A spatial linear propagation network (SLPN) system learns the affinity matrix for vision tasks. An affinity matrix is a generic matrix that defines the similarity of two points in space. The SLPN system is trained for a particular computer vision task and refines an input map (i.e., affinity matrix) that indicates pixels the share a particular property (e.g., color, object, texture, shape, etc.). Inputs to the SLPN system are input data (e.g., pixel values for an image) and the input map corresponding to the input data to be propagated. The input data is processed to produce task-specific affinity values (guidance data). The task-specific affinity values are applied to values in the input map, with at least two weighted values from each column contributing to a value in the refined map data for the adjacent column.