Generalized Procrustes Surface Analysis
The tools and techniques used in shape analysis have constantly evolved, but their objective remains fixed: to quantify the differences in shape between two objects in a consistent and meaningful manner. The hand-measurements of calipers and protractors of the past have yielded to laser scanners and landmark-placement software, but the process still involves transforming an object’s physical shape into a concise set of numerical data that can be readily analyzed by mathematical means.
Here, we present a new method to perform this transformation by taking full advantage of today’s high-power computers and high-resolution scanning technology. This method uses surface scans to calculate a shape-difference metric and perform superimposition automatically rather than relying on carefully, tediously, manually placed landmarks. This is accomplished by building upon and extending the Iterative Closest Point algorithm to behave in a manner more conducive to use in morphometric analysis. In particular, we alter the cost function to take both surfaces into account during superimposition so that the superimposition operation is symmetric. We also developed an approach similar to Generalized Procrustes Analysis to handle the superimposition of more than two surfaces at once. We have also examined some ways this new data may be used; we can, for example, calculate an averaged surface directly and visualize point-wise shape information over this surface. Finally, we demonstrate the use of this method on a set of primate skulls and compare the results of the new methodology with traditional geometric morphometric analysis.