Estimation of planar angles from non-orthogonal imaging

Abstract

Photogrammetry-based methods are traditionally used to estimate the geometrical parameters using optical images. These methods employ specific equipment, computationally sophisticated and expensive algorithms, and utilize projective geometry to reconstruct real-life scenes up to a scale. In this work, we used a computationally less-expensive method for sparse reconstruction to estimate the planar angles using two-view geometry and linear algorithms from non-orthogonal images acquired by a smartphone camera. First, intrinsic camera parameters were determined. Next, scale-invariant feature transform was used to identify the correspondence points from each pair of images. Epipolar constraint was applied on all these points to determine the essential matrix using the eight-point algorithm. Thereafter, extrinsic camera parameters were estimated from the essential matrix and combined with the intrinsic matrix to get the camera projection matrix. Finally, linear triangulation was used to get the sparse point cloud representing the scene. Planar angles were estimated by backprojecting the chosen image points and applying simple vector algebra on the obtained 3D points. The method was successful in estimating the planar angles in less than 10 s on non-curved edges with an average error of 3% by using only ten images. Given the simplicity of methods used, this technique can be integrated into a smartphone for on-site measurements as well as large deformations.