This paper presents an algorithm for tree-based representation of single images and its applications to segmentation and filtering with depth. In a our recent work, we have addressed the problem of segmentation with depth by incorporating depth ordering information into a region merging algorithm and by reasoning about depth relations through a graph model. In this paper, we extend this previous work giving a two-fold contribution. First, we propose to model each pixel statistically by its probability distribution instead of deterministically by its color value. Second, we propose a depth-oriented filter, which allows to remove foreground regions and to replace them with a plausible background. Experimental results are satisfactory.