Multi-point geometry: The geometry of 1 point in N images under perspective projection has been thoroughly investigated, identifying bilinear, trilinear, and quadrilinear relations between the projections of 1 point in 2, 3 and 4 frames respectively. The dual problem-the geometry of N points in 1 image-has been studied mostly in the context of object recognition, often assuming weak perspective or affine projection. We provide here a complete description of this problem. We employ a formalism in which multiframe and multi-point geometries appear in symmetry. Points and projections are interchangeable. We then derive bilinear equations for 6 points (dual to 3-frame geometry), trilinear equations for 7 points (dual to 3-frame geometry), and quadrilinear equations for 8 points (dual to the epipolar geometry). We show that the quadrilinear equations are dependent on the the bilinear and trilinear equations, and we show that adding more points will not generate any new equation. The new equations are used to design new algorithms for the reconstruction of shape from many frames, and for learning invariant relations for indexing into a database.


    Access

    Check access

    Check availability in my library

    Order at Subito €


    Export, share and cite



    Title :

    Shape tensors for efficient and learnable indexing


    Contributors:
    Weinshall, D. (author) / Werman, M. (author) / Shashua, A. (author)


    Publication date :

    1995-01-01


    Size :

    775267 byte




    Type of media :

    Conference paper


    Type of material :

    Electronic Resource


    Language :

    English



    Shape Tensors for Efficient and Learnable Indexing

    Werman, M. / Weinshall, D. / Shashua, A. et al. | British Library Conference Proceedings | 1995


    Aerodynamic Sensitivities over Separable Shape Tensors

    Doronina, Olga A. / Lee, Bumseok / Grey, Zachary J. et al. | AIAA | 2025


    LEARNABLE RADIO CONTROL SYSTEM

    STEVEN L GEERLINGS / MARK ZEINSTRA / JAMES E TRAINOR | European Patent Office | 2015

    Free access

    Graph-based shape indexing

    Demirci, M. F. | British Library Online Contents | 2012


    Relational Histograms for Shape Indexing

    Huet, B. / Hancock, E. R. / IEEE; Computer Society | British Library Conference Proceedings | 1998