Hello All, I've been trying to work on a 3D data set that consists of only three landmarks - 3D triangles. The data are collected in a way that they are already aligned by translation and rotation. At this point, the rotational and translational differences that remain among the subjects are aspects of the essential differences of "shape" that I want to be able to analyze. Only scaling is left to do to place the subjects into shape space.
Here's the problem. With 3D triangles the problem would get reduced to 2 (3 x 3 - 7) dimensions. That reduction in dimensionality loses important information that is contained within the 3D location of the landmarks, and so I want to avoid the reduction to two dimensions. The question is, how? I could add the invariant 0,0,0 landmark to each subject. This would create a 3D tetrahedron, and reduce the analysis to 5 dimensions. But I am not sure that this would be statistically correct. After all, does this point really add degrees of freedom to the data set when its value is invariant across all subjects? Another question would be when to add the 0,0,0 point? If it is added before scaling is applied, then this point will have an impact in determining the centroid size of each subject. If it is added after the scaling that wouldn't be a problem, but then I still wonder if this is methodologically correct. So, what are the opinions from the morphometric experts on how to handle this data? Thanks for your opinions, Thomas M. Greiner, Ph.D. Assistant Professor of Anatomy University of Wisconsin - La Crosse Department of Health Professions 4054 Health Science Center 1725 State Street La Crosse, WI 54601 Phone: (608) 785-8476 Email: [EMAIL PROTECTED] -- Replies will be sent to the list. For more information visit http://www.morphometrics.org
