Floyd-Warshall all-pair shortest path for accurate multi-marker calibration

We propose a novel method to compute the poses of randomly positioned square markers in one world coordinate frame from multiple camera views, by taking the predicted accuracy of the camera pose estimation for each marker into account. The problem of computing the best closed-form solution of the world pose of each marker is modeled as all-pair shortest path problem in graph theory. The computed world poses are further optimized by minimizing the geometric distances in images. Experimental results show that incorporating the predicted accuracy of the pose estimation for each marker yields constant high quality calibration results independent of the order of image sequences compared to cases when this knowledge is not used.