Robust Non-Rigid Registration with Reweighted Position and Transformation Sparsity

Abstract

Non-rigid registration is challenging because it is ill-posed with high degrees of freedom and is thus sensitive to noise and outliers. We propose a robust non-rigid registration method using reweighted sparsities on position and transformation to estimate the deformations between 3-D shapes. We formulate the energy function with position and transformation sparsity on both the data term and the smoothness term, and define the smoothness constraint using local rigidity. The double sparsity based non-rigid registration model is enhanced with a reweighting scheme, and solved by transferring the model into four alternately-optimized subproblems which have exact solutions and guaranteed convergence. Experimental results on both public datasets and real scanned datasets show that our method outperforms the state-of-the-art methods and is more robust to noise and outliers than conventional non-rigid registration methods.

On evaluating consensus in RANSAC surface registration

“…Notably, a very similar expression has been recently used in order to evaluate the smoothness (similarity) of local transformations needed for non‐rigid alignment [LYLG19]. With the L 1 norm, it is substantially more difficult to evaluate such metric than when the L 2 norm was used.…”

Huber-$$L_1$$-based non-isometric surface registration

“…5): consistent as-similaras-possible surface registration (CASAP) [8], as-conformalas-possible surface registration (ACAP) [29], the shape matching-based registration method that minimizes the assimilar-as-possible energy (SM-ASAP) [16] and the registration method that utilizes the point-based deformation smoothness regularization (PDS) [1]. To evaluate the registration accuracy quantitatively, we follow the criterion used in [8,11] and measure (1) distance error, which is the average distance from the vertices of the deformed template to the corresponding points on the target relative to the target bounding box diagonal, (2) intersection error, which is the number of self-intersecting faces, (3) Hausdorff error, the largest distance between two shapes with respective to the target bounding box diagonal. The statistics data can be Table 2.…”

“…They deform local features as rigidly as possible to avoid shearing and stretching artifacts. Yang et al [11] propose a dual-sparsity-based non-rigid registration, which adds orthogonality constraints on the local transformation to preserve local rigidity.…”

“…To tackle this issue, TV-L 1 model [30] is proposed to efficiently remove the outliers while preserving fine details. Based on TV-L 1 model, Yang et al [11] propose a dual sparsity registration approach on both position and transformation sparsity, allowing the positional error to concentrate on small regions. However, TV-L 1 model tends to produce piecewise constant results as shown in Werlberger et al [26].…”

Rigid Shape Registration Based on Extended Hamiltonian Learning

“…To find a (non)rigid transformation is to find a measure-preserving map. Another possible application is affine registration where shapes are distorted and there is no rigid transformation [ 40 , 41 ]. From this viewpoint, we should consider extended Hamiltonian learning on the general linear group , where more techniques should be developed.…”