Sub-pixel Position Estimation Using Iterative Parametric Fitting
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Solution Overview
Problem
Existing methods for estimating sub-pixel positions of extreme points in images are sensitive to noise and lack reliability measures, particularly when identifying maxima or minima, which is crucial in applications like optical flow and stereo camera setups.
Innovation Solution
A method that selects a group of neighboring pixels, fits a parametric function, checks the type and location of the extreme point, iteratively removes outliers to improve fit robustness, and associates the estimate with a level of uncertainty based on the number of iterations required for convergence.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a parametric function is fitted locally to pixel values to estimate sub-pixel position, then measurement precision is improved, but reliability deteriorates due to sensitivity to noise and lack of uncertainty measure
Solution Approach 1:
The patent implements an iterative feedback mechanism where the parametric function is repeatedly fitted to the data, with each iteration using the results from the previous iteration to refine the estimate. The algorithm checks convergence criteria and adjusts the fitting process based on feedback from residual analysis, thereby improving reliability while maintaining precision in noisy environments
Solution Approach 2:
The patent performs preliminary actions by first fitting the parametric function to obtain initial estimates, then using these estimates to guide subsequent refinement steps. The algorithm prepares convergence criteria and uncertainty thresholds in advance, allowing the system to assess reliability before finalizing the sub-pixel position estimate
2Measurement precision
If iterative refinement is performed to improve estimation accuracy, then measurement precision is improved, but loss of time increases due to multiple iterations
Solution Approach 1:
The patent applies partial action by performing iterations only until convergence criteria are met or a maximum number of iterations is reached, rather than performing a fixed large number of iterations. This allows the algorithm to stop early when sufficient precision is achieved, reducing computational time while maintaining adequate measurement precision
Solution Approach 2:
The algorithm establishes convergence criteria and maximum iteration limits in advance, allowing it to determine beforehand when sufficient precision has been achieved. This preliminary setup prevents unnecessary iterations and optimizes the balance between precision and computational time
Data Source
AI summary
A method for estimating a sub-pixel position of an extreme point in an image uses a parametric function. The parametric function is fitted locally to a group of neighboring pixels in the image, and a spatial position of an extreme point of the parametric function is identified. If the extreme point of the parametric function is of a different type than the extreme point in the image, or the position of the extreme point of the parametric function is located outside an area defined by the pixel positions in the group of neighboring pixels, a pixel is removed from the group of neighboring pixels and the fitting of the parametric function is repeated. In the end, the sub-pixel position is estimated as the position of the extreme point of the parametric function. A level of uncertainty of the estimated sub-pixel position is estimated as the number of repetitions needed before arriving at the estimate of the sub-pixel position.