Approximate Camera Models for Non-Earth Object Localization
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Solution Overview
Problem
Existing technologies face challenges in accurately imaging non-earth objects from space-based sensors due to the complexity of establishing a precise mathematical relationship between three-dimensional coordinates in space and two-dimensional image projections, limiting the accuracy of target location and trajectory estimation.
Innovation Solution
An approximate camera model is developed by fitting a finite projective model to a physical camera model, using sensor-based parameters and ephemeris data to estimate the location of non-earth objects in earth-centered-inertial coordinates, based on line and sample coordinates from captured images.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a physical camera model is used to establish the mathematical relationship between three-dimensional coordinates and two-dimensional image projections, then measurement precision is improved, but device complexity increases
Solution Approach 1:
The patent creates an approximate camera model that copies the essential mathematical relationship between 3D space coordinates and 2D image projections without using the full physical camera model. This approximate model uses simplified parameters (rotation matrix, translation vector, focal length, principal point) to replicate the projection behavior, thereby achieving high measurement precision while reducing device complexity.
Solution Approach 2:
The patent transforms the complex physical camera model into a simplified approximate model by changing the parameters used in the mathematical relationship. Instead of using complex sensor-based parameters, the approximate model uses standard camera parameters (rotation matrix R, translation vector t, focal length f, principal point c), which are easier to compute and interpret while maintaining sufficient accuracy for target location estimation.
2Device complexity
If a simplified approximate camera model is used, then device complexity is reduced, but measurement precision deteriorates
Solution Approach 1:
The approximate camera model carefully copies the essential projection relationship from the physical camera model. By preserving the fundamental mathematical structure (projection of 3D points through camera center to image plane) while using simplified parameters, the model achieves both low complexity and high measurement precision for target location estimation.
Solution Approach 2:
The patent applies local quality by using the approximate camera model specifically for target location and trajectory estimation tasks where high precision is needed, while avoiding its use in scenarios requiring full physical camera model accuracy. The model is optimized for the specific application context of non-earth object imaging.
3Measurement precision
If the physical camera model is used for non-earth object imaging, then measurement precision is improved, but ease of operation deteriorates
Solution Approach 1:
The patent changes the parameters from complex sensor-based parameters to standard camera parameters (rotation matrix, translation vector, focal length, principal point). These standard parameters are easier to estimate from image data and easier to interpret physically, thereby improving ease of operation while maintaining measurement precision for trajectory estimation.
Solution Approach 2:
The approximate camera model copies the projection relationship in a way that makes parameter estimation more straightforward. The simplified mathematical formulation allows for easier computation and interpretation of parameters compared to the full physical camera model, improving ease of operation without sacrificing trajectory estimation accuracy.
Data Source
AI summary
Examples of the present disclosure include a method for approximating a non-earth imaging camera model for a non-earth sensor includes obtaining a physical camera model, receiving a target range value, determining a plurality of space-based coordinates of a plurality of points about a line of sight of the sensor in proximity to a distance corresponding to the received target range value, for each of the plurality of locations, determining line and sample coordinates on an image thereof via the physical camera model based on the space-based coordinates of the plurality of points, and based on the determined line and sample coordinates for each of the plurality of points, fitting an approximate camera model thereto.