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    Area of Science:

    • Computer Vision
    • Image Formation
    • Physics-Based Modeling

    Background:

    • Linear and multilinear models like PCA, 3DMM, AAM/ASM, and multilinear tensors are widely used in computer vision for object shape and appearance analysis.
    • The applicability of these heuristic models has not been thoroughly analyzed from fundamental physical laws.

    Purpose of the Study:

    • To analyze the applicability of heuristic linear and multilinear models in computer vision based on physical laws of object motion and image formation.
    • To provide a physics-based understanding of the successes and limitations of existing computer vision approaches.
    • To identify conditions under which these models are valid.

    Main Methods:

    • Analysis of heuristic models using fundamental physical laws of object motion and image formation.
    • Mathematical proof demonstrating the multilinear approximation of image appearance space under suitable conditions.
    • Numerical analysis of physics-based model accuracy.

    Main Results:

    • The image appearance space can be closely approximated as multilinear under suitable conditions.
    • Illumination and texture subspaces are trilinearly combined with motion and deformation subspaces.
    • A physics-based analytical representation of image space is derived.

    Conclusions:

    • The study provides a physics-based foundation for understanding linear and multilinear models in computer vision.
    • Identifies the conditions under which these models are valid, explaining their successes and limitations.
    • Offers an analytical framework for image space representation based on physical factors.