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    Area of Science:

    • Computer Vision
    • Geometric Transformations
    • Image Analysis

    Background:

    • 2D homography decomposition is crucial for various computer vision tasks.
    • Existing methods can be computationally intensive or lack interpretability.
    • There is a need for efficient and geometrically intuitive decomposition techniques.

    Purpose of the Study:

    • To present two novel and efficient decomposition methods for 2D homography: Similarity-Kernel-Similarity (SKS) and Affine-Core-Affine (ACA).
    • To provide interpretable geometric parameterizations for homography transformations.
    • To enhance the computational efficiency of feature-based and deep learning-based homography estimation pipelines.

    Main Methods:

    • Similarity-Kernel-Similarity (SKS): Computes two similarity transformations using anchor points, followed by a four-parameter kernel transformation.
    • Affine-Core-Affine (ACA): Computes source and target affine transformations using anchor points, followed by a core transformation.
    • ACA achieves high computational efficiency with minimal floating-point operations and no division operations.

    Main Results:

    • Both SKS and ACA provide fast and interpretable decomposition of 2D homography.
    • ACA computes homography up to a scale with only 85 FLOPs, facilitating RANSAC and deep learning pipelines.
    • The methods extend existing Similarity-Affine-Projective (SAP) decomposition and unify 2D affine transformations.

    Conclusions:

    • SKS and ACA offer significant advantages in terms of computational efficiency and geometric interpretability for 2D homography decomposition.
    • These methods can be readily integrated as plug-in modules into existing computer vision frameworks.
    • The polynomial representation of homography elements and unified affine transformation calculation advance the field.