SGP23: Eurographics Symposium on Geometry Processing (CGF 42-5)

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https://diglib.eg.org/handle/10.2312/3607110

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3D Keypoint Estimation Using Implicit Representation Learning
(The Eurographics Association and John Wiley & Sons Ltd., 2023) Zhu, Xiangyu; Du, Dong; Huang, Haibin; Ma, Chongyang; Han, Xiaoguang; Memari, Pooran; Solomon, Justin
In this paper, we tackle the challenging problem of 3D keypoint estimation of general objects using a novel implicit representation. Previous works have demonstrated promising results for keypoint prediction through direct coordinate regression or heatmap-based inference. However, these methods are commonly studied for specific subjects, such as human bodies and faces, which possess fixed keypoint structures. They also suffer in several practical scenarios where explicit or complete geometry is not given, including images and partial point clouds. Inspired by the recent success of advanced implicit representation in reconstruction tasks, we explore the idea of using an implicit field to represent keypoints. Specifically, our key idea is employing spheres to represent 3D keypoints, thereby enabling the learnability of the corresponding signed distance field. Explicit keypoints can be extracted subsequently by our algorithm based on the Hough transform. Quantitative and qualitative evaluations also show the superiority of our representation in terms of prediction accuracy.
Attention And Positional Encoding Are (Almost) All You Need For Shape Matching
(The Eurographics Association and John Wiley & Sons Ltd., 2023) Raganato, Alessandro; Pasi, Gabriella; Melzi, Simone; Memari, Pooran; Solomon, Justin
The fast development of novel approaches derived from the Transformers architecture has led to outstanding performance in different scenarios, from Natural Language Processing to Computer Vision. Recently, they achieved impressive results even in the challenging task of non-rigid shape matching. However, little is known about the capability of the Transformer-encoder architecture for the shape matching task, and its performances still remained largely unexplored. In this paper, we step back and investigate the contribution made by the Transformer-encoder architecture compared to its more recent alternatives, focusing on why and how it works on this specific task. Thanks to the versatility of our implementation, we can harness the bi-directional structure of the correspondence problem, making it more interpretable. Furthermore, we prove that positional encodings are essential for processing unordered point clouds. Through a comprehensive set of experiments, we find that attention and positional encoding are (almost) all you need for shape matching. The simple Transformer-encoder architecture, coupled with relative position encoding in the attention mechanism, is able to obtain strong improvements, reaching the current state-of-the-art.
BPM: Blended Piecewise Möbius Maps
(The Eurographics Association and John Wiley & Sons Ltd., 2023) Rorberg, Shir; Vaxman, Amir; Ben-Chen, Mirela; Memari, Pooran; Solomon, Justin
We propose a novel Möbius interpolator that takes as an input a discrete map between the vertices of two planar triangle meshes, and outputs a continuous map on the input domain. The output map interpolates the discrete map, is continuous between triangles, and has low quasi-conformal distortion when the input map is discrete conformal. Our map leads to considerably smoother texture transfer compared to the alternatives, even on very coarse triangulations. Furthermore, our approach has a closed-form expression, is local, applicable to any discrete map, and leads to smooth results even for extreme deformations. Finally, by working with local intrinsic coordinates, our approach is easily generalizable to discrete maps between a surface triangle mesh and a planar mesh, i.e., a planar parameterization. We compare our method with existing approaches, and demonstrate better texture transfer results, and lower quasi-conformal errors.
Cross-Shape Attention for Part Segmentation of 3D Point Clouds
(The Eurographics Association and John Wiley & Sons Ltd., 2023) Loizou, Marios; Garg, Siddhant; Petrov, Dmitry; Averkiou, Melinos; Kalogerakis, Evangelos; Memari, Pooran; Solomon, Justin
We present a deep learning method that propagates point-wise feature representations across shapes within a collection for the purpose of 3D shape segmentation. We propose a cross-shape attention mechanism to enable interactions between a shape's point-wise features and those of other shapes. The mechanism assesses both the degree of interaction between points and also mediates feature propagation across shapes, improving the accuracy and consistency of the resulting point-wise feature representations for shape segmentation. Our method also proposes a shape retrieval measure to select suitable shapes for crossshape attention operations for each test shape. Our experiments demonstrate that our approach yields state-of-the-art results in the popular PartNet dataset.
