ellipse after edge detection, shape filtering, and sub-pixel edge extraction. Secondly, the coordinates of two vanishing points along the coordinate axis of the plane target are got by projective transformation matrix. Finally, using the principle of perspective invariance, the vanishing points and the ellipse general equation are used to solve the two sets of common tangent point coordinates of the ellipse image. The intersection of two sets of tangent lines is the center projection of the circular marker on the image plane. The experimental results show that compared with the traditional method of searching common tangent points, the reconstructed average distance of the extracted center image points is reduced by 32.34%, and the precise location of the circular markers is realized, and the solving process is greatly simplified, which has strong practicability.