Factor Fields: A Unified Framework for Neural Fields and Beyond
(2302.01226)Abstract
We present Factor Fields, a novel framework for modeling and representing signals. Factor Fields decomposes a signal into a product of factors, each represented by a classical or neural field representation which operates on transformed input coordinates. This decomposition results in a unified framework that accommodates several recent signal representations including NeRF, Plenoxels, EG3D, Instant-NGP, and TensoRF. Additionally, our framework allows for the creation of powerful new signal representations, such as the "Dictionary Field" (DiF) which is a second contribution of this paper. Our experiments show that DiF leads to improvements in approximation quality, compactness, and training time when compared to previous fast reconstruction methods. Experimentally, our representation achieves better image approximation quality on 2D image regression tasks, higher geometric quality when reconstructing 3D signed distance fields, and higher compactness for radiance field reconstruction tasks. Furthermore, DiF enables generalization to unseen images/3D scenes by sharing bases across signals during training which greatly benefits use cases such as image regression from sparse observations and few-shot radiance field reconstruction.
Overview
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Factor Fields introduces a unified framework for representing multi-dimensional signals, such as images and 3D geometry, using neural and classical field representations.
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The framework decomposes signals into factors, enabling the integration of various signal representations and inspiring new model creation, including the Dictionary Field (DiF).
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Factor Fields uses coordinate transformation functions and projection functions like MLPs to fit signals, facilitating sparse observations and cross-signal learning.
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Empirical tests show that Factor Fields can achieve superior approximation, compactness, and efficiency, even outperforming methods like Instant-NGP in certain aspects.
Introduction to Factor Fields
In the pursuit of improving multi-dimensional digital content representation, there's a growing interest in neural field representations. These representations aid in various computer vision and graphic applications by providing a continuous description of signals like images or 3D geometry. Factor Fields is a novel framework diving into this space, aiming to provide a unified structure for representing these signals.
Unifying Neural Field Representations
Factor Fields stands out by offering a decomposition of a signal into factors, with each factor employing a neural or classical field representation acting on transformed input coordinates. This decomposition enables homogeneous integration of signal representations, like Neural Radiance Fields (NeRF), Plenoxels, EG3D, Instant-NGP, and TensoRF, while also inspiring the conception of new models. An exemplary contribution is the introduction of the Dictionary Field (DiF). Pivotal experiments demonstrate DiF achieving improvements in terms of approximation quality, compactness, and training time, outstripping existing fast reconstruction methods. The method showcased superior results in tasks such as 2D image regressions, reconstruction of 3D Signed Distance Fields (SDFs), and creating compact models for radiance fields.
Investigation of the Framework's Components
Delving into the internal mechanics, Factor Fields aligns each factor field with a coordinate transformation function that serves to decode features across possibly transformed signal domains. A projection function such as a Multi-Layer Perceptron (MLP) then regresses from the product of these factors to output the signal. This flexible construction allows for the fitting of signals with sparse observations and even facilitates cross-signal learnings, benefitting tasks like few-shot radiance field reconstructions.
Empirical Insights and Advances
Testing the "Factor Fields" hypothesis against existing methods yielded some impressive numerical results. For instance, compared to Instant-NGP, DiF was able to halve the number of parameters needed for SDF and radiance field reconstruction while delivering comparable or superior accuracy and efficiency.
Additionally, Factor Fields framework's adaptability was validated through experiments with varying the number of factors, level number, and choice of basis/coefficient transformations. It was found that setups utilizing multi-factor representations rather than single-factor models and employing periodic transformations recorded significant quality enhancements. Furthermore, employing an element-wise product for factor connection yielded consistency in performance gains across different applications.
Conclusion and Prospects
Factor Fields framework lays a substantial groundwork for future work on powerful and efficient signal representations for multi-dimensional signals. Particularly, the framework's proficiency in handling signal reconstruction from sparse observations and its generalization capabilities render it a valuable asset. As the field progresses, Factor Fields may well become the underpinning for a myriad of implementations and innovations in diverse applications within computer vision and graphics.
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