| Locally parallel dense patterns---visual flows---define a perceptually coherent structure of particular significance to perceptual organization. Geometrically, it is argued that a proper way to investigate these structures requires the frame field approach from differential geometry, a study that leads to the notion of visual flow curvatures and to constraints on their mutual behavior. These curvatures are then used to develop a theory, and a rigorous model, of visual flow "good continuation" that extends common terminology from Gestalt psychology and from computational studies of curves.; The geometrical theory is then applied in three ways. Firstly, psychophysical exploration of the role of visual flow curvatures in human perception shows that sensitivity to these curvatures greatly affects orientation-based texture segmentation. Secondly, a contextual framework for the computation of coherent visual flows from images is developed and applied to texture, shading, and color analysis. Unlike existing approaches, the proposed framework is able to handle both sparse, dense, and multivalued data sets, while preserving line and point singularities and rejecting large scale non-flow structures. Lastly, the geometrical theory is linked to the functional organization of primary visual cortex to accurately predict the distribution of long range horizontal connections and to support their identification with those obtained mathematically. |
