Isometric registration of ambiguous and partial data

Abstract

This paper introduces a new shape matching algorithm for computing correspondences between 3D surfaces that have undergone (approximately) isometric deformations. The new approach makes two main contributions: First, the algorithm is, unlike previous work, robust to "topological noise" such as large holes or "false connections", which is both observed frequently in real-world scanner data. Second, our algorithm samples the space of feasible solutions such that uncertainty in matching can be detected explicitly. We employ a novel randomized feature matching algorithm in order to find robust subsets of geodesics to verify isometric consistency. The paper shows shape matching results for real world and synthetic data sets that could not be handled using previous deformable matching algorithms.

Approximately Isometric Shape Correspondence by Matching Pointwise Spectral Features and Global Geodesic Structures

“…Thorstensen and Keriven [2009] extended the GMDS to textured shapes. Tevs et al [2009] suggested randomized geodesic distance preserving matching algorithm. Anguelov et al [2004] proposed matching shapes by minimizing a probabilistic model based on geodesic distances between all pairs of corresponding points.…”

“…The definition of the dissimilarity is usually based on surfaces properties that remain approximately invariant under possible transformations of the shapes. Roughly speaking, descriptor-based methods [Zaharescu et al (2009);Sun et al (2009)] measure the dissimilarity between some local signatures (or, descriptors) associated with the shapes, while metric based approaches [Memoli and Sapiro (2005); Bronstein et al (2006);Memoli (2007) ;Bronstein et al (2009);Tevs et al (2009)] find correspondences by minimizing the difference between the metric structures of the two shapes. There is also a family of methods that measure dissimilarity using a mixture of several common quantities, e.g.…”

Non-rigid Shape Correspondence Using Pointwise Surface Descriptors and Metric Structures

“…At the other end, the GMDS algorithm [6] results in a non-convex optimization problem, therefore it requires good initializations in order to obtain meaningful solutions, and can be used as a refinement step for most other shape matching algorithms. Other algorithms employing geodesic distances to perform the matching were suggested by Anguelov et al [1], who optimized a joint probabilistic model over the set of all possible correspondences to obtain a sparse set of corresponding points, and by Tevs et al [36] who proposed a randomized algorithm for matching feature points based on geodesic distances between them. Zhang et al [42] performed the matching using extremal curvature feature points and a combinatorial tree traversal algorithm, but its high complexity allowed them to match only a small number of points.…”

Hierarchical Matching of Non-rigid Shapes

“…[1], who optimized a joint probabilistic model over the set of all possible correspondences to obtain a sparse set of corresponding points, and by Tevs et al . [34] who proposed a randomized algorithm for matching feature points based on geodesic distances between them. Zhang et al .…”