Regularized Cost Function for Stable Color Calibration Matrix
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Solution Overview
Problem
Current calibration methods for devices, such as printers, are resource-intensive and unstable, particularly when relying on pseudo-inverse techniques for color calibration, as they are sensitive to noise and do not span the entire spectral value space, leading to inconsistent results.
Innovation Solution
Applying a cost function that calculates an optimal value for a single variable, such as delta (δ), using a regularization parameter to generate an augmented data set that stabilizes the calibration matrix, allowing for robust color calibration across different data sets without requiring additional measurements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If pseudo-inverse techniques are used for color calibration, then calibration can be performed, but the results are unstable and sensitive to noise
Solution Approach 1:
The patent transforms the calibration problem into an optimization problem by introducing a cost function with parameters (regularization weighting parameter λ) that can be adjusted to control the trade-off between fit error and regularization cost, thereby achieving stable and precise calibration results
Solution Approach 2:
The patent employs iterative optimization where the cost function is minimized through feedback loops, adjusting the calibration matrix based on measured errors and regularization terms to converge on a stable solution that is less sensitive to noise
2Measurement precision
If off-line spectrophotometer measurement is used, then color characterization can be performed, but the process is highly resource intensive
Solution Approach 1:
The patent creates a computational model that copies the essential calibration information from limited off-line measurements, allowing the system to infer color characteristics across the entire spectral value space without requiring extensive physical measurements
Solution Approach 2:
The patent transitions from measuring only at discrete spectral points to modeling across the entire spectral dimension, using the cost function optimization to extrapolate calibration data from limited measurements to comprehensive spectral coverage
3Productivity
If calibration is performed with limited data sets, then the process becomes faster, but the calibration matrix becomes unstable with small changes in data
Solution Approach 1:
The patent applies regularization terms in the cost function that act as a cushion against data variability, preventing the calibration matrix from becoming overly sensitive to small changes in the input data by penalizing large deviations from expected calibration characteristics
Data Source
AI summary
A method, non-transitory computer readable medium, and apparatus for applying a cost function to calculate an optimal value of a single variable for a calibration application are disclosed. For example, the method identifies the single variable of the calibration application, applies a cost function to the single variable, wherein the cost function comprises a function of a fit error plus a regularization weighting parameter (λ) times a regularization cost, calculates the optimal value of the single variable based upon the cost function that is applied to the single variable and uses the optimal value of the single variable to generate a calibration matrix used for the calibration application.