• BibTex

    author = {Alim, Usman},
    title = {Rendering in shift-invariant spaces},
    booktitle = {Proceedings of Graphics Interface 2013},
    series = {GI 2013},
    year = {2013},
    issn = {0713-5424},
    isbn = {978-1-4822-1680-6},
    location = {Regina, Saskatchewan, Canada},
    pages = {189--196},
    numpages = {8},
    publisher = {Canadian Human-Computer Communications Society},
    address = {Toronto, Ontario, Canada},


We present a novel image representation method based on shift-invariant spaces. Unlike existing rendering methods, our proposed approach consists of two steps: an analog acquisition step that traces rays through the scene, and a subsequent digital processing step that filters the intermediate digital image to obtain the coefficients of a minimum-error continuous image approximation. Our approach can be easily incorporated in existing renderers with very little change and with little-to-no computational overhead. Additionally, we introduce the necessary tools needed to analyze the smoothing and post-aliasing properties of the minimum-error approximations. We provide examples of spaces --- generated by the uniform B-splines --- that can be readily used in conjunction with the two-dimensional Cartesian grid. Our experimental results demonstrate that minimum-error approximations significantly enhance image quality by preserving high-frequency details that are usually smoothed out by existing image anti-aliasing approaches.