Phase Correlation Motion Estimation Using Outer-Product Approximation
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Solution Overview
Problem
Conventional methods for sub-pixel motion estimation using phase correlation are limited by inappropriate fitting functions, leading to marginal results and high computational complexity, especially when dealing with 1-D sub-pel methods compared to 2-D methods, and are prone to sub-pixel error and bias.
Innovation Solution
A method that approximates the 2D neighborhood of the phase correlation peak with an outer-product of two 1D vectors to eliminate sub-pixel error and implements a two-pass phase correlation to eliminate sub-pel motion bias, using Fast Fourier Transform and inverse Fast Fourier Transform to generate and offset phase correlation surfaces for improved accuracy and reliability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If 1-D sub-pel methods are used to estimate motion independently in each spatial dimension, then computational complexity is reduced, but measurement precision deteriorates due to inability to capture 2-D correlation structure
Solution Approach 1:
The patent segments the 2-D sub-pel estimation problem into two independent 1-D estimations by approximating the 2-D neighborhood as an outer product of two 1-D vectors. This allows horizontal and vertical sub-pel components to be determined separately through 1-D sinc function fitting, reducing computational complexity while maintaining accuracy through the outer product approximation that preserves 2-D correlation structure.
Solution Approach 2:
The patent changes the mathematical model from requiring full 2-D least squares optimization to using separable 1-D sinc function fitting with outer product approximation. This parameter change in the estimation approach reduces computational complexity from O(N^4) to O(N^2) while maintaining measurement precision through the physically motivated sinc function model.
2Measurement precision
If 2-D sub-pel methods are used to utilize correlation values in the neighborhood of the peak, then measurement precision is improved, but device complexity increases due to more complex algorithms
Solution Approach 1:
The patent segments the complex 2-D estimation into simpler 1-D estimations that can be performed independently. By approximating the 2-D correlation surface as an outer product of two 1-D sinc functions, the method maintains the ability to use 2-D neighborhood information while avoiding the complexity of full 2-D least squares optimization.
Solution Approach 2:
The patent replaces the mechanical 2-D optimization process with a mathematical approximation using outer products of 1-D sinc functions. This substitution eliminates the need for complex 2-D iterative optimization while preserving the essential 2-D correlation information through the separable sinc function model.
3Ease of operation
If conventional 1-D fitting methods (quadratic or Gaussian) are used near the phase correlation peak, then ease of operation is improved, but measurement precision deteriorates because the fitting functions do not match the actual sinc function shape
Solution Approach 1:
The patent changes the fitting function from quadratic or Gaussian to a sinc function that matches the actual phase correlation surface shape. The sinc function fitting is performed independently in 1-D for each spatial dimension, maintaining simplicity while dramatically improving accuracy by using the correct functional form.
Solution Approach 2:
Instead of forcing the data to fit quadratic or Gaussian functions, the patent inverts the approach by using the known sinc function shape (derived from Fourier transform properties) to fit the data. This inversion to the correct functional form resolves the mismatch between the actual correlation surface and conventional fitting functions.
4Productivity
If a single pass of phase correlation is performed, then productivity is improved, but measurement precision deteriorates due to sub-pixel motion bias
Solution Approach 1:
The patent performs a preliminary integer-pel motion estimation in the first pass to establish a baseline. This preliminary action allows the second pass to focus specifically on sub-pel refinement with bias elimination, achieving high precision without requiring a completely new estimation approach from scratch.
Solution Approach 2:
The patent segments the motion estimation into two distinct passes: first for integer-pel motion, then for sub-pel refinement. This segmentation allows each pass to be optimized for its specific purpose, with the second pass eliminating bias through comparison with the first pass results, thereby achieving high precision efficiently.
Data Source
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AI summary
A method of improving accuracy and reliability of motion estimation is described herein. In one aspect, a 2D neighborhood of phase correlation peak is approximated with an outer-product of two 1D vectors to eliminate the sub-pixel error. In another aspect, estimation of reliability is improved. In yet another aspect, two-pass phase correlation is implemented to eliminate sub-pel motion bias.