Neural implicit representations, which encode a surface as the level set of a neural network applied to spatial coordinates, have proven to be remarkably effective for optimizing, compressing, and generating 3D geometry. Although these representations are easy to fit, it is not clear how to best evaluate geometric queries on the shape, such as intersecting against a ray or finding a closest point. The predominant approach is to encourage the network to have a signed distance property. However, this property typically holds only approximately, leading to robustness issues, and holds only at the conclusion of training, inhibiting the use of queries in loss functions. Instead, this work presents a new approach to perform queries directly on general neural implicit functions for a wide range of existing architectures. Our key tool is the application of range analysis to neural networks, using automatic arithmetic rules to bound the output of a network over a region; we conduct a study of range analysis on neural networks, and identify variants of affine arithmetic which are highly effective. We use the resulting bounds to develop geometric queries including ray casting, intersection testing, constructing spatial hierarchies, fast mesh extraction, closest-point evaluation, evaluating bulk properties, and more. Our queries can be efficiently evaluated on GPUs, and offer concrete accuracy guarantees even on randomly-initialized networks, enabling their use in training objectives and beyond. We also show a preliminary application to inverse rendering.
School of Electronic and Information Engineering, South China University of Technology（华南理工大学电子与信息工程学院）；South China University of Technology（华南理工大学）
This paper studies a problem of learning surface mesh via implicit functions in an emerging field of deep learning surface reconstruction, where implicit functions are popularly implemented as multi-layer perceptrons (MLPs) with rectified linear units (ReLU). To achieve meshing from learned implicit functions, existing methods adopt the de-facto standard algorithm of marching cubes; while promising, they suffer from loss of precision learned in the MLPs, due to the discretization nature of marching cubes. Motivated by the knowledge that a ReLU based MLP partitions its input space into a number…
A deep equilibrium model uses implicit layers, which are implicitly defined through an equilibrium point of an infinite sequence of computation. It avoids any explicit computation of the infinite sequence by finding an equilibrium point directly via root-finding and by computing gradients via implicit differentiation. In this paper, we analyze the gradient dynamics of deep equilibrium models with nonlinearity only on weight matrices and non-convex objective functions of weights for regression and classification. Despite non-convexity, convergence to global optimum at a linear rate is guarantee…
University of Amsterdam（阿姆斯特丹大学）；CFAR, IHPC, A*STAR（新加坡科技研究局高性能计算研究所计算机视觉与机器人研究中心）；University of Edinburgh（爱丁堡大学）；Technical University of Munich（慕尼黑工业大学）
In recent years, neural implicit representations have made remarkable progress in modeling of 3D shapes with arbitrary topology. In this work, we address two key limitations of such representations, in failing to capture local 3D geometric fine details, and to learn from and generalize to shapes with unseen 3D transformations. To this end, we introduce a novel family of graph implicit functions with equivariant layers that facilitates modeling fine local details and guaranteed robustness to various groups of geometric transformations, through local $k$-NN graph embeddings with sparse point set…
Image search engines rely on appropriately designed ranking features that capture various aspects of the content semantics as well as the historic popularity. In this work, we consider the role of colour in this relevance matching process. Our work is motivated by the observation that a significant fraction of user queries have an inherent colour associated with them. While some queries contain explicit colour mentions (such as 'black car' and 'yellow daisies'), other queries have implicit notions of colour (such as 'sky' and 'grass'). Furthermore, grounding queries in colour is not a mapping …
Massachusetts Institute of Technology (MIT)（麻省理工学院）；The University of Maryland（马里兰大学）；Harvard University（哈佛大学）
Graph Neural Networks (GNNs) have been studied through the lens of expressive power and generalization. However, their optimization properties are less well understood. We take the first step towards analyzing GNN training by studying the gradient dynamics of GNNs. First, we analyze linearized GNNs and prove that despite the non-convexity of training, convergence to a global minimum at a linear rate is guaranteed under mild assumptions that we validate on real-world graphs. Second, we study what may affect the GNNs' training speed. Our results show that the training of GNNs is implicitly accel…
ETH Zurich（苏黎世联邦理工学院）；Tsinghua University（清华大学）；Google（谷歌）；Peking University（北京大学）；Peng Cheng Laboratory（鹏城实验室）；Microsoft（微软）
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…
HKUST(GZ)（香港科技大学（广州））；Shenzhen International Graduate School, Tsinghua University（清华大学深圳国际研究生院）；HKUST（香港科技大学）
Event cameras sense the intensity changes asynchronously and produce event streams with high dynamic range and low latency. This has inspired research endeavors utilizing events to guide the challenging video superresolution (VSR) task. In this paper, we make the first attempt to address a novel problem of achieving VSR at random scales by taking advantages of the high temporal resolution property of events. This is hampered by the difficulties of representing the spatial-temporal information of events when guiding VSR. To this end, we propose a novel framework that incorporates the spatial-te…
South China University of Technology（华南理工大学）；University of California at Berkeley（加州大学伯克利分校）
Reconstruction of object or scene surfaces has tremendous applications in computer vision, computer graphics, and robotics. In this paper, we study a fundamental problem in this context about recovering a surface mesh from an implicit field function whose zero-level set captures the underlying surface. To achieve the goal, existing methods rely on traditional meshing algorithms; while promising, they suffer from loss of precision learned in the implicit surface networks, due to the use of discrete space sampling in marching cubes. Given that an MLP with activations of Rectified Linear Unit (Re…
This paper introduces Attentive Implicit Representation Networks (AIR-Nets), a simple, but highly effective architecture for 3D reconstruction from point clouds. Since representing 3D shapes in a local and modular fashion increases generalization and reconstruction quality, AIR-Nets encode an input point cloud into a set of local latent vectors anchored in 3D space, which locally describe the object's geometry, as well as a global latent description, enforcing global consistency. Our model is the first grid-free, encoder-based approach that locally describes an implicit function. The vector at…
The recent success of implicit neural scene representations has presented a viable new method for how we capture and store 3D scenes. Unlike conventional 3D representations, such as point clouds, which explicitly store scene properties in discrete, localized units, these implicit representations encode a scene in the weights of a neural network which can be queried at any coordinate to produce these same scene properties. Thus far, implicit representations have primarily been optimized to estimate only the appearance and/or 3D geometry information in a scene. We take the next step and demonstr…
State University of New York at Buffalo（纽约州立大学布法罗分校）
Learning with kernels is an important concept in machine learning. Standard approaches for kernel methods often use predefined kernels that require careful selection of hyperparameters. To mitigate this burden, we propose in this paper a framework to construct and learn a data-dependent kernel based on random features and implicit spectral distributions that are parameterized by deep neural networks. The constructed network (called KernelNet) can be applied to deep generative modeling in various scenarios, including two popular learning paradigms in deep generative models, MMD-GAN and implicit…
RaPD: Resolution-Agnostic Pixel Diffusion via Semantics-Enriched Implicit Representations
College of Electronic and Information Engineering, Tongji University（同济大学电子与信息工程学院）；vivo Mobile Communication Co., Ltd.（vivo移动通信有限公司）；Nanjing University（南京大学）
This work investigates the use of Neural implicit representations, specifically Neural Radiance Fields (NeRF), for geometrical queries and motion planning. We show that by adding the capacity to infer occupancy in a radius to a pre-trained NeRF, we are effectively learning an approximation to a Euclidean Signed Distance Field (ESDF). Using backward differentiation of the augmented network, we obtain an obstacle gradient that is integrated into an obstacle avoidance policy based on the Riemannian Motion Policies (RMP) framework. Thus, our findings allow for very fast sampling-free obstacle avoi…
