Methods, systems, and apparatus, including computer programs encoded on computer storage media, for supporting complex transfer functions on an image processor. One of the methods includes traversing, by each execution lane of an image processor using a shift-register array, a respective local support region and storing input pixels encountered during the traversal into local memory of the image processor. Each execution lane obtains from the local memory of the image processor one or more input pixels according to a complex transfer function. Each execution lane computes a respective output pixel for the kernel program using one or more input pixels obtained from the local memory according to the complex transfer function.