Uncertainty of Object Points Monoplotted from Terrestrial Images

Area of Science:

• Photogrammetry and Remote Sensing
• Geosciences and Environmental Science

Background:

• Monoplotting reconstructs 3D object points from a single oriented image using a reference surface.
• Existing monoplotting methods lack robust uncertainty estimation, limiting their application in environmental sciences.
• Accurate uncertainty quantification is crucial for deriving valuable information from historical and contemporary imagery.

Purpose of the Study:

• To estimate monoplotting uncertainty using Monte Carlo simulation, unscented transform, and variance propagation.
• To evaluate these methods for two use cases: precise point uncertainty and large-scale pixel-wise uncertainty.
• To investigate silhouette mask derivation for improved uncertainty estimation accuracy.

Main Methods:

• Monte Carlo simulation (1000 samples) for reference uncertainty estimation.
• Unscented transform for approximating uncertainty propagation.
• Classical variance propagation with tangential approximation for computational efficiency.
• Derivation and integration of silhouette masks to exclude invalid uncertainty estimates.

Main Results:

• Unscented transform (14.1% RMS error) and variance propagation (24.7% RMS error) were compared against Monte Carlo.
• For precise point uncertainty, Monte Carlo simulation is recommended due to its accuracy and computational efficiency with existing routines.
• For large-scale pixel-wise uncertainty, variance propagation provides a fast and reasonably precise solution (7.8% RMS error away from silhouettes).

Conclusions:

• Different uncertainty estimation methods are suitable for distinct monoplotting applications.
• Monte Carlo simulation offers high precision for specific point analysis, particularly for historical glacier change studies.
• Variance propagation is the preferred method for rapid, large-area uncertainty mapping, essential for image orientation and overview assessments.