A rectilinearity measurement for 3d meshes

In this paper, we propose and evaluate a novel shape measurement describing the extent to which a 3D mesh is rectilinear. Since the rectilinearity measure corresponds proportionally to the ratio of the sum of three orthogonal projected areas and the surface area of the mesh, it has the following desirable properties: 1) the estimated rectilinearity is always a number from (0,1]; 2) the estimated rectilinearity is 1 if and only if the measured 3D shape is rectilinear; 3) there are shapes whose estimated rectilinearity is arbitrarily close to 0; 4) the measurement is invariant under scale, rotation, and translation; 5) the 3D objects can be either open or closed meshes, and we can also deal with poor quality meshes; 6) the measurement is insensitive to noise and stable under small topology errors; and 7) a Genetic Algorithm (GA) can be applied to calculate the approximate rectilinearity efficiently. We have also implemented two experiments of its applications. The first experiment shows that, in some cases, the calculation of rectilinearity provides a better tool for registering the pose of 3D meshes compared to PCA. The second experiment demonstrates that the combination of this measurement and other shape descriptors can significantly improve 3D shape retrieval performance