The common self-polar triangle of separate circles: Properties and applications to camera calibration

This paper investigates the properties of the common self-polar triangle of separate coplanar circles and applies them to camera calibration. We find that any two separate circles have a unique common self-polar triangle. In particular, we show that one vertex of the common self-polar triangle lies on the line at infinity. Given three separate circles, the line at infinity can be recovered using the vertices of the common self-polar triangles. Accordingly, the vanishing line of the support plane can be obtained in their images. This allows recovering the imaged circular points, which provides good constraints on the image of the absolute conic. Compared to previous calibration methods using separate circles, our approach can avoid solving quartic equation, which often causes numerical instability. In the application, we test one calibration algorithm and accurate results are achieved.