  A surface is often modeled as a triangulated mesh of 3D points and textures
associated with faces of the mesh. The 3D points could be either sampled from
range data or derived from a set of images using a stereo or
Structure-from-Motion algorithm. When the points do not lie at critical points
of maximum curvature or discontinuities of the real surface, faces of the mesh
do not lie close to the modeled surface. This results in textural artifacts,
and the model is not perfectly coherent with a set of actual images -- the ones
that are used to texture-map its mesh. This paper presents a technique for
perfecting the 3D surface model by repositioning its vertices so that it is
coherent with a set of observed images of the object. The textural artifacts
and incoherence with images are due to the non-planarity of a surface patch
being approximated by a planar face, as observed from multiple viewpoints.
Image areas from the viewpoints are used to represent texture for the patch in
Eigenspace. The Eigenspace representation captures variations of texture, which
we seek to minimize. A coherence measure based on the difference between the
face textures reconstructed from Eigenspace and the actual images is used to
reposition the vertices so that the model is improved or faired. We refer to
this technique of model refinement as EigenFairing, by which the model is
faired, both geometrically and texturally, to better approximate the real
surface.
