Submodular Trajectory Optimization for Aerial 3D Scanning Supplementary Material

In this section, we describe our high-level strategy for data acquisition, as well as our multi-view stereo processing pipeline for estimating the scene geometry and free space. Our goals in this section are twofold. First, we would like to obtain a rough estimate of the scene geometry, in the form of a triangle mesh in real-world coordinates. Second, we would like to obtain a strictly conservative estimate of the free space, in the form of an occupancy volume in realworld coordinates. Together, these complimentary scene representations will enable us to plan trajectories that maximize the quality of a 3D reconstruction. Drone Camera Hardware Our system requires access to a drone camera that can be commanded to fly along prespecified camera trajectories, given in GPS coordinates (i.e., latitude, longitude, altitude). The drone camera must also take geotagged images of the scene at roughly constant intervals (e.g., one image every few meters). We require geotagged images, in order to establish a correspondence between the physical world and the arbitrary coordinate system of our multi-view stereo reconstruction. In our system, we use the 3D Robotics Solo drone [1] equipped with a GoPro Hero 4 camera. User Input Our system requires two bounding boxes as input, each of which can easily be drawn by a user on a 2D map (e.g., Google Maps) and extruded vertically. The first bounding box, bs, specifies the volume that the user wants to scan. The second bounding box, bc, specifies the volume that the drone is allowed to fly within. We require that bc be made sufficiently tall, so that the entire ceiling of bc is free of obstacles. This requirement is necessary to give our drone some non-trivial region of free space that it can safely explore, prior to resolving any scene geometry. We do not assume initially that any other space is free. Initial Camera Trajectory Our system begins by flying the drone in an elliptical orbit trajectory around the ceiling of bc, pointing the camera at the center of bs. For the scenes we consider in this paper, this initial elliptical trajectory consumes roughly 25% of our drone’s travel budget. Dense Multi-View Stereo After we have flown an initial camera trajectory, the first step in our image processing pipeline is to run the structure-from-motion software VisualSFM [17, 18, 19, 20] on the sequence of images acquired by our drone. Our next step is to run the depth map reconstruction step of the Multi-View Environment (MVE) [7]. In our implementation, we set the scale parameter of MVE such that the reconstructed depth maps will be at a resolution of at least 512×512 (e.g., if the images we originally capture are 2048×2048, we set the scale parameter to 2). For the scenes we consider in this paper, computing structure-from-motion and dense multi-view stereo takes roughly 15 minutes, and is the dominant cost in our explore phase. Mapping Between Coordinate Systems We perform all our trajectory planning in real-world coordinates, using the UTM coordinate system [14]. UTM coordinates are similar to GPS coordinates, in the sense that they describe positions on the surface of the Earth. However, unlike GPS coordinates, the UTM coordinate axes are approximately orthogonal, and the default UTM units are meters. Together, these properties make UTM coordinates well-suited for trajectory planning. In order to use our reconstructed scene geometry for trajectory planning, we must establish a correspondence between the UTM coordinate system and the arbitrary coordinate system of the reconstructed geometry. We estimate this correspondence by considering our sequence of geotagged camera positions (in UTM coordinates), and the sequence of estimated camera positions recovered during our structure-from-motion step (in reconstruction coordinates). We estimate the similarity transform that maps from reconstruction coordinates to UTM coordinates using standard numerical techniques [13]. Obtaining an Oriented Point Cloud and Occupancy Volume We generate an oriented point cloud of the scene geometry, and an occupancy volume of the scene’s free space,