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This paper addresses the problem of calibrating a pinhole camera using images of a symmetric object. Assuming a unit aspect ratio, and zero skew, we show that inter-image homographies can be expressed as a function of the principal point. By minimizing the symmetric transfer error of geometric distances, we thus obtain an accurate solution for the calibration parameters. We show that the approach can also be extended to a calibration technique using images of a 1D object with a fixed pivoting point. The advantage of our approach over existing methods is that we rely only on inter-image homgraphies, and hence no knowledge of the world to image homography is required. To demonstrate the effectiveness of the approach both in the case of symmetric objects and 1D objects, we present the processing results for both synthetic and real images, and provide a quantitative comparison with Zhang's flexible calibration technique (2000), and his 1D calibration method (2002).