Previous studies provided evidence in support of attention operating in three-dimensional space, and the iterative and multi-stage nature of organizational processes in relation to attention and depth. We investigated depth perception and attentional demands in grouping organizations that contain blur as a depth cue. Contrary to previous studies, in our displays, no depth from occlusion could be implied from a shared border between groups or surfaces. To evaluate depth perception, subjective reports were collected where participants indicated which elements, blurry or sharp, they perceived as closer. To examine whether depth perception from blur can alleviate attentional demands, we used an inattention paradigm. We presented displays of grouping organizations by collinearity or color similarity that were previously found to require attention and added blur to the figure or the background elements to generate depth perception. In addition, we presented similar displays containing grouping by blur similarity as a single cue. We hypothesized that adding blur would facilitate the segmentation of element groups due to their perceived depth, which might lead to a diminished demand for attention. Our results confirmed that blur led to depth perception, and that sharp elements were perceived as closer more frequently than blurry elements. Thus, these results provide novel evidence for depth from blur in grouping where no inference of occlusion can be derived from a border. However, although the results suggest that blur information was processed under inattention, little evidence was found for decreased attentional demands for grouping processes in the presence of blur.