Retrieval of the Calibration Matrix from the 3-D Projective Camera Model

By relating the projective camera model to the perspective one, the intrinsic camera parameters give rise to what is called the calibration matrix. This paper presents two new methods to retrieve the calibration matrix from the projective camera model. In both methods, a collective approach was adopted, using matrix representation. The calibration matrix was retrieved from a quadratic matrix term. The two methods were framed around a correct utilization of Cholesky factorization to decompose the quadratic matrix term. The first method used an iterative Cholesky factorization to retrieve the calibration matrix from the quadratic matrix term. The second method used Cholesky factorization to factor the quadratic matrix term but after its inversion. The basic argument behind the two methods is that: the direct use of Cholesky factorization does not reveal the correct decomposition due to the missing matrix structure in terms of lowerupper ordering. This study presents two new algorithms to rebuild the missing matrix structure. In both methods, a successful retrieval of the calibration matrix was achieved. This paper explains the key ideas behind the two methods, accommodated with a simulated example to demonstrate their validity.