Survey of 8 UAV Set-Covering Algorithms for Terrain Photogrammetry

Abstract

Remote sensing with unmanned aerial vehicles (UAVs) facilitates photogrammetry for environmental and infrastructural monitoring. Models are created with less computational cost by reducing the number of photos required. Optimal camera locations for reducing the number of photos needed for structure-from-motion (SfM) are determined through eight mathematical set-covering algorithms as constrained by solve time. The algorithms examined are: traditional greedy, reverse greedy, carousel greedy (CG), linear programming, particle swarm optimization, simulated annealing, genetic, and ant colony optimization. Coverage and solve time are investigated for these algorithms. CG is the best method for choosing optimal camera locations as it balances number of photos required and time required to calculate camera positions as shown through an analysis similar to a Pareto Front. CG obtains a statistically significant 3.2 fewer cameras per modeled area than base greedy algorithm while requiring just one additional order of magnitude of solve time. For comparison, linear programming is capable of fewer cameras than base greedy but takes at least three orders of magnitude longer to solve. A grid independence study serves as a sensitivity analysis of the CG algorithms α (iteration number) and β (percentage to be recalculated) parameters that adjust traditional greedy heuristics, and a case study at the Rock Canyon collection dike in Provo, UT, USA, compares the results of all eight algorithms and the uniqueness (in terms of percentage comparisons based on location/angle metadata and qualitative visual comparison) of each selected set. Though this specific study uses SfM, the principles could apply to other instruments such as multi-spectral cameras or aerial LiDAR.

Large-Scale Reality Modeling of a University Campus Using Combined UAV and Terrestrial Photogrammetry for Historical Preservation and Practical Use

“…Integers and implementation of combinatorial optimization in various operations such as pure mathematics, supply chain, machine learning, and, of course, UAVs arise [37]. Hammond et al [38] reiterate that given a countably infinite set, combinatorial optimization uses the set to find the optimal outcome, and specifically studies the subtopic of mathematical optimization as applied to UAV photogrammetry. Optimized UAV photogrammetry builds off camera planning and the SCP as pioneered by Victor Klee's Art Gallery problem and, later on, the structured work flow of Liu et al [39,40].…”

“…Al-Ghamdi and Al-Masalmeh [44], Hoffman et al [45], and Hammond et al [38] provide explanations of NP, NP-hard, and NP-complete problems as paraphrased in the following bullet-points:…”

“…The formulation of the SCP is analogous to the approach in Hammond et al [38], but does not choose cameras from a pre-existing set of photos and instead plans based off the a priori point cloud:…”

“…While many algorithms exist to solve the SCP for UAV photogrammetry, the base greedy algorithm often serves as the base comparison of other solutions due to leveraging both a quick solve time and a feasible (but not necessarily optimal and a low possibility of being the worst) solution [38,[47][48][49][50][51]. Adjustments to the base algorithm fine-tune the balance between solve-time and the necessary output, but the concept remains the same.…”

Extending Multi-Beam Sonar with Structure from Motion Data of Shorelines for Complete Pool Bathymetry of Reservoirs

“…Until recently, images collected from sUAV platforms were not useful for photogrammetry because the position of the camera was not known to provide sufficient accuracy and the cameras used were not of high enough quality. New computation algorithms address both of these issues by using a large number of images combined with minimal ground truth data to generate accurate terrain models [4][5][6][7]. For example, Ruberti et al [8] used sUAV imagery to assess sea cliff stability, addressing challenges similar to those encountered when developing full-pool bathymetric maps, and there have been many other studies that used sUAV imagery to generate terrain models, though in different application areas without the issue related to long, thin models [9][10][11][12][13][14].…”