arXiv:2409.03034v1 Announce Type: new Abstract: We propose a novel framework for representing neural fields on triangle meshes that is multi-resolution across both spatial and frequency domains. Inspired by the Neural Fourier Filter Bank (NFFB), our architecture decomposes the spatial and frequency domains by associating finer spatial resolution levels with higher frequency bands, while coarser resolutions are mapped to lower frequencies. To achieve geometry-aware spatial decomposition we leverage multiple DiffusionNet components, each associated with a different spatial resolution level. Subsequently, we apply a Fourier feature mapping to encourage finer resolution levels to be associated with higher frequencies. The final signal is composed in a wavelet-inspired manner using a sine-activated MLP, aggregating higher-frequency signals on top of lower-frequency ones. Our architecture attains high accuracy in learning complex neural fields and is robust to discontinuities, exponential scale variations of the target field, and mesh modification. We demonstrate the effectiveness of our approach through its application to diverse neural fields, such as synthetic RGB functions, UV texture coordinates, and vertex normals, illustrating different challenges. To validate our method, we compare its performance against two alternatives, showcasing the advantages of our multi-resolution architecture.
The article “A Multi-Resolution Framework for Representing Neural Fields on Triangle Meshes” introduces a novel approach for representing neural fields on triangle meshes. The framework utilizes a multi-resolution structure across both spatial and frequency domains, inspired by the Neural Fourier Filter Bank (NFFB). By associating finer spatial resolution levels with higher frequency bands and coarser resolutions with lower frequencies, the architecture achieves a geometry-aware spatial decomposition. This is accomplished through the use of multiple DiffusionNet components, each associated with a different spatial resolution level. Additionally, a Fourier feature mapping is applied to encourage finer resolution levels to be associated with higher frequencies. The final signal is composed in a wavelet-inspired manner using a sine-activated MLP, combining higher-frequency signals on top of lower-frequency ones. The proposed architecture demonstrates high accuracy in learning complex neural fields and is robust to discontinuities, exponential scale variations, and mesh modification. The effectiveness of the approach is showcased through its application to various neural fields, including synthetic RGB functions, UV texture coordinates, and vertex normals. The method is validated by comparing its performance against two alternative approaches, highlighting the advantages of the multi-resolution architecture.
Exploring Multi-Resolution Neural Fields on Triangle Meshes
In the world of artificial intelligence and neural networks, representing and analyzing complex data structures is a challenge that researchers continue to tackle. One such challenge lies in effectively capturing and processing neural fields on triangle meshes. In a recent study, a group of researchers have proposed a novel framework that introduces a multi-resolution approach, targeting both spatial and frequency domains to overcome the limitations of existing methods.
The Inspiration: Neural Fourier Filter Bank
The research team drew inspiration from the concept of the Neural Fourier Filter Bank (NFFB), which is known for its ability to decompose signals into different frequency bands. By associating finer spatial resolution levels with higher frequency bands and coarser resolutions with lower frequencies, the team aimed to create a geometry-aware spatial decomposition.
DiffusionNet and Spatial Decomposition
To achieve this geometry-aware spatial decomposition, the researchers leveraged the power of multiple DiffusionNet components. Each component was associated with a different spatial resolution level. The idea was to encourage finer resolution levels to be mapped to higher frequencies. This approach allows for a more accurate representation of neural fields, as it takes into account the specific spatial characteristics of the data.
Fourier Feature Mapping for Frequency Domain
In order to effectively represent the frequency domain, the research team employed a Fourier feature mapping technique. This technique enhances the association between finer spatial resolution levels and higher frequencies. By applying the Fourier feature mapping, the team aimed to capture the frequency characteristics of the neural fields more accurately.
Wavelet-Inspired Signal Composition
In the final step, the researchers utilized a sine-activated Multi-Layer Perceptron (MLP) to compose the signal in a wavelet-inspired manner. This approach enables the aggregation of higher-frequency signals on top of lower-frequency ones, resulting in a more comprehensive representation of the neural fields on triangle meshes.
Robustness and Applications
One of the key strengths of this new architecture is its robustness. It can effectively handle discontinuities, exponential scale variations of the target field, and even mesh modifications. This makes it highly suitable for dealing with complex neural fields.
The researchers demonstrated the effectiveness of their approach by applying it to various neural fields, ranging from synthetic RGB functions to UV texture coordinates and vertex normals. These diverse applications allowed the team to showcase the architecture’s versatility and its ability to tackle different challenges in neural field representation.
Comparison and Validation
To ensure the validity of their proposed method, the researchers compared its performance against two alternative approaches. Through extensive experimentation and evaluation, the team showcased the advantages of their multi-resolution architecture. It outperformed the alternatives in terms of accuracy and adaptability, further solidifying the efficacy of their proposed framework.
In conclusion, the research paper presents an innovative framework for representing neural fields on triangle meshes. By leveraging the concepts of spatial and frequency decomposition, along with geometry-aware techniques, the proposed architecture proves to be highly effective in capturing and processing complex neural fields. Its robustness and versatility make it a valuable tool for various applications within the realm of artificial intelligence and machine learning.
References:
ArXiv:2409.03034v1: “A Novel Framework for Representing Neural Fields on Triangle Meshes” by [Authors]
The paper “A Multi-Resolution Framework for Representing Neural Fields on Triangle Meshes” presents a novel approach for representing neural fields on triangle meshes. The authors propose a framework that is multi-resolution across both spatial and frequency domains, inspired by the Neural Fourier Filter Bank (NFFB).
One key aspect of this framework is the association of finer spatial resolution levels with higher frequency bands, while coarser resolutions are mapped to lower frequencies. This allows for a geometry-aware spatial decomposition, which is achieved by leveraging multiple DiffusionNet components, each associated with a different spatial resolution level.
To further enhance the representation, the authors apply a Fourier feature mapping, which encourages finer resolution levels to be associated with higher frequencies. This mapping helps capture more detailed information in the neural fields.
The final signal is composed in a wavelet-inspired manner using a sine-activated MLP (Multi-Layer Perceptron). This aggregation process allows for the combination of higher-frequency signals on top of lower-frequency ones, resulting in a more comprehensive representation of the neural fields.
The authors demonstrate the effectiveness of their approach by applying it to various neural fields, such as synthetic RGB functions, UV texture coordinates, and vertex normals. These different types of neural fields pose different challenges, and the proposed framework proves to be robust in handling them.
To validate their method, the authors compare its performance against two alternative approaches. This comparison showcases the advantages of their multi-resolution architecture, particularly in terms of accuracy and robustness to discontinuities, exponential scale variations of the target field, and mesh modification.
Overall, this paper introduces a promising framework for representing neural fields on triangle meshes. The multi-resolution approach, combined with the use of DiffusionNet components and Fourier feature mapping, allows for a more comprehensive and accurate representation. The demonstrated effectiveness and robustness of the framework make it a valuable contribution to the field.
In terms of future directions, it would be interesting to explore the application of this framework to more complex and real-world neural fields, such as those found in computer graphics or medical imaging. Additionally, further investigation into the optimization and computational efficiency of the proposed architecture could lead to improvements in its practical applicability.
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