Visual saliency based on extended manifold ranking and third-order optimization refinement

•we use background weight map to provide seeds for manifold ranking.•we extend the traditional manifold ranking to second-order formula.•we establish a third-order smoothness framework to optimize the saliency map. Graph-based approaches for saliency detection have attracted much attention and been exploited widely in recent years. In this paper, we present a new method to promote the performance of existing manifold ranking algorithms. Initially, we use background weight map to provide seeds for manifold ranking; Next, we extend the traditional manifold ranking to second-order formula and add a weight mask to its fitting term. Finally, for further improvement of the performance, we establish a third-order smoothness framework to optimize the saliency map. In the experiments, we compare two versions (manifold ranking with and without optimization) of our model with seven previous methods and test them on several benchmark datasets. Different kinds of strategies are also adopted for evaluation and the results demonstrate that our method achieves the state-of-the-art.