Machine Vision and Applications. In this paper we describe a novel use for a well known temporal constraint term in the framework of variational correspondence methods. The new use, that we call spatial constraining, allows bounding of the solution based on what is known of the solution beforehand. 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 spatial constraint term enables fusion of information between high- and low-level vision systems: high-level makes a hypothesis of a possible scene setup which then is tested by the low-level, 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.