Deep Deformation Detail Synthesis for Thin Shell Models
(The Eurographics Association and John Wiley & Sons Ltd., 2023) Chen, Lan; Gao, Lin; Yang, Jie; Xu, Shibiao; Ye, Juntao; Zhang, Xiaopeng; Lai, Yu-Kun; Memari, Pooran; Solomon, Justin
In physics-based cloth animation, rich folds and detailed wrinkles are achieved at the cost of expensive computational resources and huge labor tuning. Data-driven techniques make efforts to reduce the computation significantly by utilizing a preprocessed database. One type of methods relies on human poses to synthesize fitted garments, but these methods cannot be applied to general cloth animations. Another type of methods adds details to the coarse meshes obtained through simulation, which does not have such restrictions. However, existing works usually utilize coordinate-based representations which cannot cope with large-scale deformation, and requires dense vertex correspondences between coarse and fine meshes. Moreover, as such methods only add details, they require coarse meshes to be sufficiently close to fine meshes, which can be either impossible, or require unrealistic constraints to be applied when generating fine meshes. To address these challenges, we develop a temporally and spatially as-consistent-as-possible deformation representation (named TS-ACAP) and design a DeformTransformer network to learn the mapping from low-resolution meshes to ones with fine details. This TS-ACAP representation is designed to ensure both spatial and temporal consistency for sequential large-scale deformations from cloth animations. With this TS-ACAP representation, our DeformTransformer network first utilizes two mesh-based encoders to extract the coarse and fine features using shared convolutional kernels, respectively. To transduct the coarse features to the fine ones, we leverage the spatial and temporal Transformer network that consists of vertex-level and frame-level attention mechanisms to ensure detail enhancement and temporal coherence of the prediction. Experimental results show that our method is able to produce reliable and realistic animations in various datasets at high frame rates with superior detail synthesis abilities compared to existing methods.
Factored Neural Representation for Scene Understanding
(The Eurographics Association and John Wiley & Sons Ltd., 2023) Wong, Yu-Shiang; Mitra, Niloy J.; Memari, Pooran; Solomon, Justin
A long-standing goal in scene understanding is to obtain interpretable and editable representations that can be directly constructed from a raw monocular RGB-D video, without requiring specialized hardware setup or priors. The problem is significantly more challenging in the presence of multiple moving and/or deforming objects. Traditional methods have approached the setup with a mix of simplifications, scene priors, pretrained templates, or known deformation models. The advent of neural representations, especially neural implicit representations and radiance fields, opens the possibility of end-to-end optimization to collectively capture geometry, appearance, and object motion. However, current approaches produce global scene encoding, assume multiview capture with limited or no motion in the scenes, and do not facilitate easy manipulation beyond novel view synthesis. In this work, we introduce a factored neural scene representation that can directly be learned from a monocular RGB-D video to produce object-level neural presentations with an explicit encoding of object movement (e.g., rigid trajectory) and/or deformations (e.g., nonrigid movement). We evaluate ours against a set of neural approaches on both synthetic and real data to demonstrate that the representation is efficient, interpretable, and editable (e.g., change object trajectory). Code and data are available at: http://geometry.cs.ucl.ac.uk/projects/2023/factorednerf/.
Feature-Preserving Offset Mesh Generation from Topology-Adapted Octrees
(The Eurographics Association and John Wiley & Sons Ltd., 2023) Zint, Daniel; Maruani, Nissim; Rouxel-Labbé, Mael; Alliez, Pierre; Memari, Pooran; Solomon, Justin
We introduce a reliable method to generate offset meshes from input triangle meshes or triangle soups. Our method proceeds in two steps. The first step performs a Dual Contouring method on the offset surface, operating on an adaptive octree that is refined in areas where the offset topology is complex. Our approach substantially reduces memory consumption and runtime compared to isosurfacing methods operating on uniform grids. The second step improves the output Dual Contouring mesh with an offset-aware remeshing algorithm to reduce the normal deviation between the mesh facets and the exact offset. This remeshing process reconstructs concave sharp features and approximates smooth shapes in convex areas up to a user-defined precision. We show the effectiveness and versatility of our method by applying it to a wide range of input meshes. We also benchmark our method on the Thingi10k dataset: watertight and topologically 2-manifold offset meshes are obtained for 100% of the cases.
