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Edge detection algorithms often produce broken edges, especially in noisy images. We propose an algorithm based on discrete particle swarm optimisation (PSO) to detect continuous edges in noisy images. A constrained PSO-based algorithm with a new objective function is proposed to address noise and reduce broken edges. The localisation accuracy of the new algorithm is compared with that of a modified version of the Canny algorithm as a Gaussian-based edge detector, the robust rank order (RRO)-based algorithm as a statistical based edge detector, and our previously developed PSO-based algorithm. Pratt's figure of merit is used as a measure of localisation accuracy for these edge detection algorithms. Experimental results show that the performance of the new algorithm is higher than the Canny and RRO algorithms in the images corrupted by two different types of noise (impulsive and Gaussian noise). The new algorithm also detects edges more accurately and smoothly than our previously developed algorithm in noisy images.