Logarithmic Spiral Flight Paths for Aerial Imaging
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Traditional straight, linear, parallel camera trajectories used in digital image capture, especially in Structure from Motion (SfM) processing, introduce systematic errors known as the 'doming' effect, leading to inaccurate 3D topographic models and limiting their wider use.
Innovation Solution
The use of logarithmic spiral trajectories derived from predetermined basis angles and constant tangent angles, which are scaled and transformed to cover the area of interest, providing non-traditional camera placement paths that avoid the doming deformation effect.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If traditional straight, linear, parallel camera trajectories are used, then the flight path planning is simple and easy to implement, but systematic errors known as the 'doming' effect are introduced, leading to inaccurate 3D topographic models
Solution Approach 1:
The patent applies curvature by replacing straight linear trajectories with curved logarithmic spiral paths. The camera platform follows a logarithmic spiral trajectory where the angle between the radial line from the target and the tangent line to the spiral remains constant. This curved path distribution eliminates the parallel imaging direction problem that causes doming errors, while still maintaining systematic coverage of the target area.
Solution Approach 2:
The patent changes the trajectory parameters from constant straight-line paths to logarithmic spiral paths defined by specific mathematical parameters. The trajectory is characterized by a constant tangent angle between the radial line and the spiral tangent, with the spiral equation r = e^((θ-π)×cot(ψ)) where ψ is the constant tangent angle. This parameter transformation resolves the doming error while maintaining coverage efficiency.
2Manufacturing precision
If convergent image capture along curved trajectories is used, then SfM surface deformation is mitigated, but the coverage efficiency and time required to capture all areas decreases
Solution Approach 1:
The patent uses logarithmic spiral curvature to achieve both accurate SfM processing and efficient area coverage. The spiral trajectory naturally converges on the target area while maintaining a constant tangent angle, providing optimal viewing directions for SfM algorithms. The mathematical properties of the logarithmic spiral ensure that the trajectory can be scaled and repeated to cover large areas efficiently, unlike simple circular trajectories.
Solution Approach 2:
The patent segments the coverage area into multiple logarithmic spiral trajectories that can be independently planned and executed. The trajectories are scaled according to the target area dimensions and can be arranged in a systematic pattern, allowing efficient coverage of large regions while maintaining the beneficial curved path characteristics for each individual trajectory segment.
3Device complexity
If traditional linear parallel flight lines are used, then the flight path is simple to navigate, but the radial lens distortion correction becomes inaccurate, producing systematic broad-scale errors
Solution Approach 1:
The patent applies curved logarithmic spiral trajectories that naturally provide varying angles of view throughout the flight path. This curvature ensures that the camera does not maintain a constant parallel orientation to the ground, thereby improving the geometric conditions for radial distortion correction. The changing viewing angles provide better constraints for accurate distortion parameter estimation during photogrammetric processing.
Data Source
AI summary
A method and system for developing a flight plan for taking images from an area of interest is disclosed. A series of trajectories is determined. Each trajectory is determined based on a logarithmic spiral curve derived from a range of predetermined basis angles and selecting a constant tangent angle between a radial line from the location of an image sensor to a target location, and a tangent line to the logarithmic spiral curve at the location of the image sensor. A set of trajectories from the series of trajectories is selected. The selected trajectories are scaled to cover the area of interest. The selected trajectories are transformed to coordinates corresponding to the area of interest. The set of scaled and transformed trajectories are stored as the flight plan for taking images of the area of interest.