Simplifying the Reconstruction of 3D Models using Parameter Elimination

Reconstructing large models from images is a significant challenge for computer vision, computer graphics, and related fields. In this paper, we present an approach for simplifying the reconstruction process by mathematically eliminating external camera parameters. This results in less parameters to estimate and in an overall significantly more robust and accurate reconstruction. We reformulate the problem in such a manner as to be able to identify invariants, eliminate superfluous parameters, and measure the performance of our formulation under various conditions. We compare a two-step camera orientation-free method, where the majority of the points are reconstructed using a linear equation set, and a camera position-and- orientation free method, using a degree-two equation set. Both approaches use a full perspective camera and are applied to synthetic and real-world datasets.