Rectilinearity of 3D meshes

In this paper, we propose and evaluate a novel shape measure describing the extent to which a 3D polygon mesh is rectilinear. The rectilinearity measure is based on the maximum ratio of the surface area to the sum of three orthogonal projected areas of the mesh. It has the following desirable properties: 1) the estimated rectilinearity is always a number from (0,1]; 2) the measure is invariant under scale, rotation, and translation; 3) the 3D objects can be either open or closed meshes, and we can also deal with degenerate meshes; 4) the measure is insensitive to noise, stable under small topology errors, and robust against face deletion and mesh simplification. Moreover, a genetic algorithm (GA) can be applied to compute the approximate rectilinearity efficiently. We find that the calculation of rectilinearity can be used to normalize the pose of 3D meshes, and in many cases it performs better than the principal component analysis (PCA) based method. By applying a simple selection criterion, the combination of these two methods results in a new pose normalization algorithm which not only provides a higher successful alignment rate but also corresponds better with intuition. Finally, we carry out several experiments showing that both the rectilinearity based pose normalization preprocessing and the combined signatures, which consist of the rectilinearity measure and other shape descriptors, can significantly improve the performance of 3D shape retrieval