Local operators, used in many image processing tasks, involve replacing each pixel in an image with a value computed within a local neighborhood of that pixel. Computing such operators at the video rate requires a computing power which is not provided by conventional computers. Though computationally expensive, local operators are highly regular. Thus, a VLSI implementation appears particularly appropriate. This correspondence presents systolic algorithms for tasks such as connected component determination, distance transform, and relaxation, which are defined in terms of local operators.