As‐Conformal‐As‐Possible Surface Registration

Abstract

We present a non-rigid surface registration technique that can align surfaces with sizes and shapes that are different from each other, while avoiding mesh distortions during deformation. The registration is constrained locally as conformal as possible such that the angles of triangle meshes are preserved, yet local scales are allowed to change. Based on our conformal registration technique, we devise an automatic registration and interactive registration technique, which can reduce user interventions during template fitting. We demonstrate the versatility of our technique on a wide range of surfaces.

Consistent as-similar-as-possible non-isometric surface registration

“…Although these techniques utilize similar mapping to enable them to address size difference and shear distortion, they do not consider the smoothness regularization, which shows that they are incapable of handling large changes in pose or shape. Yoshiyasu et al [32] incorporated smooth regularization into the total energy; however, it is a unweighted energy, which does not take into account the impact of the length of edges. Moreover, the discrete cell they adopt is spokes, which leads to an inconsistent energy.…”

“…Given the cell C i on mesh S corresponding to vertex i, and its deformed version C i on mesh S , we define the approximate similar transformation between the two cells. Unlike [23,30,32] regarding spokes as the cell, the cell chosen in our paper is spokes and rims (denoted as E i ) in order to arrive at an analyzable energy [7]. If the deformation C i → C i is similar, then there exists a scale factor s i > 0 and a rotation matrix R i such that…”

“…Many works [9,30,32] regard the closest points as goal positions; however, correspondences chosen by these approaches are not quite appropriate as they only consider distances between the closest points of template and target surface. Inspired by [21,22], we concern feature descriptors and smooth factor additionally.…”

“…The deformed positions of vertices in the dense mesh can be calculated from the transformations of the deformation graph. We use the same approach as [32] to rebuild the dense mesh. Again, all the constraints are performed to fit the dense mesh to the target (Fig.…”

“…Similar registration fits the deformation gradient into a similarity matrix, which is an isotropic scale factor s times a rotation matrix R. The scale factor is able to handle size difference, while the rotation matrix part prevents local stretch and distortion. Thus, it has been widely used in methods [21,30,32] to align surfaces with different sizes and details. However, the energies they adopt to constrain the local deformation similarity are not consistent.…”