ARAP++: an extension of the local/global approach to mesh parameterization

Wang, Zhao; Luo, Zhongxuan; Zhang, Jielin; Saucan, Emil

doi:10.1631/fitee.1500184

Cited by 17 publications

(8 citation statements)

References 40 publications

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“…In addition, the angle distortion between the deformed template S and the original template S is determined in order to quantify the amount of shearing introduced due to nonrigid registration. This is achieved by simply averaging the absolute deviation between the inner-triangle angles of S and S over all triangles [54].…”

Section: Experiments and Resultsmentioning

confidence: 99%

Learning the shape of female breasts: an open-access 3D statistical shape model of the female breast built from 110 breast scans

et al. 2022

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We present the Regensburg Breast Shape Model (RBSM)—a 3D statistical shape model of the female breast built from 110 breast scans acquired in a standing position, and the first publicly available. Together with the model, a fully automated, pairwise surface registration pipeline used to establish dense correspondence among 3D breast scans is introduced. Our method is computationally efficient and requires only four landmarks to guide the registration process. A major challenge when modeling female breasts from surface-only 3D breast scans is the non-separability of breast and thorax. In order to weaken the strong coupling between breast and surrounding areas, we propose to minimize the variance outside the breast region as much as possible. To achieve this goal, a novel concept called breast probability masks (BPMs) is introduced. A BPM assigns probabilities to each point of a 3D breast scan, telling how likely it is that a particular point belongs to the breast area. During registration, we use BPMs to align the template to the target as accurately as possible inside the breast region and only roughly outside. This simple yet effective strategy significantly reduces the unwanted variance outside the breast region, leading to better statistical shape models in which breast shapes are quite well decoupled from the thorax. The RBSM is thus able to produce a variety of different breast shapes as independently as possible from the shape of the thorax. Our systematic experimental evaluation reveals a generalization ability of 0.17 mm and a specificity of 2.8 mm. To underline the expressiveness of the proposed model, we finally demonstrate in two showcase applications how the RBSM can be used for surgical outcome simulation and the prediction of a missing breast from the remaining one. Our model is available at https://www.rbsm.re-mic.de/.

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Section: Experiments and Resultsmentioning

confidence: 99%

Learning the shape of female breasts: an open-access 3D statistical shape model of the female breast built from 110 breast scans

et al. 2022

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“…Additionally, for parameterizations of balancing distortions, some well-developed numerical methods, including the as-rigid-as-possible surface parameterization [51,72], the most isometric parametrization [41,20], the isometric distortion minimization [59], and boundary first flattening [61], have been proposed to reach a trade-off between minimizing the angle and area distortions.…”

Section: Previous Workmentioning

confidence: 99%

A Novel Algorithm for Volume-Preserving Parameterizations of 3-Manifolds

Yueh¹,

Li²,

Lin³

et al. 2019

SIAM J. Imaging Sci.

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Manifold parameterizations have been applied to various fields of commercial industries. Several efficient algorithms for the computation of triangular surface mesh parameterizations have been proposed in recent years. However, the computation of tetrahedral volumetric mesh parameterizations is more challenging due to the fact that the number of mesh points would become enormously large when the higher-resolution mesh is considered and the bijectivity of parameterizations is more difficult to guarantee. In this paper, we develop a novel volumetric stretch energy minimization algorithm for volume-preserving parameterizations of simply connected 3-manifolds with a single boundary under the restriction that the boundary is a spherical area-preserving mapping. In addition, our algorithm can also be applied to compute spherical angle-and area-preserving parameterizations of genus-zero closed surfaces, respectively. Several numerical experiments indicate that the developed algorithms are more efficient and reliable compared to other existing algorithms. Numerical results on applications of the manifold partition and the mesh processing for three-dimensional printing are demonstrated thereafter to show the robustness of the proposed algorithm.

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“…Similarly, Yu et al [17] used polar factorization to introduce area-angle preserving mappings, in which area distortion increases as angle distortion decreases. ARAP (As Rigid As Possible) algorithms divide the parameterization into two optimization steps-local parameterization and global parameterization-performing these steps iteratively one after another until convergence [18][19][20]. These algorithms produce different bijective parameterizations, but since the weighting parameters are nonoptimized (as they are user-defined), the resulting parameterization is rarely the optimal distance-preserving map.…”

Section: Distance-preserving Mesh Parameterizationmentioning

confidence: 99%

Quasi-Isometric Mesh Parameterization Using Heat-Based Geodesics and Poisson Surface Fills

et al. 2019

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In the context of CAD, CAM, CAE, and reverse engineering, the problem of mesh parameterization is a central process. Mesh parameterization implies the computation of a bijective map ϕ from the original mesh M ∈ R 3 to the planar domain ϕ ( M ) ∈ R 2 . The mapping may preserve angles, areas, or distances. Distance-preserving parameterizations (i.e., isometries) are obviously attractive. However, geodesic-based isometries present limitations when the mesh has concave or disconnected boundary (i.e., holes). Recent advances in computing geodesic maps using the heat equation in 2-manifolds motivate us to revisit mesh parameterization with geodesic maps. We devise a Poisson surface underlying, extending, and filling the holes of the mesh M. We compute a near-isometric mapping for quasi-developable meshes by using geodesic maps based on heat propagation. Our method: (1) Precomputes a set of temperature maps (heat kernels) on the mesh; (2) estimates the geodesic distances along the piecewise linear surface by using the temperature maps; and (3) uses multidimensional scaling (MDS) to acquire the 2D coordinates that minimize the difference between geodesic distances on M and Euclidean distances on R 2 . This novel heat-geodesic parameterization is successfully tested with several concave and/or punctured surfaces, obtaining bijective low-distortion parameterizations. Failures are registered in nonsegmented, highly nondevelopable meshes (such as seam meshes). These cases are the goal of future endeavors.

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ARAP++: an extension of the local/global approach to mesh parameterization

Cited by 17 publications

References 40 publications

Learning the shape of female breasts: an open-access 3D statistical shape model of the female breast built from 110 breast scans

Learning the shape of female breasts: an open-access 3D statistical shape model of the female breast built from 110 breast scans

A Novel Algorithm for Volume-Preserving Parameterizations of 3-Manifolds

Quasi-Isometric Mesh Parameterization Using Heat-Based Geodesics and Poisson Surface Fills

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