Photonics provides a promising approach for image processing by spatial filtering, with the advantage of faster speeds and lower power consumption compared to electronic digital solutions. However, traditional optical spatial filters suffer from bulky form factors that limit their portability. Here we present a new approach based on pixel arrays of plasmonic directional image sensors, designed to selectively detect light incident along a small, geometrically tunable set of directions. The resulting imaging systems can function as optical spatial filters without any external filtering elements, leading to extreme size miniaturization. Furthermore, they offer the distinct capability to perform multiple filtering operations at the same time, through the use of sensor arrays partitioned into blocks of adjacent pixels with different angular responses. To establish the image processing capabilities of these devices, we present a rigorous theoretical model of their filter transfer function under both coherent and incoherent illumination. Next, we use the measured angle-resolved responsivity of prototype devices to demonstrate two examples of relevant functionalities: (1) the visualization of otherwise invisible phase objects and (2) spatial differentiation with incoherent light. These results are significant for a multitude of imaging applications ranging from microscopy in biomedicine to object recognition for computer vision.