The operation of the double phase conjugate mirror (DPCM) is described. It can be regarded as a bidirectional spatial light modulator and controllable filter. Two independent image-bearing beams that may be derived from different lasers exchange their spatial information as they are coupled into each other in a photorefractive crystal. The DPCM is also shown to be an optical thresholder and spatial filtering device, displaying edge enhancement. We propose the use of a resonator with two facing DPCMs to implement iterative image processing algorithms.