Estimation of Projection Matrices from a Sparse Set of Feature Points for 3D Tree Reconstruction from Multiple Images

Abstract

3D reconstruction of trees is an important task for tree analysis but the most affordable approach to capture real objects is with a camera. Although, there already exist methods for 3D reconstruction of trees from multiple photographs, they mostly handle only self-standing trees captured at narrow angles. In fact, dense feature detection and matching is in most cases only the first step of the reconstructionand requires a large set of features and high similarity between individual pictures. However, capturing trees in the orchard is in most cases possible only at wider angles between the individual pictures and with overlapping branches from other trees, which prevents reliable feature matching. We introduce a new approach for estimating projection matrices to produce 3D point clouds of trees from multiple photographs. By manually relating a smaller number of points on images to reference objects, we substitute the missing dense set of features. We assign to each image a projection matrix and minimize the projection error between the images and reference objects using simulated annealing. Thereby, we produce correct projection matrices for further steps in 3D reconstruction. Our approach is tested on a simple application for 3D reconstruction of trees to produce a 3D point cloud. We analyze convergence rates of the optimization and show that the proposed approach can produce feasible projection matrices from a sufficiently large set of feature points. In the future, this approach will be a part of a complete system for tree reconstruction and analysis.