A Linear Metric Reconstruction by Complex Eigen-Decomposition

quadratic equation is eigen-decomposed to build a linear This paper proposes a linear algorithm for metric equation to compute the projective-to-Euclidean trans-reconstruction from projective reconstruction. Metric formation matrix. reconstruction problem is equivalent to estimating the projective transformation matrix that converts projective reconstruction to Euclidean reconstruction. We build 2 Background on Auto-Calibration a quadratic form from dual absolute conic projection equation with respect to the elements of the transformation matrix. The matrix of quadratic form of rank 2 is then eigen-decomposed to produce a linear estimate. The comparison of results of our linear algorithm to results of bundle adjustment, applied to sets of synthetic image data having Gaussian image noise, shows reasonable error ranges.