Pelican Imaging patent application US20150091900 "Systems and Methods for Depth-Assisted Perspective Distortion Correction" by Samuel Yang, Manohar Srikanth, Dan Lelescu, and Kartik Venkataraman proposes a solution to the common selfie problem:
"Close range portraiture photographs, such as self-portraits, are often perceived as having apparent perspective distortions at typical image viewing distances, even if the optics produce a geometrically accurate perspective projection of the scene. A mismatch in the field of view of the camera and that of the viewing display configuration can result in the perceived distortion, which in portraiture photographs, tends to magnify the size of the nose and chin, among other features. These distortions are especially common with photographs taken with mobile device cameras due to the wide angular field of view typical of such cameras and close range nature of many self-portraits and candid portraits."
Pelican proposes to use the depth information to post-process the image and fix the distortions: