Pierre-Alain Fayolle
We describe in this short note a technique to convert an implicit surface into a Signed Distance Function (SDF) while exactly preserving the zero level-set of the implicit. The proposed approach relies on embedding the input implicit in the final layer of a neural network, which is trained to minimize a loss function characterizing the SDF.
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Multilayer perceptrons (MLPs) have been successfully used to represent 3D shapes implicitly and compactly, by mapping 3D coordinates to the corresponding signed distance values or occupancy values. In this paper, we propose a novel positional encoding scheme, called Spline Positional Encoding, to map the input coordinates to a high dimensional space before passing them to MLPs, for helping to recover 3D signed distance fields with fine-scale geometric details from unorganized 3D point clouds. We verified the superiority of our approach over other positional encoding schemes on tasks of 3D shap…
We propose a differentiable sphere tracing algorithm to bridge the gap between inverse graphics methods and the recently proposed deep learning based implicit signed distance function. Due to the nature of the implicit function, the rendering process requires tremendous function queries, which is particularly problematic when the function is represented as a neural network. We optimize both the forward and backward passes of our rendering layer to make it run efficiently with affordable memory consumption on a commodity graphics card. Our rendering method is fully differentiable such that loss…
Geometric implicit neural representations for signed distance functions
本文综述了利用微分几何正则化改进有符号距离函数隐式神经表示的方法，重点分析几何损失函数与采样方案，并总结了其在点云和图像表面重建中的进展。
LGSDF: Continual Global Learning of Signed Distance Fields Aided by Local Updating
LGSDF通过前端动态网格局部更新与后端持续自监督隐式学习相结合，解决了ESDF重建中原始观测冲突导致的建图精度差问题，在多个场景中构建出比SOTA方法更精确的ESDF地图和网格。
NeuralSSD: A Neural Solver for Signed Distance Surface Reconstruction
针对现有隐式场参数化难以确保曲面与输入数据紧密拟合的问题，提出基于神经伽辽金法的NeuralSSD方法，通过新型能量方程和卷积网络提升曲面重建精度与泛化性，在ShapeNet等数据集上取得最优结果。
Neural implicit shape representations are an emerging paradigm that offers many potential benefits over conventional discrete representations, including memory efficiency at a high spatial resolution. Generalizing across shapes with such neural implicit representations amounts to learning priors over the respective function space and enables geometry reconstruction from partial or noisy observations. Existing generalization methods rely on conditioning a neural network on a low-dimensional latent code that is either regressed by an encoder or jointly optimized in the auto-decoder framework. He…
In recent years, implicit surface representations through neural networks that encode the signed distance have gained popularity and have achieved state-of-the-art results in various tasks (e.g. shape representation, shape reconstruction, and learning shape priors). However, in contrast to conventional shape representations such as polygon meshes, the implicit representations cannot be easily edited and existing works that attempt to address this problem are extremely limited. In this work, we propose the first method for efficient interactive editing of signed distance functions expressed thr…
SDFoam: Signed-Distance Foam for explicit surface reconstruction
SDFoam通过联合学习显式Voronoi图与隐式SDF，提升网格重建精度与效率，实现更清晰的视图一致表面。
Approximating Signed Distance Fields With Sparse Ellipsoidal Radial Basis Function Networks: A Dynamic Multi-Objective Optimization Strategy
本文提出一种动态多目标优化策略，利用稀疏椭球径向基函数网络高效近似隐式表面的带符号距离场，实现紧凑表示和高精度计算。
Recent progress in neural implicit functions has set new state-of-the-art in reconstructing high-fidelity 3D shapes from a collection of images. However, these approaches are limited to closed surfaces as they require the surface to be represented by a signed distance field. In this paper, we propose NeAT, a new neural rendering framework that can learn implicit surfaces with arbitrary topologies from multi-view images. In particular, NeAT represents the 3D surface as a level set of a signed distance function (SDF) with a validity branch for estimating the surface existence probability at the …
Recently, neural networks have been used as implicit representations for surface reconstruction, modelling, learning, and generation. So far, training neural networks to be implicit representations of surfaces required training data sampled from a ground-truth signed implicit functions such as signed distance or occupancy functions, which are notoriously hard to compute. In this paper we introduce Sign Agnostic Learning (SAL), a deep learning approach for learning implicit shape representations directly from raw, unsigned geometric data, such as point clouds and triangle soups. We have tested …
Recent advances in learning 3D shapes using neural implicit functions have achieved impressive results by breaking the previous barrier of resolution and diversity for varying topologies. However, most of such approaches are limited to closed surfaces as they require the space to be divided into inside and outside. More recent works based on unsigned distance function have been proposed to handle complex geometry containing both the open and closed surfaces. Nonetheless, as their direct outputs are point clouds, robustly obtaining high-quality meshing results from discrete points remains an op…
Local Surface Parameterizations via Smoothed Geodesic Splines
本文提出一种基于有符号隐式函数和投影函数的两阶段局部参数化方法，通过径向采样与样条插值支持多种几何表示，并应用于局部纹理和曲面曲线绘制。
RoCoSDF: Row-Column Scanned Neural Signed Distance Fields for Freehand 3D Ultrasound Imaging Shape Reconstruction
针对徒手3D超声成像中厚探头导致多视图数据形状重建难的问题，提出RoCoSDF框架，通过编码多视图SDF并在归一化空间融合、加正则项优化，无需大规模预训练即可实现更精准的形状重建。
Medial Axis Aware Learning of Signed Distance Functions
本文提出一种新的变分方法，用于计算高精度的全局符号距离函数，通过高阶变分公式考虑梯度的跳跃集，以提高计算精度。
We describe a two-level method for computing a function whose zero-level set is the surface reconstructed from given points scattered over the surface and associated with surface normal vectors. The function is defined as a linear combination of compactly supported radial basis functions (CSRBFs). The method preserves the simplicity and efficiency of implicit surface interpolation with CSRBFs and the reconstructed implicit surface owns the attributes, which are previously only associated with globally supported or globally regularized radial basis functions, such as exhibiting less extra zero-…
Points as Tori: Fast Pointwise Signed Distance for Point Clouds
该研究提出一种计算点云符号距离的方法，通过用环面局部拟合点云，利用预训练网络输出参数，无需全局优化和空间离散化且易并行化，基于新理论统一相关方法，可直接用于点云应用，无需显式重建。
We introduce a new implicit shape representation called Primary Ray-based Implicit Function (PRIF). In contrast to most existing approaches based on the signed distance function (SDF) which handles spatial locations, our representation operates on oriented rays. Specifically, PRIF is formulated to directly produce the surface hit point of a given input ray, without the expensive sphere-tracing operations, hence enabling efficient shape extraction and differentiable rendering. We demonstrate that neural networks trained to encode PRIF achieve successes in various tasks including single shape re…
Recent techniques have been successful in reconstructing surfaces as level sets of learned functions (such as signed distance fields) parameterized by deep neural networks. Many of these methods, however, learn only closed surfaces and are unable to reconstruct shapes with boundary curves. We propose a hybrid shape representation that combines explicit boundary curves with implicit learned interiors. Using machinery from geometric measure theory, we parameterize currents using deep networks and use stochastic gradient descent to solve a minimal surface problem. By modifying the metric accordin…
Shrinking: Reconstruction of Parameterized Surfaces from Signed Distance Fields
针对传统方法从有符号距离场重建曲面会丢失隐式神经表示的连续性与可微性的问题，提出迭代收缩参数化初始球面的重建方法，保留可微性与参数化特性，在测试中取得有竞争力的重建质量，可支撑多种下游图形与几何学习应用。
Implicit representations of geometry, such as occupancy fields or signed distance fields (SDF), have recently re-gained popularity in encoding 3D solid shape in a functional form. In this work, we introduce medial fields: a field function derived from the medial axis transform (MAT) that makes available information about the underlying 3D geometry that is immediately useful for a number of downstream tasks. In particular, the medial field encodes the local thickness of a 3D shape, and enables O(1) projection of a query point onto the medial axis. To construct the medial field we require nothin…