Graph-Based Synthesis for Skin Micro Wrinkles
(The Eurographics Association and John Wiley & Sons Ltd., 2023) Weiss, Sebastian; Moulin, Jonathan; Chandran, Prashanth; Zoss, Gaspard; Gotardo, Paulo; Bradley, Derek; Memari, Pooran; Solomon, Justin
We present a novel graph-based simulation approach for generating micro wrinkle geometry on human skin, which can easily scale up to the micro-meter range and millions of wrinkles. The simulation first samples pores on the skin and treats them as nodes in a graph. These nodes are then connected and the resulting edges become candidate wrinkles. An iterative optimization inspired by pedestrian trail formation is then used to assign weights to those edges, i.e., to carve out the wrinkles. Finally, we convert the graph to a detailed skin displacement map using novel shape functions implemented in graphics shaders. Our simulation and displacement map creation steps expose fine controls over the appearance at real-time framerates suitable for interactive exploration and design. We demonstrate the effectiveness of the generated wrinkles by enhancing state-of-art 3D reconstructions of real human subjects with simulated micro wrinkles, and furthermore propose an artist-driven design flow for adding micro wrinkles to fictional characters.
HalfedgeCNN for Native and Flexible Deep Learning on Triangle Meshes
(The Eurographics Association and John Wiley & Sons Ltd., 2023) Ludwig, Ingmar; Tyson, Daniel; Campen, Marcel; Memari, Pooran; Solomon, Justin
We describe HalfedgeCNN, a collection of modules to build neural networks that operate on triangle meshes. Taking inspiration from the (edge-based) MeshCNN, convolution, pooling, and unpooling layers are consistently defined on the basis of halfedges of the mesh, pairs of oppositely oriented virtual instances of each edge. This provides benefits over alternative definitions on the basis of vertices, edges, or faces. Additional interface layers enable support for feature data associated with such mesh entities in input and output as well. Due to being defined natively on mesh entities and their neighborhoods, lossy resampling or interpolation techniques (to enable the application of operators adopted from image domains) do not need to be employed. The operators have various degrees of freedom that can be exploited to adapt to application-specific needs.
HexBox: Interactive Box Modeling of Hexahedral Meshes
(The Eurographics Association and John Wiley & Sons Ltd., 2023) Zoccheddu, Francesco; Gobbetti, Enrico; Livesu, Marco; Pietroni, Nico; Cherchi, Gianmarco; Memari, Pooran; Solomon, Justin
We introduce HexBox, an intuitive modeling method and interactive tool for creating and editing hexahedral meshes. Hexbox brings the major and widely validated surface modeling paradigm of surface box modeling into the world of hex meshing. The main idea is to allow the user to box-model a volumetric mesh by primarily modifying its surface through a set of topological and geometric operations. We support, in particular, local and global subdivision, various instantiations of extrusion, removal, and cloning of elements, the creation of non-conformal or conformal grids, as well as shape modifications through vertex positioning, including manual editing, automatic smoothing, or, eventually, projection on an externally-provided target surface. At the core of the efficient implementation of the method is the coherent maintenance, at all steps, of two parallel data structures: a hexahedral mesh representing the topology and geometry of the currently modeled shape, and a directed acyclic graph that connects operation nodes to the affected mesh hexahedra. Operations are realized by exploiting recent advancements in gridbased meshing, such as mixing of 3-refinement, 2-refinement, and face-refinement, and using templated topological bridges to enforce on-the-fly mesh conformity across pairs of adjacent elements. A direct manipulation user interface lets users control all operations. The effectiveness of our tool, released as open source to the community, is demonstrated by modeling several complex shapes hard to realize with competing tools and techniques.
Lightweight Curvature Estimation on Point Clouds with Randomized Corrected Curvature Measures
(The Eurographics Association and John Wiley & Sons Ltd., 2023) Lachaud, Jacques-Olivier; Coeurjolly, David; Labart, Céline; Romon, Pascal; Thibert, Boris; Memari, Pooran; Solomon, Justin
The estimation of differential quantities on oriented point cloud is a classical step for many geometry processing tasks in computer graphics and vision. Even if many solutions exist to estimate such quantities, they usually fail at satisfying both a stable estimation with theoretical guarantee, and the efficiency of the associated algorithm. Relying on the notion of corrected curvature measures [LRT22, LRTC20] designed for surfaces, the method introduced in this paper meets both requirements. Given a point of interest and a few nearest neighbours, our method estimates the whole curvature tensor information by generating random triangles within these neighbours and normalising the corrected curvature measures by the corrected area measure. We provide a stability theorem showing that our pointwise curvatures are accurate and convergent, provided the noise in position and normal information has a variance smaller than the radius of neighbourhood. Experiments and comparisons with the state-of-the-art confirm that our approach is more accurate and much faster than alternatives. The method is fully parallelizable, requires only one nearest neighbour request per point of computation, and is trivial to implement.
