This paper presents new efficient architectures for high-speed implementation of direct form and local state-space form two-dimensional recursive digital filters. Unlike one-dimensional recursive systems, two-dimensional recursive digital filter algorithms possess a large amount of inherent concurrency, which can be exploited for fine-grain pipelining and/or parallelism. The locus of these concurrent computations is referred to as the concurrent computation region. We exploit this concurrency to derive fine-grain pipelined and one-dimensional block architectures for implementation of two-dimensional recursive digital filters by appropriate interleaving (or indexing) of the input samples, without requiring any algorithm transformation and without any hardware overhead. We extend the lookahead computation and incremental computation techniques to two dimensions, and use these to derive new two-dimensional incremental block filter architectures. The multiplication complexity of our two-dimensional incremental block filter is 0(max [formula omitted], as opposed to [formula omitted] of existing block structures, where L1 X L2 corresponds to the block size. Fine-grain pipelined two-dimensional block structures are also presented. The index mapping functions are used to derive delay operators for various architectures.