Two New Algorithms to Retrieve the Calibration Matrix from the 3-d Projective Camera Model

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