Homunculus Warping: Conveying importance using self-intersection-free non-homogeneous mesh deformation

Size matters. Human perception most naturally relates relative extent, area or volume to importance, nearness and weight. Reversely, conveying importance of something by depicting it at a different size is a classic artistic principle, in particular when importance varies across a domain. One striking example is the neuronal homunculus; a human figure where the size of each body part is proportional to the neural density on that part. In this work we propose an approach which changes local size of a 2D image or 3D surface and, at the same time, minimizes distortion, prevails smoothness, and, most importantly, avoids fold-overs (collisions). We employ a parallel, two-stage optimization process, that scales the shape non-uniformly according to an interactively-defined importance map and then solves for a nearby, self-intersection-free configuration. The results include an interactive 3D-rendered version of the classic sensorical homunculus but also a range of images and surfaces with different importance maps.