Maximum Likelihood Coordinates
(The Eurographics Association and John Wiley & Sons Ltd., 2023) Chang, Qingjun; Deng, Chongyang; Hormann, Kai; Memari, Pooran; Solomon, Justin
Any point inside a d-dimensional simplex can be expressed in a unique way as a convex combination of the simplex's vertices, and the coefficients of this combination are called the barycentric coordinates of the point. The idea of barycentric coordinates extends to general polytopes with n vertices, but they are no longer unique if n>d+1. Several constructions of such generalized barycentric coordinates have been proposed, in particular for polygons and polyhedra, but most approaches cannot guarantee the non-negativity of the coordinates, which is important for applications like image warping and mesh deformation. We present a novel construction of non-negative and smooth generalized barycentric coordinates for arbitrary simple polygons, which extends to higher dimensions and can include isolated interior points. Our approach is inspired by maximum entropy coordinates, as it also uses a statistical model to define coordinates for convex polygons, but our generalization to non-convex shapes is different and based instead on the project-and-smooth idea of iterative coordinates. We show that our coordinates and their gradients can be evaluated efficiently and provide several examples that illustrate their advantages over previous constructions.
Neural Representation of Open Surfaces
(The Eurographics Association and John Wiley & Sons Ltd., 2023) Christiansen, Thor V.; Bærentzen, Jakob Andreas; Paulsen, Rasmus R.; Hannemose, Morten R.; Memari, Pooran; Solomon, Justin
Neural implicit surfaces have emerged as an effective, learnable representation for shapes of arbitrary topology. However, representing open surfaces remains a challenge. Different methods, such as unsigned distance fields (UDF), have been proposed to tackle this issue, but a general solution remains elusive. The generalized winding number (GWN), which is often used to distinguish interior points from exterior points of 3D shapes, is arguably the most promising approach. The GWN changes smoothly in regions where there is a hole in the surface, but it is discontinuous at points on the surface. Effectively, this means that it can be used in lieu of an implicit surface representation while providing information about holes, but, unfortunately, it does not provide information about the distance to the surface necessary for e.g. ray tracing, and special care must be taken when implementing surface reconstruction. Therefore, we introduce the semi-signed distance field (SSDF) representation which comprises both the GWN and the surface distance. We compare the GWN and SSDF representations for the applications of surface reconstruction, reconstruction from partial data, interpolation, and latent vector analysis using two very different data sets. We find that both the GWN and SSDF are well suited for neural representation of open surfaces.
Partial Matching of Nonrigid Shapes by Learning Piecewise Smooth Functions
(The Eurographics Association and John Wiley & Sons Ltd., 2023) Bensaid, David; Rotstein, Noam; Goldenstein, Nelson; Kimmel, Ron; Memari, Pooran; Solomon, Justin
Learning functions defined on non-flat domains, such as outer surfaces of non-rigid shapes, is a central task in computer vision and geometry processing. Recent studies have explored the use of neural fields to represent functions like light reflections in volumetric domains and textures on curved surfaces by operating in the embedding space. Here, we choose a different line of thought and introduce a novel formulation of partial shape matching by learning a piecewise smooth function on a surface. Our method begins with pairing sparse landmarks defined on a full shape and its part, using feature similarity. Next, a neural representation is optimized to fit these landmarks, efficiently interpolating between the matched features that act as anchors. This process results in a function that accurately captures the partiality. Unlike previous methods, the proposed neural model of functions is intrinsically defined on the given curved surface, rather than the classical embedding Euclidean space. This representation is shown to be particularly well-suited for representing piecewise smooth functions. We further extend the proposed framework to the more challenging part-to-part setting, where both shapes exhibit missing parts. Comprehensive experiments highlight that the proposed method effectively addresses partiality in shape matching and significantly outperforms leading state-of-the-art methods in challenging benchmarks. Code is available at https://github.com/davidgip74/ Learning-Partiality-with-Implicit-Intrinsic-Functions
Poisson Manifold Reconstruction - Beyond Co-dimension One
(The Eurographics Association and John Wiley & Sons Ltd., 2023) Kohlbrenner, Maximilian; Lee, Singchun; Alexa, Marc; Kazhdan, Misha; Memari, Pooran; Solomon, Justin
Screened Poisson Surface Reconstruction creates 2D surfaces from sets of oriented points in 3D (and can be extended to codimension one surfaces in arbitrary dimensions). In this work we generalize the technique to manifolds of co-dimension larger than one. The reconstruction problem consists of finding a vector-valued function whose zero set approximates the input points. We argue that the right extension of screened Poisson Surface Reconstruction is based on exterior products: the orientation of the point samples is encoded as the exterior product of the local normal frame. The goal is to find a set of scalar functions such that the exterior product of their gradients matches the exterior products prescribed by the input points. We show that this setup reduces to the standard formulation for co-dimension 1, and leads to more challenging multi-quadratic optimization problems in higher co-dimension. We explicitly treat the case of co-dimension 2, i.e., curves in 3D and 2D surfaces in 4D. We show that the resulting bi-quadratic problem can be relaxed to a set of quadratic problems in two variables and that the solution can be made effective and efficient by leveraging a hierarchical approach.
