DA Wand: Distortion-Aware Selection using Neural Mesh Parameterization

We present a neural technique for learning to select a local sub-region around a point which can be used for mesh parameterization. The motivation for our framework is driven by interactive workflows used for decaling, texturing, or painting on surfaces. Our key idea is to incorporate segmentation probabilities as weights of a classical parameterization method, implemented as a novel differentiable parameterization layer within a neural network framework. We train a segmentation network to select 3D regions that are parameterized into 2D and penalized by the resulting distortion, giving rise to segmentations which are distortion-aware. Following training, a user can use our system to interactively select a point on the mesh and obtain a large, meaningful region around the selection which induces a low-distortion parameterization. Our code and project page are currently available.Comment: Project page: https://threedle.github.io/DA-Wand/ Code: https://github.com/threedle/DA-Wan

Neural Surface Maps

Maps are arguably one of the most fundamental concepts used to define and operate on manifold surfaces in differentiable geometry. Accordingly, in geometry processing, maps are ubiquitous and are used in many core applications, such as paramterization, shape analysis, remeshing, and deformation. Unfortunately, most computational representations of surface maps do not lend themselves to manipulation and optimization, usually entailing hard, discrete problems. While algorithms exist to solve these problems, they are problem-specific, and a general framework for surface maps is still in need. In this paper, we advocate considering neural networks as encoding surface maps. Since neural networks can be composed on one another and are differentiable, we show it is easy to use them to define surfaces via atlases, compose them for surface-to-surface mappings, and optimize differentiable objectives relating to them, such as any notion of distortion, in a trivial manner. In our experiments, we represent surfaces by generating a neural map that approximates a UV parameterization of a 3D model. Then, we compose this map with other neural maps which we optimize with respect to distortion measures. We show that our formulation enables trivial optimization of rather elusive mapping tasks, such as maps between a collection of surfaces

TextDeformer: Geometry Manipulation using Text Guidance

We present a technique for automatically producing a deformation of an input triangle mesh, guided solely by a text prompt. Our framework is capable of deformations that produce both large, low-frequency shape changes, and small high-frequency details. Our framework relies on differentiable rendering to connect geometry to powerful pre-trained image encoders, such as CLIP and DINO. Notably, updating mesh geometry by taking gradient steps through differentiable rendering is notoriously challenging, commonly resulting in deformed meshes with significant artifacts. These difficulties are amplified by noisy and inconsistent gradients from CLIP. To overcome this limitation, we opt to represent our mesh deformation through Jacobians, which updates deformations in a global, smooth manner (rather than locally-sub-optimal steps). Our key observation is that Jacobians are a representation that favors smoother, large deformations, leading to a global relation between vertices and pixels, and avoiding localized noisy gradients. Additionally, to ensure the resulting shape is coherent from all 3D viewpoints, we encourage the deep features computed on the 2D encoding of the rendering to be consistent for a given vertex from all viewpoints. We demonstrate that our method is capable of smoothly-deforming a wide variety of source mesh and target text prompts, achieving both large modifications to, e.g., body proportions of animals, as well as adding fine semantic details, such as shoe laces on an army boot and fine details of a face

Neural Semantic Surface Maps

We present an automated technique for computing a map between two genus-zero shapes, which matches semantically corresponding regions to one another. Lack of annotated data prohibits direct inference of 3D semantic priors; instead, current State-of-the-art methods predominantly optimize geometric properties or require varying amounts of manual annotation. To overcome the lack of annotated training data, we distill semantic matches from pre-trained vision models: our method renders the pair of 3D shapes from multiple viewpoints; the resulting renders are then fed into an off-the-shelf image-matching method which leverages a pretrained visual model to produce feature points. This yields semantic correspondences, which can be projected back to the 3D shapes, producing a raw matching that is inaccurate and inconsistent between different viewpoints. These correspondences are refined and distilled into an inter-surface map by a dedicated optimization scheme, which promotes bijectivity and continuity of the output map. We illustrate that our approach can generate semantic surface-to-surface maps, eliminating manual annotations or any 3D training data requirement. Furthermore, it proves effective in scenarios with high semantic complexity, where objects are non-isometrically related, as well as in situations where they are nearly isometric

