This project involves an investigation of methods for simplfying large, complex, multidimensional datasets prior to visualization. We are studying the use of feature preserving mesh simplification algorithms to address this goal. We call this type of multidimensional data reduction feature preserving data simplification.
Consider a multidimensional dataset where each sample point contains n values representing the n data attributes encoded within the dataset. If we view sample point locations as vertices, we can triangulate their positions to form an underlying mesh. The n attributes can now be seen as n features arrayed across the surface of the mesh. Feature preserving mesh simplification is designed to simplify a mesh, while at the same time maintaining both its geometric and surface feature details. Since our problem is cast in an identical context, feature preserving mesh simplification should be applicable to our data reduction goals.
One limitation of many simplification algorithms is their inability to handle large numbers of surface properties in a time and space efficient manner. Many algorithms were originally designed to handle RGB triples, surface normals, or texture (u,v) coordinates. Since our datasets can contains tens or even hundres of attributes, we must find a way to overcome this limitation. Moreover, we would like our solution to apply without modification to any of a broad range of existing simplification algorithms.
We have decided to use principal component analysis (PCA) to identify a small number of axes (or combinations of attributes) that best capture the variability within a dataset. The error computations that control vertex modifications are performed in this PCA space; since the number of axes is small, the algorithms can now perform their computations efficiently. Techniques must also be developed to move between PCA space and the full-detail space represented by the dataset. Once simplification is completed, the remaining sample points are displayed in full detail (i.e., with all attributes shown in their native form) to the viewer.
Jason Walter (MS, 2001)