We investigate the use of multi-agent systems to solve classical image processing tasks, such as colour quantization and segmentation. We frame the task as an optimal control problem, where the objective is to steer the multi-agent dynamics to obtain colour clusters that segment the image. To do so, we balance the total variation of the colour field and fidelity to the original image. The solution is obtained resorting to primal-dual splitting and the method of multipliers. Numerical experiments, implemented in parallel with CUDA, demonstrate the efficacy of the approach and its potential for high-dimensional data.

翻译：本文研究了利用多智能体系统解决经典图像处理任务（如色彩量化和图像分割）的方法。我们将该任务构建为最优控制问题，其目标是通过调控多智能体动力学特性来获得能够分割图像的色彩聚类。为此，我们在色彩场的全变差与原始图像保真度之间进行权衡。该问题的求解采用了原始-对偶分裂法与乘子法。基于CUDA并行实现的数值实验验证了该方法的有效性，并展示了其在高维数据处理中的应用潜力。