Learning Delaunay Surface Elements for Mesh Reconstruction

We present a method for reconstructing triangle meshes from point clouds. Existing learning-based methods for mesh reconstruction mostly generate triangles individually, making it hard to create manifold meshes. We leverage the properties of 2D Delaunay triangulations to construct a mesh from manifold surface elements. Our method first estimates local geodesic neighborhoods around each point. We then perform a 2D projection of these neighborhoods using a learned logarithmic map. A Delaunay triangulation in this 2D domain is guaranteed to produce a manifold patch, which we call a Delaunay surface element. We synchronize the local 2D projections of neighboring elements to maximize the manifoldness of the reconstructed mesh. Our results show that we achieve better overall manifoldness of our reconstructed meshes than current methods to reconstruct meshes with arbitrary topology

Differentiable Surface Triangulation

Triangle meshes remain the most popular data representation for surface geometry. This ubiquitous representation is essentially a hybrid one that decouples continuous vertex locations from the discrete topological triangulation. Unfortunately, the combinatorial nature of the triangulation prevents taking derivatives over the space of possible meshings of any given surface. As a result, to date, mesh processing and optimization techniques have been unable to truly take advantage of modular gradient descent components of modern optimization frameworks. In this work, we present a differentiable surface triangulation that enables optimization for any per-vertex or per-face differentiable objective function over the space of underlying surface triangulations. Our method builds on the result that any 2D triangulation can be achieved by a suitably perturbed weighted Delaunay triangulation. We translate this result into a computational algorithm by proposing a soft relaxation of the classical weighted Delaunay triangulation and optimizing over vertex weights and vertex locations. We extend the algorithm to 3D by decomposing shapes into developable sets and differentiably meshing each set with suitable boundary constraints. We demonstrate the efficacy of our method on various planar and surface meshes on a range of difficult-to-optimize objective functions. Our code can be found online: https://github.com/mrakotosaon/diff-surface-triangulation

Neural Cages for Detail-Preserving 3D Deformations

We propose a novel learnable representation for detail-preserving shape deformation. The goal of our method is to warp a source shape to match the general structure of a target shape, while preserving the surface details of the source. Our method extends a traditional cage-based deformation technique, where the source shape is enclosed by a coarse control mesh termed \emph{cage}, and translations prescribed on the cage vertices are interpolated to any point on the source mesh via special weight functions. The use of this sparse cage scaffolding enables preserving surface details regardless of the shape's intricacy and topology. Our key contribution is a novel neural network architecture for predicting deformations by controlling the cage. We incorporate a differentiable cage-based deformation module in our architecture, and train our network end-to-end. Our method can be trained with common collections of 3D models in an unsupervised fashion, without any cage-specific annotations. We demonstrate the utility of our method for synthesizing shape variations and deformation transfer.Comment: accepted for oral presentation at CVPR 2020, code available at https://github.com/yifita/deep_cag

Neural Convolutional Surfaces

This work is concerned with a representation of shapes that disentangles fine, local and possibly repeating geometry, from global, coarse structures. Achieving such disentanglement leads to two unrelated advantages: i) a significant compression in the number of parameters required to represent a given geometry; ii) the ability to manipulate either global geometry, or local details, without harming the other. At the core of our approach lies a novel pipeline and neural architecture, which are optimized to represent one specific atlas, representing one 3D surface. Our pipeline and architecture are designed so that disentanglement of global geometry from local details is accomplished through optimization, in a completely unsupervised manner. We show that this approach achieves better neural shape compression than the state of the art, as well as enabling manipulation and transfer of shape details. Project page at http://geometry.cs.ucl.ac.uk/projects/2022/cnnmaps/