Neural subdivision

Liu, Hsueh-Ti Derek; Kim, Vladimir G.; Chaudhuri, Siddhartha; Aigerman, Noam; Jacobson, Alec

doi:10.1145/3386569.3392418

Cited by 51 publications

(42 citation statements)

References 52 publications

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“…We compute the prolongation by maintaining an intrinsic parametrization, as opposed to extrinsic prolongtaion based on 3D spatial coordinates (cf. [Liu and Jacobson 2019;Manson and Schaefer 2011]). Specifically, we parameterize the high-resolution mesh using the coarsened mesh to obtain a bijective map between the two (see Fig.…”

Section: Intrinsic Prolongationmentioning

confidence: 99%

“…4.3 to formulate the joint variable and then flatten both patches to a consistent UV domain. To determine whether the collapse and the flattening is valid, we refer to the Appendix B in [Liu et al 2020] for more details. During the querying stage, for a given query point represented as barycentric coordinates, we simply go through the list of local joint UV parameterization we stored from the decimation stage and update the barycentric coordinates successively using the method described in Fig.…”

Section: Successive Self-parameterizationmentioning

confidence: 99%

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Surface multigrid via intrinsic prolongation

et al. 2021

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Fig. 1. We introduce a novel geometric multigrid solver for curved surfaces. Our key ingredient is an intrinsic prolongation operator computed via parameterizing the high resolution shape via its coarsened counterpart, visualized using colored triangles. By recursively applying this self-parameterization, we obtain a hierarchy (from left to right) for our multigrid method (e.g., to solve heat geodesics [Crane et al. 2017], far left). ©model by Benoît Rogez under CC BY-NC.This paper introduces a novel geometric multigrid solver for unstructured curved surfaces. Multigrid methods are highly efficient iterative methods for solving systems of linear equations. Despite the success in solving problems defined on structured domains, generalizing multigrid to unstructured curved domains remains a challenging problem. The critical missing ingredient is a prolongation operator to transfer functions across different multigrid levels. We propose a novel method for computing the prolongation for triangulated surfaces based on intrinsic geometry, enabling an efficient geometric multigrid solver for curved surfaces. Our surface multigrid solver achieves better convergence than existing multigrid methods. Compared to direct solvers, our solver is orders of magnitude faster. We evaluate our method on many geometry processing applications and a wide variety of complex shapes with and without boundaries. By simply replacing the direct solver, we upgrade existing algorithms to interactive frame rates, and shift the computational bottleneck away from solving linear systems.

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Section: Intrinsic Prolongationmentioning

confidence: 99%

Section: Successive Self-parameterizationmentioning

confidence: 99%

Surface multigrid via intrinsic prolongation

et al. 2021

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“…Beyond 2D data, the idea of analogy has also been used for transferring 3D geometric details from one shape to another. We omit the discussion on methods that are not based on analogies, such as mesh cloning [ZHW∗06; TSS∗11] and geometric learning [LKC∗20; HHGC20; WAK∗20; CKF∗21; LZ21], and focus on analogy‐based techniques. Ma et al [MHS∗14] propose a method for 3D style transfer based on patch‐based assembly.…”

Section: Related Workmentioning

confidence: 99%

Normal‐Driven Spherical Shape Analogies

Liu

Jacobson

2021

Computer Graphics Forum

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This paper introduces a new method to stylize 3D geometry. The key observation is that the surface normal is an effective instrument to capture different geometric styles. Centered around this observation, we cast stylization as a shape analogy problem, where the analogy relationship is defined on the surface normal. This formulation can deform a 3D shape into different styles within a single framework. One can plug‐and‐play different target styles by providing an exemplar shape or an energy‐based style description (e.g., developable surfaces). Our surface stylization methodology enables Normal Captures as a geometric counterpart to material captures (MatCaps) used in rendering, and the prototypical concept of Spherical Shape Analogies as a geometric counterpart to image analogies in image processing.

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“…In our work we do not just learn a sizing field but a frame field which incorperates both sizing and directional information for the purpose of quadmeshing. L iu et al learn the position of new vertices created by a subdivision step in [LKC∗20]. Their method only has to consider local shape information for the subdivision scheme.…”

Section: Related Workmentioning

confidence: 99%

Learning Direction Fields for Quad Mesh Generation

Dielen

Lim

Lyon

et al. 2021

Computer Graphics Forum

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State of the art quadrangulation methods are able to reliably and robustly convert triangle meshes into quad meshes. Most of these methods rely on a dense direction field that is used to align a parametrization from which a quad mesh can be extracted. In this context, the aforementioned direction field is of particular importance, as it plays a key role in determining the structure of the generated quad mesh. If there are no user‐provided directions available, the direction field is usually interpolated from a subset of principal curvature directions. To this end, a number of heuristics that aim to identify significant surface regions have been proposed. Unfortunately, the resulting fields often fail to capture the structure found in meshes created by human experts. This is due to the fact that experienced designers can leverage their domain knowledge in order to optimize a mesh for a specific application. In the context of physics simulation, for example, a designer might prefer an alignment and local refinement that facilitates a more accurate numerical simulation. Similarly, a character artist may prefer an alignment that makes the resulting mesh easier to animate. Crucially, this higher level domain knowledge cannot be easily extracted from local curvature information alone. Motivated by this issue, we propose a data‐driven approach to the computation of direction fields that allows us to mimic the structure found in existing meshes, which could originate from human experts or other sources. More specifically, we make use of a neural network that aggregates global and local shape information in order to compute a direction field that can be used to guide a parametrization‐based quad meshing method. Our approach is a first step towards addressing this challenging problem with a fully automatic learning‐based method. We show that compared to classical techniques our data‐driven approach combined with a robust model‐driven method, is able to produce results that more closely exhibit the ground truth structure of a synthetic dataset (i.e. a manually designed quad mesh template fitted to a variety of human body types in a set of different poses).

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Neural subdivision

Cited by 51 publications

References 52 publications

Surface multigrid via intrinsic prolongation

Surface multigrid via intrinsic prolongation

Normal‐Driven Spherical Shape Analogies

Learning Direction Fields for Quad Mesh Generation

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