Rational Polynomial Camera Model Coefficient Estimation
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Solution Overview
Problem
The use of physical camera models in photogrammetric processing is hindered by proprietary information and complex mathematical requirements, while Rational Polynomial Camera (RPC) models require coefficients generated from physical camera models, making it difficult to implement without known interior sensor configurations or manufacturer-provided coefficients.
Innovation Solution
The method involves retrieving camera and object space coordinates, determining grid coordinates by intersecting height surfaces with lines extending between camera and object positions, and estimating RPC model coefficients by fitting rational polynomials to these coordinates, allowing for the generation of RPC coefficients without a physical camera model.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a physical camera model is used to represent geometric relationships, then measurement precision is improved, but device complexity increases due to proprietary information requirements and complex mathematical models
Solution Approach 1:
The patent creates a simplified copy of the camera's geometric behavior through the RPC model with polynomial coefficients. Instead of using the complex physical camera model with proprietary parameters, the invention generates a polynomial-based mathematical copy that replicates the essential geometric relationships between image space and object space coordinates, making the model accessible and implementable without proprietary information
Solution Approach 2:
The patent transforms the camera model from using proprietary physical parameters (focal length, principal point, distortion coefficients) to using polynomial coefficients (a0, a1, a2, b0, b1, b2, etc.). This parameter transformation allows the same geometric functionality to be achieved with different, non-proprietary parameters that can be generated through the described methodology
2Ease of operation
If an RPC model is used instead of a physical camera model, then ease of operation is improved, but measurement precision deteriorates because RPC coefficients require generation from physical camera models or manufacturer provision
Solution Approach 1:
The patent enables the RPC model to be self-sufficient by providing a methodology to generate the necessary polynomial coefficients directly from image space and object space coordinate correspondences. This self-service capability eliminates the dependency on proprietary physical camera models or manufacturer-provided coefficients, allowing the RPC model to operate independently while maintaining geometric accuracy
3Measurement precision
If physical camera model information is required to generate RPC coefficients, then measurement precision is maintained, but loss of information increases due to proprietary information unavailability
Solution Approach 1:
The patent extracts the essential geometric relationship information directly from observable data (image space coordinates and corresponding object space coordinates) without requiring the intermediary proprietary physical camera model parameters. By taking out only the necessary coordinate correspondences and using polynomial fitting to derive coefficients, the method eliminates dependence on unavailable proprietary information while preserving geometric accuracy
Data Source
AI summary
One aspect of the invention is embodied in a number of machine-readable media having stored thereon sequences of instructions which, when executed by a machine, cause the machine to perform a number of actions. The actions include, for each of a plurality of image space coordinates of a camera image, retrieving 1) a corresponding camera position, and 2) corresponding object space coordinates on an object surface that is represented by the camera image. Then, for each of a plurality of height surfaces (chosen with respect to the object surface), a grid coordinate defined by an intersection between the height surface, and a line extending between the camera position and the object space coordinates, is determined. The determined grid coordinates are then associated with their corresponding image space coordinates. Finally, coefficients for a rational polynomial camera model are estimated by fitting rational polynomials to at least the grid coordinates and image space coordinates.