Image Structure of Scene Dynamics

The dynamics of a spatio-temporal scene is described by diierential and integral geometric invariants of the image structure of that scene at various resolutions. This image structure is represented by continuous, semi-discrete or discrete similarity jet-spaces of spatio-temporally bounded input images. These jet-spaces are found by extending classical scale space theory for spatio-temporally bounded input images. Next the scene dynamics on a restricted region of space-time is identiied with a frame bundle endowed with an aane or a metric-aane connection. Consequently, the dynamics is captured by the Cartan structure equations, in which the torsion and the curvature arise naturally. The fundamental invariants of the scene dynamics are derived on the basis of the connections, the torsion tensors and the curvature tensors. Non-metricity is studied for scene dynamics with a metric-aane connection. The analogies and diierences between our diierential geometric theory and defect and gauge theories are pointed out. Finally, the fundamental diierential and integral invariants of scene dynamics are identiied with those latent in the similarity jet-space of an updated input image.