Hybrid Lie semi-group and cascade structures for the generalized Gaussian derivative model for visual receptive fields
The paper derives mathematical relationships between spatial and spatio-temporal receptive field responses using a generalized Gaussian derivative model. It establishes both infinitesimal differential relations, linking parameter changes to semi-group generators, and macroscopic cascade smoothing properties, which describe how coarse scale responses are computed from finer ones. This provides a theoretical basis for designing efficient computational schemes for biological vision models.