Polygonal approximation (PA) is a challenging problem and has its wide applications in computer vision, electronic imaging, image classification, image visualization, pattern recognition and image analysis. This paper proposes a stochastic technique-based firefly algorithm (FA) for PA. FA customizes a kind of randomization by searching a set of solutions where PA requires more combinations of approximation to find an optimal solution. The significant feature of the FA is real random sample generation and attractive features. The attractiveness and brightness of the firefly have been used efficiently to solve the approximation problem by detecting the dominant points (DPs) with fewer iterations to produce better results. Thus, this technique achieves the main goal of PA that is a minimum error value with a lesser number of DPs. While compared with other similar algorithms, FA is independent of velocities which are considered as an advantage for this algorithm. Subsequently, the multiswarm nature of FA allows finding multiple optimal solutions concurrently. The experimental results show that the proposed algorithm generates better solutions compared with other algorithms.