Sparse Non-rigid Registration of 3D Shapes

• Published in: Computer graphics forum Vol. 34; no. 5; pp. 89 - 99
• Main Authors: Yang, Jingyu, Li, Ke, Li, Kun, Lai, Yu-Kun
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01.08.2015
• Subjects: 3-D graphics; Analysis; Categories and Subject Descriptors (according to ACM CCS); Estimates; I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Hierarchy and geometric transformations; Image processing systems; Noise; Outliers (statistics); Registration; Regularization; Scanning; Sensors; Studies; Tasks; Three dimensional; Transformations
• ISSN: 0167-7055; 1467-8659
• DOI: 10.1111/cgf.12699

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 overfitting issue due to underdetermination. The common wisdom in previous methods is to impose an ℓ2‐norm regularization on the local transformation differences. However, the ℓ2‐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 ℓ1‐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.