We present a framework for analysis and processing of multimedia systems integrating e.g. video, audio and text. The analysis consists of various initialisations of multimedia in terms of joint (non-)local geometric and topological equivalences invariant under a so-called gauge group. Various initialisations of equivalences can readily be used as means to (re)- structure, query and search content-based relational associative multimedia database systems. The processing consists of multimedia consistent filtration schemes of those equivalences. These analysis-related filtration schemes are envisaged by definition to be invariant under the gauge group and to be robust to Lyapunov and structural instabilities due to various noise types and severe morphological transformations, respectively. The latter invariance and robustness allow us to construct distinctive (task-oriented) discriminative multimedia database systems. The filtration schemes are finally described in terms of (non-)local symmetries, conservation laws and curvatures. These descriptions then form the ingredients for natural transformations between the schemes that actually bridge the semantic gaps between different multimedia database systems.