# Salient Region Detection Using Diffusion Process with Nonlocal Connections
## 1 Introduction
[24] set virtual boundary nodes as the absorbing nodes in a Markov chain, and computed the absorbed time from transient node to absorbing nodes as the metric of saliency value. [PERSON] et al. [26] proposed a method to learn optimal seeds for object saliency via combining the low-level and mid-level vision features. [PERSON] et al. [27] exploited the relationship between the saliency detection and the Markov absorption probability to construct the saliency map. [PERSON] et al. [28] used the most dominant eigenvectors to re-synthesize the diffusion matrix and construct the seed vector based on the correlations of diffusion maps between the non-border nodes. [PERSON] et al. [29] proposed the regularized random walks ranking to formulate pixel-wised saliency maps from the superpixel-based background and foreground saliency estimations. [PERSON] et al. [30] introduced the Cellular Automata mechanism into saliency detection via analyzing the intrinsic relevance of similar regions through interactions with neighbors. [PERSON] et al. [31] devised a co-transduction algorithm to fuse both boundary and object labels based on an inter propagation scheme. [PERSON] et al. [32] employed the Teaching-to-Learn and Learning-to-Teach strategies to logically propagate the unlabeled superpixels from simple to difficult. [PERSON] et al. [34] propagated the background-driven saliency information on an optimized graph. [PERSON] et al. [9] proposed a bottom-up salient region detection diffusion-based method by integrating compactness and local contrast cues. [PERSON] et al. [16] propagated the saliency and background seed vectors on a two-layer sparse graph. Most above-mentioned diffusion-based methods ranked the saliency values on 2-layer neighborhood graph (or 2-layer sparse graph) by connecting each node to its neighboring nodes and the nodes sharing common boundaries with its neighboring nodes (or the most similar node that shares a common boundary with its neighboring nodes). In other words, most of them merely exploited the intrinsic relevance of local regions via measuring the similarities between each other. However, when the neighborhood nodes of salient regions are inhomogeneous or incoherent, the local connective weights, which are supposed to have a high value, may be low. Thus, the saliencyinformation may be ranked with an inaccurate connective weight. Naturally, as shown in Figure 1, the inner salient region may be inhomogeneous, and the background may be wrongly highlighted. In this paper, we put forward an effective method to overcome these issues. In term of the local relevance, the 2-layer sparse graph is adopted to optimize the local connections as well as [16], which is conducted by connecting each node to its neighboring nodes and the most similar node that shares a common boundary with its neighboring nodes. In term of the nonlocal relevance of different elements, we extend the nonlocal intrinsic relevance into the 2-layer sparse graph by connecting each node to the \"true-foreground\" and \"true-background\" seeds. As shown in Figure 2f, our proposed graph can effectively highlight the salient regions with a consistent value. What is more, the use of the nonlocal connections can effectively improve the performances of 2-layer neighborhood graph, which can be illustrated in Figure 2d. Second, to address the defect of the center-biased Gaussian model, we design a saliency-biased Gaussian model to refine the initial saliency maps generated by the compactness and uniqueness cues. Finally, a single-layer updating and multi-layer integrating scheme is generated to highlight the salient regions and make full use of the multi-scale saliency information. The contributions of our paper can be summarized as follows:  
1. The nonlocal intrinsic relevance is exploited into the 2-layer sparse graph, and with the saliency information based on different feature cues, we construct the new foreground and background biased diffusion matrix. 2. A saliency-biased Gaussian model is presented to overcome the defect of the center-biased model.