Lazy Neurons for Good Shape or Filling in the Gaps...The Mind's Way

The phenomenon of visual curve completion, where the visual system completes the missing part (e.g., due to occlusion) between two contour fragments, is a major problem in perceptual organization research, both behaviorally and computationally.  Previous computational approaches for the shape of percetually completed curves typically follow an axiomatic approach via formal descriptions of desired, image-based perceptual properties (e.g, minimum total curvature, roundedness, etc...). Unfortunately, however, it is difficult to determine such desired properties psychophysically and indeed there is no consensus in the literature for what they should be.  Instead, in this paper we suggest to exploit the fact that curve completion occurs in early vision in order to formalize the problem in a space that  abstracts the primary visual cortex (For the technically inclined, this space is called the unit tangent bundle associated with R²).  We show that a single basic principle of “minimum energy consumption” in this space not only results in a rigorous, non axiomatic, computational theory,  but also makes excellent predictions and explanations for  recent perceptual findings  in the literature