Related papers: 1-Lipschitz Neural Distance Fields

The advancements in neural rendering have increased the need for techniques that enable intuitive editing of 3D objects represented as neural implicit surfaces. This paper introduces a novel neural algorithm for parameterizing neural…

This paper presents a tractable algorithm for estimating an unknown Lipschitz function from noisy observations and establishes an upper bound on its convergence rate. The approach extends max-affine methods from convex shape-restricted…

We introduce a novel depth estimation technique for multi-frame structured light setups using neural implicit representations of 3D space. Our approach employs a neural signed distance field (SDF), trained through self-supervised…

Neural implicit methods have achieved high-quality 3D object surfaces under slight specular highlights. However, high specular reflections (HSR) often appear in front of target objects when we capture them through glasses. The complex…

The subgradient method is one of the most fundamental algorithmic schemes for nonsmooth optimization. The existing complexity and convergence results for this method are mainly derived for Lipschitz continuous objective functions. In this…

This note establishes a theoretical framework for finding (potentially overparameterized) approximations of a function on a compact set with a-priori bounds for the generalization error. The approximation method considered is to choose,…

Implicit neural representations are powerful for geometric modeling, but their practical use is often limited by the high computational cost of network evaluations. We observe that implicit representations require progressively lower…

Important research efforts have focused on the design and training of neural networks with a controlled Lipschitz constant. The goal is to increase and sometimes guarantee the robustness against adversarial attacks. Recent promising…

Training neural networks under a strict Lipschitz constraint is useful for provable adversarial robustness, generalization bounds, interpretable gradients, and Wasserstein distance estimation. By the composition property of Lipschitz…

In the field of computer vision, the numerical encoding of 3D surfaces is crucial. It is classical to represent surfaces with their Signed Distance Functions (SDFs) or Unsigned Distance Functions (UDFs). For tasks like representation…

Neural reconstruction and rendering strategies have demonstrated state-of-the-art performances due, in part, to their ability to preserve high level shape details. Existing approaches, however, either represent objects as implicit surface…

The Lipschitz constant is an important quantity that arises in analysing the convergence of gradient-based optimization methods. It is generally unclear how to estimate the Lipschitz constant of a complex model. Thus, this paper studies an…

Neural signed distance functions (SDFs) have shown remarkable capability in representing geometry with details. However, without signed distance supervision, it is still a challenge to infer SDFs from point clouds or multi-view images using…

It has been argued in the past that high-dimensional neural networks do not exhibit local minima capable of trapping an optimisation algorithm. However, the relationship between loss surface modality and the neural architecture parameters,…

Whole-brain surface extraction is an essential topic in medical imaging systems as it provides neurosurgeons with a broader view of surgical planning and abnormality detection. To solve the problem confronted in current deep learning skull…

Distances are pervasive in machine learning. They serve as similarity measures, loss functions, and learning targets; it is said that a good distance measure solves a task. When defining distances, the triangle inequality has proven to be a…

Surveillance and surveying are two important applications of empirical research. A major part of terrain modelling is supported by photographic surveys which are used for capturing expansive natural surfaces using a wide range of sensors --…

In recent years, the neural implicit surface has emerged as a powerful representation for multi-view surface reconstruction due to its simplicity and state-of-the-art performance. However, reconstructing smooth and detailed surfaces in…

Deriving sharp and computable upper bounds of the Lipschitz constant of deep neural networks is crucial to formally guarantee the robustness of neural-network based models. We analyse three existing upper bounds written for the $l^2$ norm.…

In recent years, neural distance functions trained via volumetric ray marching have been widely adopted for multi-view 3D reconstruction. These methods, however, apply the ray marching procedure for the entire scene volume, leading to…