Vignetting Correction via Polynomial Curve Fitting
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Solution Overview
Problem
Existing methods for vignetting correction in digital image processing require high storage capacity for precise fractional correction values, making them costly and inefficient.
Innovation Solution
A method using polynomial curve fitting, specifically approximating vignetting correction values with a hyperbolic cosine function and reducing computational load through forward differencing, allowing for low-cost implementation and calibration.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a look up table of correction factors is used for vignetting correction, then correction precision is improved, but storage requirements increase
Solution Approach 1:
The patent replaces the storage-based lookup table approach with a computational approach using polynomial curve fitting. Instead of storing pre-computed correction factors for each pixel, the system calculates correction values in real-time using a mathematical model (polynomial function) that approximates the vignetting effect. This substitution of storage with computation resolves the contradiction by eliminating the need for large storage capacity while maintaining correction precision.
Solution Approach 2:
The patent transforms the correction approach by changing from storing fixed correction values to using variable parameters in a polynomial function. The correction is performed by evaluating a polynomial equation with coefficients that are determined during calibration, rather than storing lookup tables. This parameter transformation allows the system to achieve high precision correction with minimal storage, as only the polynomial coefficients need to be stored rather than full lookup tables.
2Device complexity
If polynomial curve fitting with hyperbolic cosine approximation is used, then computational load is reduced, but manufacturing precision requirements increase
Solution Approach 1:
The patent uses parameter changes by approximating the complex vignetting correction function with a hyperbolic cosine function, which can be represented as a polynomial. This approximation reduces computational complexity compared to using lookup tables or more complex mathematical models. The polynomial coefficients are determined through calibration, and once obtained, they can be implemented with standard computational operations, reducing the hardware complexity while maintaining adequate precision for the application.
Data Source
AI summary
Methods and apparatuses for vignetting correction of imager pixels signals. A polynomial correction surface is determined based on a pixel array center, height, and width, surface fitting parameters, and pixel coordinates. The pixel signal is then multiplied by the corresponding value from the polynomial correction surface to create a vignetting corrected signal.