| Non-rigid registration of 3D shapes is an essential task of increasing importance as commodity depth sensors become more widely available for scanning dynamic scenes.Non-rigid registration is much more challenging than rigid registration as it estimates a set of local transformations instead of a single global transformation,and hence is prone to the over-fitting issue due to under determination.The common wisdom in previous methods is to impose an 2?-norm regularization on the local transformation differences.However,the 2?-norm regularization tends to bias the solution towards outliers and noise with heavy-tailed distribution,which is verified by the poor goodness of-fit of the Gaussian distribution over transformation differences.On the contrary,Laplacian distribution fits well with the transformation differences,suggesting the use of a sparsity prior.We propose a sparse non-rigid registration(SNR)method with an 1?-norm regularized model for transformation estimation,which is effectively solved by an alternate direction method(ADM)under the augmented Lagrangian framework.We also devise a multi-resolution scheme for robust and progressive registration.Results on both public datasets and our scanned datasets show the superiority of our method,particularly in handling large-scale deformations as well as outliers and noise.The main contributions of this work are summarized as:1)We propose a sparse non-rigid registration method.The SNR model is constructed based on the verified observation that non-rigid transformations are piecewise smooth on the underlying graph,and is able to handle flexible deformations of local geometries.The SNR model is transferred into a series of alternating optimization sub-problems with exact solutions and guaranteed convergence.we also propose a non-rigid registration method with sparse position and transform constraints,which can achieve better results.2)We establish a multi-resolution non-rigid registration scheme.The template and target shapes are down-sampled into low resolution versions of several scales.The non-rigid registration at the full resolution is obtained in a coarse-to-fine manner.This strategy is not only more efficient,but also prevents the method from trapping into poor local minimums,providing robust registration for complicated deformations.we propose a doubly-sparse non-rigid registration method.3)We propose a global non-rigid registration method.We reconstruct the shape which scanned in several different views.We use the proposed sparse non-rigid registration method,create a optimization problem with exact solutions,and reconstruct all the views into a whole shape. |
