Camera Parameter Estimation Using Single Unknown Distortion Model
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Solution Overview
Problem
Existing methods for estimating camera lens distortion, such as polynomial approximation, face challenges in accurately modeling radial distortion across a range of lenses from low to wide-angle, leading to unstable calculations and difficulty in deriving analytical inverse transformations, especially when dealing with adaptive distortion changes like those encountered with zoom lenses.
Innovation Solution
A camera parameter estimation apparatus and method that uses a model with a single unknown to express radial distortion, incorporating a data obtaining unit for image corresponding points and an approximation order for polynomial approximation, allowing for the estimation of geometric and lens distortion parameters based on these points and order.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If polynomial approximation is used to model radial distortion, then the distortion can be expressed mathematically, but the approximation order needs to be increased to deal with large distortion which leads to unstable numerical calculation due to over fitting
Solution Approach 1:
The patent changes the parameter representation from polynomial coefficients to a single distortion parameter k that scales with radial distance. This allows the same model structure to work across different approximation orders without the instability of high-order polynomial fitting, as the distortion magnitude is controlled by a single parameter rather than multiple polynomial coefficients.
Solution Approach 2:
The patent introduces a dynamic scaling factor based on radial distance from the optical center. The distortion model adapts to different distortion magnitudes by scaling the base distortion pattern according to the distance from the center, allowing the same approximation order to handle both small and large distortion cases without requiring changes in polynomial order.
2Adaptability or versatility
If high order polynomial approximation is used to support wide-angle lenses, then large distortion can be modeled, but it leads to unstable numerical calculation due to over fitting
Solution Approach 1:
The patent creates a universal distortion model that works across different lens types (from low to wide-angle) using a single parameter k and a fixed approximation order. The model is scaled dynamically based on the specific lens characteristics, eliminating the need to change polynomial order for different lens types while maintaining calculation stability.
3Manufacturing precision
If polynomial approximation of high order is used, then wide-angle lens distortion can be supported, but approximation of low order leaves distortion while approximation of high order leads to unstable numerical calculation
Solution Approach 1:
The patent extracts the essential distortion characteristic into a single parameter k that represents the overall distortion magnitude. By separating the distortion magnitude (parameter k) from the distortion pattern (fixed polynomial basis), the model achieves high correction accuracy without requiring high polynomial orders, thus reducing model complexity while maintaining precision.
Data Source
AI summary
A camera parameter estimation apparatus 10 for estimating geometric parameters of a camera that has shot an image of an object and a lens distortion parameter of a lens distortion model represented by a single unknown. The camera parameter estimation apparatus 10 includes: a data obtaining unit 11 that obtains image corresponding points relating to the object and an approximation order for polynomial approximation of the lens distortion model; and a parameter estimation unit 12 that estimates, based on the image corresponding points and the approximation order, the geometric parameter and the lens distortion parameter that minimize an error function representing a specific transformation of the image corresponding points.