We present a novel implicit representation -- neural halfspace representation (NH-Rep), to convert manifold B-Rep solids to implicit representations. NH-Rep is a Boolean tree built on a set of implicit functions represented by the neural network, and the composite Boolean function is capable of representing solid geometry while preserving sharp features. We propose an efficient algorithm to extract the Boolean tree from a manifold B-Rep solid and devise a neural network-based optimization approach to compute the implicit functions. We demonstrate the high quality offered by our conversion algo…
Signed distance map (SDM) is a common representation of surfaces in medical image analysis and machine learning. The computational complexity of SDM for 3D parametric shapes is often a bottleneck in many applications, thus limiting their interest. In this paper, we propose a learning based SDM generation neural network which is demonstrated on a tridimensional cochlea shape model parameterized by 4 shape parameters. The proposed SDM Neural Network generates a cochlea signed distance map depending on four input parameters and we show that the deep learning approach leads to a 60 fold improvemen…
ViscoReg: Neural Signed Distance Functions via Viscosity Solutions
本文提出ViscoReg，通过粘性解理论稳定神经符号距离函数训练，优于SIREN、DiGS和StEik等方法，在ShapeNet和3D场景重建数据集上表现优异。
Stochastic Signed Distance Processes
提出随机符号距离过程（SSDP），将SDF体渲染重新解释为概率表面渲染，通过首次通过时间分布建模，在DTU和MobileBrick数据集上优于NeuS等基线方法。
Volumetrically Consistent Implicit Atlas Learning via Neural Diffeomorphic Flow for Placenta MRI
本文提出一种体积一致的隐式模型，结合SDF重建与神经微分流，学习胎盘的共享模板，通过体积正则化提升变形一致性，实现胎盘MRI的统一空间映射。
Recently, neural implicit surfaces learning by volume rendering has become popular for multi-view reconstruction. However, one key challenge remains: existing approaches lack explicit multi-view geometry constraints, hence usually fail to generate geometry consistent surface reconstruction. To address this challenge, we propose geometry-consistent neural implicit surfaces learning for multi-view reconstruction. We theoretically analyze that there exists a gap between the volume rendering integral and point-based signed distance function (SDF) modeling. To bridge this gap, we directly locate th…
Exploring Differential Geometry in Neural Implicits
该研究提出一种结合微分几何的神经隐式框架，通过含高阶导数项的损失泛函与基于曲率的非均匀采样，在保证几何精度的同时提升训练效率，并可估计点采样曲面的微分测度。
Marching Neurons: Accurate Surface Extraction for Neural Implicit Shapes
针对神经隐式形状表面提取不精确的问题，提出一种基于神经元域划分和深度优先遍历的解析提取方法，实现高精度且快速的网格生成。
Optimizing 3D Geometry Reconstruction from Implicit Neural Representations
针对隐式神经表示难以保留高频细节且计算成本高的问题，提出整合周期性激活函数、位置编码和法线的新方法，以降低开销并增强3D形状精细细节与锐利特征的捕捉能力。
FIRe: Fast Inverse Rendering using Directional and Signed Distance Functions
针对神经3D隐式表示渲染时单光线需多次网络评估导致速度慢的问题，提出方向距离函数DDF，结合SDF实现单光线单次评估渲染，基于此的FIRe算法在单视图深度3D重建中精度更高且迭代速度快15倍以上。
Few-Shot Unsupervised Implicit Neural Shape Representation Learning with Spatial Adversaries
针对无监督下从稀疏3D点云学习神经符号距离函数的难题，提出利用形状周围对抗样本作为正则化项的方法，在合成与真实数据上有效提升了SDF学习效果。
Representing 3D surfaces as level sets of continuous functions over $\mathbb{R}^3$ is the common denominator of neural implicit representations, which recently enabled remarkable progress in geometric deep learning and computer vision tasks. In order to represent 3D motion within this framework, it is often assumed (either explicitly or implicitly) that the transformations which a surface may undergo are homeomorphic: this is not necessarily true, for instance, in the case of fluid dynamics. In order to represent more general classes of deformations, we propose to apply this theoretical framew…
RBF Your SDF: Radial Basis Function Interpolation of Signed Distance Fields with Implied Tangent Points
提出一种结合切球观察与径向基函数插值所有数据的方法，通过检测受限切点保留表面角点，利用单位分解扩展至大网格，在多个分辨率下提升重建精度。
Procedural Multiscale Geometry Modeling using Implicit Functions
本文提出一种基于隐式函数与自适应球体追踪的过程化多尺度几何建模框架，可实时合成颗粒、纤维、多孔和层状体积材料，并支持从图像与SDF示例中重建材料。
Synchronized-tracing of implicit surfaces
本文提出一种基于瓦片的隐式曲面渲染管线，利用低分辨率A-buffer和稀疏自底向上树遍历同步线程并即时剪枝blobtree，无需预处理即可高效渲染数千图元组成的曲面。
We introduce a novel approach for rendering static and dynamic 3D neural signed distance functions (SDF) in real-time. We rely on nested neighborhoods of zero-level sets of neural SDFs, and mappings between them. This framework supports animations and achieves real-time performance without the use of spatial data-structures. It consists of three uncoupled algorithms representing the rendering steps. The multiscale sphere tracing focuses on minimizing iteration time by using coarse approximations on earlier iterations. The neural normal mapping transfers details from a fine neural SDF to a surf…
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