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When a material is subjected to uniaxial stress, it elongates or contracts in the direction of the applied force, and also undergoes changes in the perpendicular directions. This behavior is crucial for understanding how materials behave under stress and is governed by mechanical properties such as Poisson's ratio v, which measures the ratio of transverse strain to axial strain.
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A Precision Analysis of Camera Distortion Models.

Zhongwei Tang, Rafael Grompone von Gioi, Pascal Monasse

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
    |March 24, 2017
    PubMed
    Summary

    Identifying the best camera distortion model is crucial for subpixel precision. Polynomial models offer a secure, fast, and accurate solution for modeling real camera distortions, even at high precision levels.

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    Area of Science:

    • Computer Vision
    • Optical Engineering
    • Computational Photography

    Background:

    • Accurate camera distortion modeling is essential for subpixel precision in computer vision tasks.
    • Existing models often struggle with non-radially symmetric distortions or involve complex numerical methods.
    • The choice of distortion model impacts both accuracy and computational efficiency.

    Purpose of the Study:

    • To compare the precision of five classic camera distortion models for direct and inverse distortion estimation.
    • To identify the most suitable model for achieving high subpixel precision in real-world camera distortion.
    • To evaluate the numerical stability and speed of different distortion modeling approaches.

    Main Methods:

    • Review and comparison of five classic camera distortion models (radially symmetric, polynomial, rational).
    • Evaluation of direct and inverse distortion modeling precision.
    • Numerical experiments focusing on estimation as a numerical problem, including non-linear minimization versus linear problems.
    • Validation through three independent experimental setups: Lensfun library, non-parametric fitting, and straight-line photography.

    Main Results:

    • Polynomial models, despite lacking direct physical interpretation, effectively handle both radial and non-radial distortions without needing a distortion center.
    • All models except polynomial estimation involve non-linear minimization, posing higher numerical risks.
    • High-degree polynomial models, though requiring more terms, were easily estimated, fast, and provided precise distortion modeling without overfitting, achieving 1/100 pixel accuracy.

    Conclusions:

    • Polynomial distortion models are recommended for high-precision camera distortion modeling due to their numerical security and speed.
    • The estimation of polynomial distortion models presents a linear problem, making it more robust and efficient than non-linear minimization methods.
    • Extensive experiments validate the effectiveness of polynomial models for accurate and reliable camera distortion correction across various scenarios.