A Case-Study of Inconsistent Surface Reconstruction in Recent Literature Resulting from Octree Rotation-Variance

Abstract

We review the use of octree and PCA (Principle Component Analysis) in current literature and explore a leading piece of research, as a case study, to highlight how overlooking octree rotation-variance has resulted in inconsistent results. We provide a simple method using PCA to re-orientate an octree to the intrinsic-orientation defined by data variance. In our case-study we explore and provide a method for consistency within multi-scale CSRBFs (Compactly Supported Radial Basis Functions). By utilizing PCA we provide rotation-invariant multi-scale surface reconstructions. We show, by curvature analysis, that the original surface reconstruction method is variant to data orientation and that our approach results in rotation-invariant reconstructions. In addition we also provide a technique for more flexibility when choosing a CSRBF for use with multi-scale surface reconstruction.