Multi-scale geometry detail recovery on surfaces via Empirical Mode Decomposition

Abstract

In this paper, to recover the missing geometry details on 3D surfaces, we develop a novel geometry detail recovery algorithm for 3D surfaces based on Empirical Mode Decomposition (EMD). EMD is a powerful tool for processing non-linear and non-stationary signals and has been successfully used in 3D surface analysis and processing. Given a signal defined on 3D surface, EMD could represent the signal in a multi-scale fashion and decompose the signal into a number of Intrinsic Mode Functions (IMFs) and a residue, which usually encode the multi-level finer-scale details and the overall shape of the signal, respectively. Benefiting from the multi-scale representation of geometry details, the EMD-based multi-scale geometry detail recovery algorithm is developed. Our strategy starts from an initial smooth filling of a hole and then transfers the desirable details from the most similar region to the smoothly-filled surface within the framework of EMD. Taking the advantages of EMD, we first apply EMD on the whole completed surface to obtain the multi-scale representation of geometry details. Then, the most similar region corresponding to the hole region is located by the patch descriptor constructed from Heat Kernel Signature (HKS). Finally, the missing geometry details can be effectively recovered by transferring the geometry details from the found similar region to the smoothly-filled surface. Traditional methods, such as context-based methods or example-based methods, usually cut the similar patch and paste them onto the hole region, and they require to match with the hole boundary, are complex in general. In contrast, our method is simple and can transfer different scale details individually or in a concerted way, which makes our algorithm more flexible and can achieve versatile detail recovery results. Comprehensive experiments and quantitative comparisons on popular models have been used to demonstrate the effectiveness of our EMD-based multi-scale geometry detail recovery algorithm.