In this paper we present a two-dimensional cellular hypercube architecture for image processing that combines features of the conventional hypercube and cellular logic architectures for 2-D computation cells. A unified theory of parallel binary image processing, binary image algebra (BIA), serves as a software tool for designing parallel image processing algorithms. To match the hardware to the software, we characterize the cellular processors using the same algebraic structure as BIA. The two-dimensional cellular hypercube image processor is a cellular SIMD machine with N2 cells and has a simple overall organization, low cell complexity and fast processing ability. An optical cellular hypercube implementation of BIA is proposed which offers parallel input/output and global interconnection capabilities which are difficult to do in planar VLSI technology.