It is shown how false operator responses due to missing or uncertain data can be significantly reduced or eliminated. It is shown how operators having a higher degree of selectivity and higher tolerance against noise can be constructed using simple combinations of appropriately chosen convolutions. The theory is based on linear operations and is general in that it allows for both data and operators to be scalars, vectors or tensors of higher order. Three new methods are represented: normalized convolution, differential convolution and normalized differential convolution. All three methods are examples of the power of the signal/certainty-philosophy, i.e., the separation of both data and operator into a signal part and a certainty part. Missing data are handled simply by setting the certainty to zero. In the case of uncertain data, an estimate of the certainty must accompany the data. Localization or windowing of operators is done using an applicability function, the operator equivalent to certainty, not by changing the actual operator coefficients. Spatially or temporally limited operators are handled by setting the applicability function to zero outside the window.<>


    Access

    Check access

    Check availability in my library

    Order at Subito €


    Export, share and cite



    Title :

    Normalized and differential convolution


    Contributors:


    Publication date :

    1993-01-01


    Size :

    786468 byte





    Type of media :

    Conference paper


    Type of material :

    Electronic Resource


    Language :

    English



    Super-resolution reconstruction of astronomical images using time-scale adaptive normalized convolution

    GUO, Rui / SHI, Xiaoping / ZHU, Yi et al. | British Library Online Contents | 2018


    Self-normalized linear tests

    Gangputra, S. / Geman, D. | IEEE | 2004


    Normalized performance comparison techniques

    ZAMANZAD GAVIDEL SAEED / TUZI GERTI / ALI SYED et al. | European Patent Office | 2022

    Free access

    Normalized object occupancy determination

    FEIT ANDREW JAMES / HENDY NOURELDIN EHAB | European Patent Office | 2025

    Free access

    Self-Normalized Linear Tests

    Gangaputra, S. / Geman, D. / IEEE Computer Society | British Library Conference Proceedings | 2004