In this paper, we formulate saliency detection as a problem of computing the absorption time of absorbing Markov chains on image graphs. We construct a graph where image superpixels serve as transient nodes and boundary superpixels are designated as absorbing nodes. The expected absorption time from each transient node to the absorbing boundary nodes effectively measures the dissimilarity between interior regions and the image boundary, naturally distinguishing salient objects from the background. To handle false positives that arise from homogeneous background regions near the image center, we further leverage the equilibrium distribution of an ergodic Markov chain to refine the saliency map. Experiments on four benchmark datasets demonstrate that our method achieves competitive or superior performance compared to state-of-the-art approaches.

Salient object detection aims to identify the most visually prominent regions in an image. It has wide applications in image segmentation, content-aware resizing, object recognition, and visual tracking. Most existing approaches compute saliency based on local or global contrast: local methods compare each pixel or region with its neighbors, while global methods compare regions against the entire image statistics. While effective, contrast-based methods may fail when the salient object has similar color distribution to the background or when the background is complex and heterogeneous.

Recent works have explored the use of boundary prior — the observation that image boundaries are predominantly occupied by background regions. Methods such as geodesic saliency leverage this prior by computing the shortest geodesic distance from each region to the image boundary. In this paper, we propose a principled formulation based on absorbing Markov chains that naturally integrates the boundary prior with a global diffusion process. The absorption time captures both local appearance similarity and global connectivity structure, providing a more robust saliency measure than simple distance metrics.

Saliency detection methods can be broadly categorized into local contrast-based, global contrast-based, and boundary prior-based approaches. Itti et al.'s classic model uses multi-scale center-surround differences. Cheng et al. proposed global contrast using histogram-based color distance. Wei et al. introduced geodesic saliency based on boundary connectivity. Our work is most related to graph-based diffusion methods such as Yang et al.'s manifold ranking approach, but differs in using absorbing rather than regular random walks. The absorbing formulation provides a natural and principled way to incorporate the boundary prior through the designation of absorbing states.

We first over-segment the input image into superpixels using SLIC. A graph G = (V, E) is constructed where each superpixel is a node and edges connect spatially adjacent superpixels. The edge weight between nodes i and j is defined as w_ij = exp(-||c_i - c_j||^2 / (2 * sigma^2)), where c_i and c_j are the mean color vectors in CIELAB space and sigma is a bandwidth parameter. The transition probability matrix P of the Markov chain is derived by row-normalizing the weight matrix. Superpixels touching the image boundary are designated as absorbing nodes — once the random walker reaches these nodes, it is absorbed and stops.

In an absorbing Markov chain, the expected absorption time y_i for a transient node i represents the expected number of steps a random walker starting at node i takes before being absorbed by any boundary node. This can be computed from the fundamental matrix N = (I - Q)^{-1}, where Q is the sub-matrix of the transition matrix corresponding to transient nodes. The absorption time is y = N * 1 (the row sums of N). Intuitively, salient regions that differ from the background will have longer absorption times because the random walker must traverse through dissimilar regions to reach the boundary. Conversely, background regions similar to the boundary have short absorption times. To address the false positive problem for homogeneous regions far from boundaries, we compute the equilibrium distribution of an ergodic version of the chain (by removing absorbing states) and use it to normalize the absorption times, suppressing large central background regions.

We evaluate the proposed method on four benchmark datasets: MSRA-B (5000 images), ECSSD (1000 images), DUT-OMRON (5168 images), and PASCAL-S (850 images). We compare against fourteen state-of-the-art methods using standard metrics including Precision-Recall curves, F-measure, and Mean Absolute Error (MAE). Our method consistently achieves top-tier performance across all datasets. On MSRA-B, we achieve the highest F-measure of 0.903, outperforming geodesic saliency (0.871) and manifold ranking (0.889). On the more challenging DUT-OMRON dataset, our method shows particularly strong improvements, demonstrating robustness to complex backgrounds. Ablation experiments confirm that both the absorbing Markov chain formulation and the equilibrium distribution refinement contribute positively to the final performance.

We have proposed a novel saliency detection method based on absorbing Markov chains. By treating boundary superpixels as absorbing states and computing the expected absorption time for each interior region, our method naturally integrates the boundary prior with a principled diffusion process. The additional refinement using equilibrium distributions effectively addresses the false positive problem. Our approach achieves state-of-the-art results on multiple benchmarks with a clean and mathematically grounded formulation. Future directions include extending the framework to video saliency detection with temporal absorbing states and exploring learning-based approaches for adaptive graph construction.