EigenFairing: 3D Model Fairing using Image Coherence

Abstract: 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.