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On Quadratic Interpolation of Image Cross-Correlation for Subpixel Motion Extraction
Bian Xiong1,2, Qinghua Zhang1,2, Vincent Baltazart1
1COSYS-SII, Université Gustave Eiffel, IFSTTAR, 44344 Bouguenais, France.
Sensors (Basel, Switzerland)
|February 15, 2022
Summary
Quadratic surface fitting (QSF) for subpixel motion extraction can fail. This study analytically identifies conditions for QSF maximum existence and proposes modifications to improve its reliability in digital image correlation.
Area of Science:
- Image Processing
- Computer Vision
- Optical Measurement
Background:
- Digital image correlation (DIC) is crucial for motion extraction in video analysis.
- Subpixel refinement methods enhance displacement estimation accuracy.
- Quadratic surface fitting (QSF) is a common DIC subpixel refinement technique balancing accuracy and computational cost.
Purpose of the Study:
- To analytically investigate the mathematical conditions governing the existence of a maximum in QSF.
- To identify failure cases of the QSF method in subpixel motion extraction.
- To propose algorithm modifications for enhancing QSF reliability.
Main Methods:
- Analytical investigation of the QSF method using counterexamples.
- Rigorous mathematical analysis to establish conditions for quadratic surface maximum.
- Development of modified algorithms to address QSF failure cases.
- Experimental validation using diverse image datasets.
Main Results:
- Demonstration that the fitted quadratic surface in QSF does not always possess a maximum, contrary to common assumptions.
- Establishment of precise mathematical criteria for the existence of a QSF maximum.
- Proposed algorithmic improvements effectively handle QSF failure cases, enhancing subpixel motion extraction.
Conclusions:
- The QSF method's reliability for subpixel motion extraction is contingent on specific mathematical conditions.
- Understanding these conditions is vital for accurate DIC analysis.
- The proposed modifications offer a more robust QSF approach for digital image correlation applications.
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