Current alignment algorithms for registering range data captured from a 3D scanner assume that the range data depicts identical geometry taken from different views.  However, in the presence of scanner calibration errors, the data will be slightly warped. These warps often cause current alignment algorithms to converge slowly, find the wrong alignment, or even diverge. In this paper, we present a method for aligning warped range data represented by polygon meshes. Our strategy can be characterized as a coarse-to-fine hierarchical approach, where we assume that since the warp is global, we can compensate for it by treating each mesh as a collection of smaller piecewise rigid sections, which can translate and rotate with respect to each other. We split the meshes subject to several constraints, in order to ensure that the resulting sections converge reliably.

 

I submitted a longer version of “A Hierarchical Method” as my Master’s thesis.  It won Stanford’s Christopher Stephenson Award for best Master’s thesis in the Computer Science department in 2003.

Results on the face of Michelangelo’s David. Top: alignment and merging under incorrect calibration. The lips exhibit gross misalignments on the order of 1.9 mm. Bottom: our results. The artifacts in the lips have been greatly reduced.

Results on a marble fragment of the Forma Urbis Romae. Left: computer rendering of mesh from alignment and merging under incorrect calibration. Left inset: blurring of the map due to incorrect alignment. Plot shows that a sample incision is shallow (at a depth of 0.25 mm) and incorrectly shows two minima. Right: results of our technique on same input scans. One of the sub-meshes is overlaid in a darker gray. Right inset: the blurring is greatly reduced, and the depth of the incision measures 0.5 mm, which is more consistent with the approximate depth of the Forma Urbis incisions.