A parallel digital optical cellular image processor (DOCIP) functionally comprises an array of identical I-bit processing elements or cells, a fixed interconnection network, and a control unit. Four interconnection network topologies are described, and include two variants of a mesh-connected array and two variants of a cellular hypercube network. The instruction sets of these single-instruction multiple-data (SIMD) machines are based on a mathematical morphological theory, binary image algebra (BIA), which provide an inherently parallel programming structure for their control. Physically, a DOCIP architecture uses a holographic optical element in a 3D free-space optical system to implement off-chip interconnections, and an optoelectronic spatial light modulator to implement a 2D array of nonlinear processing elements and (optionally) local on-chip interconnections. Two examples are given. The first, an experimental implementation of a single 54-gate cell of the DOCIP, uses an optically recorded hologram for within-cell optical interconnections, and a spatial light modulator for a 2D array of optically accessible gates. The second, a design for an efficient and more manufacturable architecture, uses a computer-generated diffractive optical element for cell-to-cell interconnections, and a 20 smart-pixel array of DOCIP cells, each cell having electronic logic and optical input/output.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>