Seeing Implicit Neural Representations as Fourier Series

Benbarka, Nuri; Höfer, Timon; Riaz, Hamd ul-moqeet; Zell, Andreas

doi:10.48550/arxiv.2109.00249

Cited by 5 publications

(7 citation statements)

References 21 publications

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“…Here, we explore the main properties of this definition in implicit surface reconstruction. For example, its first layer is related to a Fourier feature mapping [5], which allows us to represent high-frequency three-dimensional implicit functions.…”

Section: Neural Implicit Function Architecturementioning

confidence: 99%

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Differential Geometry for Neural Implicit Models

Novello¹,

Silva²,

Lopes³

et al. 2022

Preprint

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We introduce a neural implicit framework that bridges discrete differential geometry of triangle meshes and continuous differential geometry of neural implicit surfaces. It exploits the differentiable properties of neural networks and the discrete geometry of triangle meshes to approximate them as the zero-level sets of neural implicit functions.To train a neural implicit function, we propose a loss function that allows terms with high-order derivatives, such as the alignment between the principal directions, to learn more geometric details.During training, we consider a non-uniform sampling strategy based on the discrete curvatures of the triangle mesh to access points with more geometric details. This sampling implies faster learning while preserving geometric accuracy.We present the analytical differential geometry formulas for neural surfaces, such as normal vectors and curvatures. We use them to render the surfaces using sphere tracing. Additionally, we propose a network optimization based on singular value decomposition to reduce the number of parameters.S KdS = 2πχ(S), where K is the Gaussian curvature , and χ(S) is the Euler characteristic of S. This work proposes a sampling based on the curvature to select points with important geometric details during the training.

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Section: Neural Implicit Function Architecturementioning

confidence: 99%

“…The normal N i is defined by the average of the normal vectors of the faces adjacent to the vertex p i . The discrete shape operator S i at p i can be computed using Equation (5).…”

Section: Samplingmentioning

confidence: 99%

Differential Geometry for Neural Implicit Models

Novello¹,

Silva²,

Lopes³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Evidently, sines allow the network to more accurately represent finer details. The use of sines is related to Fourier features [38], for which the aforementioned property has been theoretically explained [39] using the NTK framework [40]. We chose SIREN as our architecture due to its simplicity and effectiveness.…”

Section: Siren Representationmentioning

confidence: 99%

3D Neural Sculpting (3DNS): Editing Neural Signed Distance Functions

Petros¹,

Maragos²,

Roussos³

2022

Preprint

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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 through neural networks, allowing free-form editing. Inspired by 3D sculpting software for meshes, we use a brush-based framework that is intuitive and can in the future be used by sculptors and digital artists. In order to localize the desired surface deformations, we regulate the network by using a copy of it to sample the previously expressed surface. We introduce a novel framework for simulating sculpting-style surface edits, in conjunction with interactive surface sampling and efficient adaptation of network weights. We qualitatively and quantitatively evaluate our method in various different 3D objects and under many different edits. The reported results clearly show that our method yields high accuracy, in terms of achieving the desired edits, while at the same time preserving the geometry outside the interaction areas.

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“…Wang et al [WLYT21] showed that the choice of the frequency of γ i biases the network to learn certain, band-width limited frequency content, where lower encoding frequencies result in blurry reconstruction, and higher encoding frequencies introduce salt-andpepper artifacts. For more stable optimization, one approach is to mask out high-frequency encoding terms at the beginning of the optimization, and progressively increase the high-frequency encoding weights in a coarse-to-fine manner [LMTL21,BHumRZ21]. SAPE proposed a more sophisticate masking scheme [HPG * 21], which also allowed the encoding of spatially varying weights.…”

Section: Overcoming Spectral Biasmentioning

confidence: 99%

Neural Fields in Visual Computing and Beyond

Xie¹,

Takikawa²,

Saito³

et al. 2021

Preprint

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Advances in machine learning have increased interest in solving visual computing problems using a class of coordinate-based neural networks that parameterize physical properties of scenes or objects across space and time. These methods, which we call neural fields, have seen widespread success in applications such as 3D shape and image synthesis, animation of human bodies, 3D reconstruction, and pose estimation. Rapid progress has led to numerous papers, but a formulation and review of the problems in visual computing has not yet emerged. We provide context, mathematical grounding, and a review of 251 papers in the literature on neural fields. In Part I, we focus on neural fields techniques by identifying common components of neural field methods, including different generalization, representation, forward map, architecture, and manipulation methods. In Part II, we focus on applications of neural fields to different problems in visual computing, and beyond (e.g., robotics, audio). Our review shows the breadth of topics already covered in visual computing, both historically and in current incarnations, and highlights the improved quality, flexibility, and capability brought by neural field methods. Finally, we present a companion website that contributes a living database that can be continually updated by the community. CCS Concepts

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Seeing Implicit Neural Representations as Fourier Series

Cited by 5 publications

References 21 publications

Differential Geometry for Neural Implicit Models

Differential Geometry for Neural Implicit Models

3D Neural Sculpting (3DNS): Editing Neural Signed Distance Functions

Neural Fields in Visual Computing and Beyond

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