Interactive modeling method of outdoor trees based on sparse images

Abstract: The creation of realistic outdoor trees is a challenging problem in the area of modeling natural phenomenon because trees have complex geometric structures. Currently, there are two major methods to achieve this goal. One approach models trees from image sequences. This approach requires more than 16 images and wide view angles to reconstruct tree point clouds and camera pose, and the reconstruction process is not easily implemented for non-expert users because of some complex computer vision techniques. The other approach uses a laser range scanner to acquire a point cloud for modeling trees. However, we need expensive hardware to obtain the point cloud. Furthermore, the background segmentation, the hole filling and the registration process of a point cloud is very cumbersome. In this paper, we present a low cost interactive modeling method to reconstruct real-world trees from sparse images. Our method has the advantage of preserving the branch structures of real trees with few images and limited viewing angle. Based on two input photographs taken from different views with the coverage of 90 degrees and 4 to 7 in-between photographs, we developed an interactive editing system to extract the node positions, the thickness of branches and the tree hierarchy from the front view image. The interactive editing system consists of branch (or node) drawing and modifying, branch (or node) inserting and deleting, thickness modifying, Hermite spline interpolation and tree hierarchy reconstruction parts. Next, we chose main branches as references, and interactively matched the corresponding branches from the side view image by making use of the in-between images. Then, we adapted the node positions using the editing system to obtain the depth information for each branch. By combining the extracted two dimensional node positions and the thickness of branch from the front view and the depth information from the side view, we drew the three dimensional tree using generalized cylinders. However, the reconstructed tree model showed distortion where the branches in the distance appeared smaller and the branches at close range appeared larger compared with the branches in the photograph. It can be explained by the double perspective projection phenomenon where the real-world objects have been transformed twice through taking photographs and through perspective transformation in OpenGL. We propose a perspective calibration method to avoid the distortion of reconstructed tree models. Leaves are difficult to be identified from images even by the interactive method. Thus, we designed a leaf arrangement algorithm and added leaves to each branch according to leaf phyllotaxis. Finally, we demonstrated the realistic reconstruction of a variety of tree species including apple trees, cherry trees and maple trees. The number of nodes of the reconstructed trees ranges from 736 to 1250, and the average reconstruction time is around 80 minutes for a medium scale tree. The result showed that our method is effective to model real world trees having clear branches and sparse leaves.