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A new parallel algorithm for image component labeling with local operators on SIMD mesh connected computers is presented, providing a positive answer to the open question posed by several researchers whether there exists an O(n)-time and O(log n)-space local labeling algorithm on SIMD mesh connected computers. The algorithm uses a pipeline mechanism with stack-like data structures to achieve the lower bound of O(n) in time complexity and O(log n) in space complexity. Furthermore, the algorithm has very small multiplicative constants in its complexities.