In this paper, we apply the PSO method 'Particle Swarm Optimization' to reconstruct a 3d object from a 3d point cloud using supershapes. Reconstructing a 3d object from a 3d point cloud obtained from different devices is very important in many fields. For instance, the use of 3d scanners is very common in the field of medicine. Thus, a good reconstruction of the 3d point cloud given by the device can be very helpful. This problematic can be summed up in finding the surface that approximate the best the point cloud provided at the beginning. The rarity of works applying optimization methods and especially metaheuristics to this kind of issues in the literature makes the originality of this work. We have opted in our work to use a population-based metaheuristic method. The parametric surfaces employed in our work are the recent forms introduced recently by Gielis; called supershapes. We have also used the radial Euclidean distance in the definition of the fitness function. This function will serve as an indicator of dissimilarities between the original form and the reconstructed one. Our approach has been quite successful in providing very satisfactory results compared to the existing results in the literature.
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