Shape and Enlightenment in Vision


			    David Kriegman
	     Center for Computational Vision and Control
	Depts. of Electrical Engineering and Computer Science
			   Yale University

  An object's appearance depends on both the observer's viewpoint and the  il-
  lumination.   The  question  arises:  What is the set of images of an object
  under all viewing conditions?  In this talk, we focus on enlightenment,  in-
  cluding  multiple,  extended  light sources and shadowing.  It will be shown
  that the set of n-pixel images of an object of any shape and with a  general
  reflectance  function, seen under all possible illumination conditions forms
  a convex cone in R^n.  If the object is convex with a Lambertian reflectance
  function and is illuminated by an arbitrary number of point light sources at
  infinity, this illumination cone is polyhedral and can be  constructed  from
  three  or more images; recognition from a single image can be cast as deter-
  mining set membership.  This leads to another question: What objects are in-
  distinguishable  from  only  their images?  It will be shown that if two ob-
  jects differ by a ``generalized bas-relief transformation,'' then their  il-
  lumination  cones  are identical.  For each image of a surface produced by a
  light source, there exists an identical image of the bas-relief produced  by
  a transformed light source. This equality holds for both shaded and shadowed
  regions.  Since antiquity, artists have been aware of  this  ambiguity  when
  creating  flattened  bas-relief sculptures which give an exaggerated percep-
  tion of depth.  For a moving observer, the set of all possible motion fields
  for  a  bas-relief is identical to the set produced by a full relief.  Thus,
  neither small observer motions nor changes of illumination can  resolve  the
  bas-relief ambiguity.  These results are consistent with recent psychophysi-
  cal studies and have lead to new methods for shape reconstruction from  sha-
  dows.   They  have  been  used in a face recognition system which is trained
  with a small number of well-illuminated images, yet which can perform recog-
  nition  under  illumination extremes where faces are heavily shadowed.  When
  compared to competitive techniques, our method had  an  order  of  magnitude
  fewer errors.


        Informal gathering in DCL Lounge at 3:30 p.m.