Camera Calibration With Second-Order Distortion Correction
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Solution Overview
Problem
Existing camera calibration methods, particularly for security or identification documents, fail to accurately determine distances due to neglecting second-order distortion, leading to imprecise transformations between image and world coordinates, especially at the edges of images.
Innovation Solution
A method involving a calibration plate with known points, using a nonlinear and derivative-free approximation method like the downhill simplex or simulated annealing algorithm, iteratively optimizes transformation parameters to include both first- and second-order distortions, ensuring accurate transformations by minimizing deviation through iterative optimization.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If only first-order distortion is considered in camera calibration, then the calibration process is simpler and faster, but the measurement precision deteriorates, especially at image edges
Solution Approach 1:
The patent extends the distortion correction model by adding second-order distortion parameters (k2) to the traditional first-order model. This parameter expansion allows the calibration to account for higher-order radial distortion effects, significantly improving distance measurement accuracy at image edges while maintaining a manageable calibration process through the use of polynomial-based correction functions
2Measurement precision
If more complex distortion models are used to improve accuracy, then measurement precision improves, but the device complexity increases
Solution Approach 1:
The patent employs a systematic extension of the distortion model from first-order to second-order polynomial terms. This approach improves accuracy by capturing higher-order radial distortion effects while maintaining mathematical tractability through the use of standardized polynomial forms, avoiding the need for overly complex numerical models
Solution Approach 2:
The patent implements an iterative optimization process that uses feedback from calibration point measurements to refine distortion parameters. The algorithm repeatedly adjusts the second-order distortion coefficients (k2) based on the deviation between measured and expected calibration point positions, converging to optimal values that maximize measurement accuracy
3Measurement precision
If second-order distortion is included in calibration, then distance determination accuracy at image edges improves, but the calculation complexity increases
Solution Approach 1:
The patent introduces second-order distortion parameters (k2) to the radial correction model, enabling accurate compensation for higher-order distortion effects. The polynomial-based approach allows analytical computation of correction terms, improving edge distance accuracy without requiring complex numerical inversion procedures
Solution Approach 2:
The patent replaces complex numerical optimization methods with a more efficient polynomial-based correction approach. By formulating the second-order distortion correction in terms of polynomial expansions, the system achieves high accuracy through straightforward mathematical computations rather than iterative mechanical optimization processes
Data Source
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AI summary
The invention relates to a method for calibrating a camera with a calibration plate (100), comprising the steps: recording the calibration plate (100) together with the calibration points (101); determining the position of the plurality of calibration points (101) in image coordinates by means of an evaluation unit (S2); transforming the image coordinates of the calibration points (101) into world coordinates by means of a predetermined initial transformation rule To, which contains parameters to which predetermined starting values are assigned, wherein the parameters include the coefficients for a perspective transformation, for a correction of first-order distortion and for a correction of second-order distortion (S3).Iterative optimization of the values of the parameters of the transformation rule T using a nonlinear and derivative-free approximation method based on the deviation of the recorded position of the majority of calibration points (101) from the known position of the calibration points (101) on the calibration plate (100) and/or based on the deviation of the recorded distance between two of the recorded calibration points (101) and the known distance between the two corresponding calibration points (101) on the calibration plate (100), as long as,until the deviation in one iteration step no longer differs from a deviation in an immediately subsequent iteration step, or differs by at most a tolerance value (S5). The invention further relates to a method for measuring a security or identification document using a camera and a method for transforming at least one position or distance from world coordinates into image coordinates.