Finding Surface Correspondences Using Symmetry Axis Curves

Figure 1: The proposed framework for isometric shape matching allows establishing dense correspondences between symmetric shapes in a principled way. Here, we first estimate a single map in an appropriate quotient space and then use it to generate 8 different point-to-point maps between two octopus models. Each correspondence is shown by transferring the XYZ functions from the target onto the source and rendering them as RGB channels on the mesh. Note, e.g. the location of the orange arm. AbstractWe introduce a novel method for non-rigid shape matching, designed to address the symmetric ambiguity problem present when matching shapes with intrinsic symmetries. Unlike the majority of existing methods which try to overcome this ambiguity by sampling a set of landmark correspondences, we address this problem directly by performing shape matching in an appropriate quotient space, where the symmetry has been identified and factored out. This allows us to both simplify the shape matching problem by matching between subspaces, and to return multiple solutions with equally good dense correspondences. Remarkably, both symmetry detection and shape matching are done without establishing any landmark correspondences between either points or parts of the shapes. This allows us to avoid an expensive combinatorial search present in most intrinsic symmetry detection and shape matching methods. We compare our technique with state-of-the-art methods and show that superior performance can be achieved both when the symmetry on each shape is known and when it needs to be estimated.

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Shape Matching via Quotient Spaces

Ovsjanikov

Mérigot

Pătrăucean

et al. 2013

“…Our symmetry‐aware region‐wise matching is related to methods that incorporate symmetry into the correspondence‐finding pipeline, such as [LKF12, THW*14, OMPG13], among others. Our method is different in its efficiency, robustness and ability to handle different shape representations, while also being useful downstream in pointwise matching techniques.…”

Section: Related Workmentioning

confidence: 99%

Robust Structure‐Based Shape Correspondence

Kleiman

Ovsjanikov

2018

We present a robust method to find region‐level correspondences between shapes, which are invariant to changes in geometry and applicable across multiple shape representations. We generate simplified shape graphs by jointly decomposing the shapes, and devise an adapted graph‐matching technique, from which we infer correspondences between shape regions. The simplified shape graphs are designed to primarily capture the overall structure of the shapes, without reflecting precise information about the geometry of each region, which enables us to find correspondences between shapes that might have significant geometric differences. Moreover, due to the special care we take to ensure the robustness of each part of our pipeline, our method can find correspondences between shapes with different representations, such as triangular meshes and point clouds. We demonstrate that the region‐wise matching that we obtain can be used to find correspondences between feature points, reveal the intrinsic self‐similarities of each shape and even construct point‐to‐point maps across shapes. Our method is both time and space efficient, leading to a pipeline that is significantly faster than comparable approaches. We demonstrate the performance of our approach through an extensive quantitative and qualitative evaluation on several benchmarks where we achieve comparable or superior performance to existing methods.

“…Most recently twisting symmetry flips can be reduced by penalizing transformations that deviate too much from a pure rotation [ATCO*10] or large deformation distortions [ZSCO*08]. Global reflective symmetry axis curves are found to be robust for shape correspondences [LKF12]. The work of [OMPG13] is designed to address the symmetric ambiguity problem present when matching shapes with intrinsic symmetries, and thus shares the same goal as ours.…”

Section: Related Workmentioning

confidence: 99%

Symmetry Robust Descriptor for Non‐Rigid Surface Matching

Zhang

Yin

Foong

2013

Figure 1: Signed angle field computation: (a) a human model; (b) the harmonic field from the red point on the right foot to the green point on the left hand; (c) the two gradient fields of the harmonic fields derived from four points on the hands and feet; (d) the signed angle field ranging from −π to π and visualized from blue to red. AbstractIn this paper, we propose a novel shape descriptor that is robust in differentiating intrinsic symmetric points on geometric surfaces. Our motivation is that even the state-of-the-art shape descriptors and non-rigid surface matching algorithms suffer from symmetry flips. They cannot differentiate surface points that are symmetric or near symmetric. Hence a left hand of one human model may be matched to a right hand of another. Our Symmetry Robust Descriptor (SRD) is based on a signed angle field, which can be calculated from the gradient fields of the harmonic fields of two point pairs. Experiments show that the proposed shape descriptor SRD results in much less symmetry flips compared to alternative methods. We further incorporate SRD into a stand-alone algorithm to minimize symmetry flips in finding sparse shape correspondences. SRD can also be used to augment other modern non-rigid shape matching algorithms with ease to alleviate symmetry confusions.