arXiv subjects

Luiz Schirmer

Publications and source records attributed to Luiz Schirmer.

7 recordsLinked to original sources

arXiv2026

M-plicits: Neural Implicit Surfaces via Nested Multiscale Residuals

Encoding input coordinates with sinusoidal functions into multi-layer perceptrons (MLPs) has proven effective for implicit neural representations (INRs) of surfaces defined as zero-level sets. However, existing methods often struggle to balance training efficiency, rendering speed, and noise robustness: single-MLP approaches are expensive at inference, grid-based representations are fast but can limit surface smoothness and overfit input noise, and previous multiscale approaches frequently capture noise and produce artifacts due to hard spectral truncation. To address these limitations, we propose M-plicits, a multiscale framework that models surfaces as a residual sum of MLPs trained via a sequence of nested neighborhoods. Unlike existing residual approaches that rely on standard domain-wide sampling and require costly mesh extraction for visualization, our method strictly localizes supervision to narrow bands around the previous zero-level sets. This nested design naturally provides robustness against noisy input data: the coarse network acts as a low-pass filter that establishes a clean geometric prior, while subsequent residuals progressively refine the geometry without fitting to high-frequency artifacts. We further introduce a multiscale sphere-tracing algorithm and a GEMM-based analytical normal computation that bypasses auto-differentiation entirely, yielding high-fidelity real-time rendering. On Stanford and Thingi32, M-plicits achieves the best mean Chamfer distance in the coarse configuration and the best median Chamfer distance and IoU in the fine configuration, with substantially better noise robustness than iNGP, BACON, and IDF, while using an order of magnitude fewer parameters than grid-based baselines. Code, models, and data are available at https://github.com/dsilvavinicius/m-plicits.

cs.CV↗

arXiv2025

Geometric implicit neural representations for signed distance functions

\textit{Implicit neural representations} (INRs) have emerged as a promising framework for representing signals in low-dimensional spaces. This survey reviews the existing literature on the specialized INR problem of approximating \textit{signed distance functions} (SDFs) for surface scenes, using either oriented point clouds or a set of posed images. We refer to neural SDFs that incorporate differential geometry tools, such as normals and curvatures, in their loss functions as \textit{geometric} INRs. The key idea behind this 3D reconstruction approach is to include additional \textit{regularization} terms in the loss function, ensuring that the INR satisfies certain global properties that the function should hold -- such as having unit gradient in the case of SDFs. We explore key methodological components, including the definition of INR, the construction of geometric loss functions, and sampling schemes from a differential geometry perspective. Our review highlights the significant advancements enabled by geometric INRs in surface reconstruction from oriented point clouds and posed images.

cs.CV↗

arXiv2024

High-Resolution Detection of Earth Structural Heterogeneities from Seismic Amplitudes using Convolutional Neural Networks with Attention layers

Earth structural heterogeneities have a remarkable role in the petroleum economy for both exploration and production projects. Automatic detection of detailed structural heterogeneities is challenging when considering modern machine learning techniques like deep neural networks. Typically, these techniques can be an excellent tool for assisted interpretation of such heterogeneities, but it heavily depends on the amount of data to be trained. We propose an efficient and cost-effective architecture for detecting seismic structural heterogeneities using Convolutional Neural Networks (CNNs) combined with Attention layers. The attention mechanism reduces costs and enhances accuracy, even in cases with relatively noisy data. Our model has half the parameters compared to the state-of-the-art, and it outperforms previous methods in terms of Intersection over Union (IoU) by 0.6% and precision by 0.4%. By leveraging synthetic data, we apply transfer learning to train and fine-tune the model, addressing the challenge of limited annotated data availability.

cs.CV↗

arXiv2023

Neural Implicit Surface Evolution

This work investigates the use of smooth neural networks for modeling dynamic variations of implicit surfaces under the level set equation (LSE). For this, it extends the representation of neural implicit surfaces to the space-time $\mathbb{R}^3\times \mathbb{R}$, which opens up mechanisms for continuous geometric transformations. Examples include evolving an initial surface towards general vector fields, smoothing and sharpening using the mean curvature equation, and interpolations of initial conditions. The network training considers two constraints. A data term is responsible for fitting the initial condition to the corresponding time instant, usually $\mathbb{R}^3 \times \{0\}$. Then, a LSE term forces the network to approximate the underlying geometric evolution given by the LSE, without any supervision. The network can also be initialized based on previously trained initial conditions, resulting in faster convergence compared to the standard approach.

cs.LG↗

arXiv2022

Neural Implicit Mapping via Nested Neighborhoods

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 surface nested on a neighborhood of its zero-level set. It is smooth and it does not depend on surface parametrizations. As a result, it can be used to fetch smooth normals for discrete surfaces such as meshes and to skip later iterations when sphere tracing level sets. Finally, we propose an algorithm for analytic normal calculation for MLPs and describe ways to obtain sequences of neural SDFs to use with the algorithms.

cs.GR↗

arXiv2022

Multiresolution Neural Networks for Imaging

We present MR-Net, a general architecture for multiresolution neural networks, and a framework for imaging applications based on this architecture. Our coordinate-based networks are continuous both in space and in scale as they are composed of multiple stages that progressively add finer details. Besides that, they are a compact and efficient representation. We show examples of multiresolution image representation and applications to texturemagnification, minification, and antialiasing. This document is the extended version of the paper [PNS+22]. It includes additional material that would not fit the page limitations of the conference track for publication.

cs.CV↗

arXiv2022

Exploring Differential Geometry in Neural Implicits

We introduce a neural implicit framework that exploits the differentiable properties of neural networks and the discrete geometry of point-sampled surfaces to approximate them as the level sets of neural implicit functions. To train a neural implicit function, we propose a loss functional that approximates a signed distance function, and allows terms with high-order derivatives, such as the alignment between the principal directions of curvature, to learn more geometric details. During training, we consider a non-uniform sampling strategy based on the curvatures of the point-sampled surface to prioritize points with more geometric details. This sampling implies faster learning while preserving geometric accuracy when compared with previous approaches. We also use the analytical derivatives of a neural implicit function to estimate the differential measures of the underlying point-sampled surface.

cs.GR↗