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This paper presents a connected coherence tree algorithm (CCTA) for image segmentation with no prior knowledge. It aims to find regions of semantic coherence based on the proposed epsiv-neighbor coherence segmentation criterion. More specifically, with an adaptive spatial scale and an appropriate intensity-difference scale, CCTA often achieves several sets of coherent neighboring pixels which maximize the probability of being a single image content (including kinds of complex backgrounds). In practice, each set of coherent neighboring pixels corresponds to a coherence class (CC). The fact that each CC just contains a single equivalence class (EC) ensures the separability of an arbitrary image theoretically. In addition, the resultant CCs are represented by tree-based data structures, named connected coherence tree (CCT)s. In this sense, CCTA is a graph-based image analysis algorithm, which expresses three advantages: (1) its fundamental idea, epsiv-neighbor coherence segmentation criterion, is easy to interpret and comprehend; (2) it is efficient due to a linear computational complexity in the number of image pixels; (3) both subjective comparisons and objective evaluation have shown that it is effective for the tasks of semantic object segmentation and figure-ground separation in a wide variety of images. Those images either contain tiny, long and thin objects or are severely degraded by noise, uneven lighting, occlusion, poor illumination, and shadow.