Deformable 3D Shape Registration Based on Local Similarity Transforms

Abstract

In this paper, a new method for deformable 3D shape registration is proposed. The algorithm computes shape transitions based on local similarity transforms which allows to model not only as-rigid-as-possible deformations but also local and global scale. We formulate an ordinary differential equation (ODE) which describes the transition of a source shape towards a target shape. We assume that both shapes are roughly pre-aligned (e.g., frames of a motion sequence). The ODE consists of two terms. The first one causes the deformation by pulling the source shape points towards corresponding points on the target shape. Initial correspondences are estimated by closestpoint search and then refined by an efficient smoothing scheme. The second term regularizes the deformation by drawing the points towards locally defined rest positions. These are given by the optimal similarity transform which matches the initial (undeformed) neighborhood of a source point to its current (deformed) neighborhood. The proposed ODE allows for a very efficient explicit numerical integration. This avoids the repeated solution of large linear systems usually done when solving the registration problem within general-purpose non-linear optimization frameworks. We experimentally validate the proposed method on a variety of real data and perform a comparison with several state-of-the-art approaches.

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

“…Yamazaki et al [30] extended ARAP energy to as-similar-as-possible (ASAP) energy with spokes discrete cells. The work in [21] is a variation of shape matching [19] called similarity shape matching. 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.…”

“…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. Starting from the closest points on the target, we then flood over their neighbors to find out the smallest matching energy points until converge.…”

“…We then compare our registration technique to other state-of-the-art algorithms: as-conformal-as-possible surface registration (ACAP) [32], similarity-invariant shape registration (ASAP) [30], the embedded deformation technique (ED) [26], the shape matching-based registration technique that minimizes the as-similar-as-possible energy (SM-ASAP) [21], the Laplacian surface editing technique (LSE) [24] and the registration technique that utilizes the point-based deformation smoothness regularization (PDS) [2] in Fig. 6.…”

“…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.…”

Texture Overlay Onto Non-Rigid Surface Using Commodity Depth Camera

“…Drawback of this method is that the processing cost increases due to the iterative process. Papazov and Burschka proposed a method for deformable 3-D shape registration by computing shape transitions based on local similarity transforms (Papazov and Burschka, 2011). They formulated an ordinary differential equation which describes the transition of a source shape towards a target shape.…”