This paper proposes a new method for optical-flow and stereo estimation based on the inclusion of both spatial and temporal constraints in a variational framework. These constraints bound the solution based on a priori information, or in other words, based on what is known of a possible solution or how it is expected to change temporally. This knowledge can be something that (a) is known since the geometrical properties of the scene are known or (b) is deduced by a higher-level algorithm capable of inferring this information. In the latter case, the constraint terms enable the exchange of information between high- and low-level vision systems: the high-level system makes a hypothesis of a possible scene setup which is then tested by the low-level one, recurrently. Since high-level vision systems incorporate knowledge of the world that surrounds us, this kind of hypothesis testing loop between the high- and low-level vision systems should converge to a more coherent solution.