Feature-preserving, mesh-free empirical mode decomposition for point clouds and its applications

摘要

Point clouds have been extensively employed to represent 3D shapes with the increasing availability of various data acquisition devices/technologies. As a result, more novel techniques are urgently needed for point clouds' analysis and processing. To date, empirical mode decomposition (EMD) has become a powerful and effective analytical tool for non-stationary, non-linear signals, and has been widely applied to time series processing. Despite the fact that EMD has exhibited its potential in 3D geometry processing, extending the existing techniques of EMD to operate directly on point clouds remains to be extremely challenging. This is primarily because of imperfect point clouds, as well as their absence of topological information. In this paper, we develop a multi-scale mesh-free EMD algorithm for point clouds and their analysis and processing. The multi-scale mesh-free EMD is achieved by iteratively extracting the detail level from the input signal and leaving the overall shape in residue. Furthermore, in order to preserve sharp features during point-based EMD analysis/processing, we devise an anisotropic structure measurement assisted envelope computation scheme. The structure measurement is computed by the eigenvalue decomposition of voting tensor, which could faithfully characterize the structure of any input model. Under the guidance of the structure measurement, the envelope is computed in a structure-aware manner and the sharp features are well preserved. Unlike previous feature-preserving EMD methods for meshed models, our algorithm does not explicitly resort to sharp feature detection, which is more suitable for complex geometric models. With the well decomposed multi-scale representation, we could explore various applications of point clouds, such as detail enhancement and smoothing, feature points extraction, and feature-preserving denoising. We showcase comprehensive experimental results to demonstrate the utility of our novel multi-scale mesh-free EMD algorithm.