PowerRTF: Power Diagram based Restricted Tangent Face for Surface Remeshing
(The Eurographics Association and John Wiley & Sons Ltd., 2023) Yao, Yuyou; Liu, Jingjing; Fei, Yue; Wu, Wenming; Zhang, Gaofeng; Yan, Dong-Ming; Zheng, Liping; Memari, Pooran; Solomon, Justin
Triangular meshes of superior quality are important for geometric processing in practical applications. Existing approximative CVT-based remeshing methodology uses planar polygonal facets to fit the original surface, simplifying the computational complexity. However, they usually do not consider surface curvature. Topological errors and outliers can also occur in the close sheet surface remeshing, resulting in wrong meshes. With this regard, we present a novel method named PowerRTF, an extension of the restricted tangent face (RTF) in conjunction with the power diagram, to better approximate the original surface with curvature adaption. The idea is to introduce a weight property to each sample point and compute the power diagram on the tangent face to produce area-controlled polygonal facets. Based on this, we impose the variable-capacity constraint and centroid constraint to the PowerRTF, providing the trade-off between mesh quality and computational efficiency. Moreover, we apply a normal verification-based inverse side point culling method to address the topological errors and outliers in close sheet surface remeshing. Our method independently computes and optimizes the PowerRTF per sample point, which is efficiently implemented in parallel on the GPU. Experimental results demonstrate the effectiveness, flexibility, and efficiency of our method.
Quadratic-Attraction Subdivision
(The Eurographics Association and John Wiley & Sons Ltd., 2023) Karciauskas, Kestutis; Peters, Jorg; Memari, Pooran; Solomon, Justin
The idea of improving multi-sided piecewise polynomial surfaces, by explicitly prescribing their behavior at a central surface point, allows for decoupling shape finding from enforcing local smoothness constraints. Quadratic-Attraction Subdivision determines the completion of a quadratic expansion at the central point to attract a differentiable subdivision surface towards bounded curvature, with good shape also in-the-large.
SGP 2023 CGF 42-5: Frontmatter
(The Eurographics Association and John Wiley & Sons Ltd., 2023) Memari, Pooran; Solomon, Justin; Memari, Pooran; Solomon, Justin
A Shape Modulus for Fractal Geometry Generation
(The Eurographics Association and John Wiley & Sons Ltd., 2023) Schor, Alexa L.; Kim, Theodore; Memari, Pooran; Solomon, Justin
We present an efficient new method for computing Mandelbrot-like fractals (Julia sets) that approximate a user-defined shape. Our algorithm is orders of magnitude faster than previous methods, as it entirely sidesteps the need for a time-consuming numerical optimization. It is also more robust, succeeding on shapes where previous approaches failed. The key to our approach is a versor-modulus analysis of fractals that allows us to formulate a novel shape modulus function that directly controls the broad shape of a Julia set, while keeping fine-grained fractal details intact. Our formulation contains flexible artistic controls that allow users to seamlessly add fractal detail to desired spatial regions, while transitioning back to the original shape in others. No previous approach allows Mandelbrot-like details to be ''painted'' onto meshes.
Singularity-Free Frame Fields for Line Drawing Vectorization
(The Eurographics Association and John Wiley & Sons Ltd., 2023) Guțan, Olga; Hegde, Shreya; Berumen, Erick Jimenez; Bessmeltsev, Mikhail; Chien, Edward; Memari, Pooran; Solomon, Justin
State-of-the-art methods for line drawing vectorization rely on generated frame fields for robust direction disambiguation, with each of the two axes aligning to different intersecting curve tangents around junctions. However, a common source of topological error for such methods are frame field singularities. To remedy this, we introduce the first frame field optimization framework guaranteed to produce singularity-free fields aligned to a line drawing. We first perform a convex solve for a roughly-aligned orthogonal frame field (cross field), and then comb away its internal singularities with an optimal transport–based matching. The resulting topology of the field is strictly maintained with the machinery of discrete trivial connections in a final, non-convex optimization that allows non-orthogonality of the field, improving smoothness and tangent alignment. Our frame fields can serve as a drop-in replacement for frame field optimizations used in previous work, improving the quality of the final vectorizations.

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