Monocular Depth by Nonlinear Diffusion

Following the phenomenological approach of gestaltists, sparse monocular depth cues such as T- and X-junctions and the local convexity are crucial to identify the shape and depth relationships of depicted objects. According to Kanizsa, mechanisms called a modal and modal completion permit to transform these local relative depth cues into a global depth reconstruction. In this paper, we propose a mathematical and computational translation of gestalt depth perception theory, from the detection of local depth cues to their synthesis into a consistent global depth perception. The detection of local depth cues is built on the response of a line segment detector (LSD), which works in a linear time relative to the image size without any parameter tuning. The depth synthesis process is based on the use of a nonlinear iterative filter which is asymptotically equivalent to the Perona-Malik partial differential equation (PDE). Experimental results are shown on several real images and demonstrate that this simple approach can account a variety of phenomena such as visual completion, transparency and self-occlusion.