Neural field methods have seen great progress in various long-standing tasks
in computer vision and computer graphics, including novel view synthesis and
geometry reconstruction. As existing neural field methods try to predict some
coordinate-based continuous target values, such as RGB for Neural Radiance
Field (NeRF), all of these methods are regression models and are optimized by
some regression loss. However, are regression models really better than
classification models for neural field methods? In this work, we try to visit
this very fundamental but overlooked question for neural fields from a machine
learning perspective. We successfully propose a novel Neural Field Classifier
(NFC) framework which formulates existing neural field methods as
classification tasks rather than regression tasks. The proposed NFC can easily
transform arbitrary Neural Field Regressor (NFR) into its classification
variant via employing a novel Target Encoding module and optimizing a
classification loss. By encoding a continuous regression target into a
high-dimensional discrete encoding, we naturally formulate a multi-label
classification task. Extensive experiments demonstrate the impressive
effectiveness of NFC at the nearly free extra computational costs. Moreover,
NFC also shows robustness to sparse inputs, corrupted images, and dynamic
scenes.

神经场分类器 (NFC) 是一种新颖的神经场方法，将神经场方法转化为分类任务而不是回归任务，并通过使用目标编码模块和优化分类损失来实现，从机器学习的角度回答了神经场方法的回归模型是否比分类模型更好的问题。NFC 在几乎不增加计算成本的情况下展示了令人印象深刻的有效性，并且对稀疏输入、损坏的图像和动态场景也表现出鲁棒性。

通过目标编码和分类损失实现的神经场分类器

Neural Field Classifiers via Target Encoding and Classification Loss

Recently, Neural Radiance Field (NeRF) has shown great success in rendering
novel-view images of a given scene by learning an implicit representation with
only posed RGB images. NeRF and relevant neural field methods (e.g., neural
surface representation) typically optimize a point-wise loss and make
point-wise predictions, where one data point corresponds to one pixel.
Unfortunately, this line of research failed to use the collective supervision
of distant pixels, although it is known that pixels in an image or scene can
provide rich structural information. To the best of our knowledge, we are the
first to design a nonlocal multiplex training paradigm for NeRF and relevant
neural field methods via a novel Stochastic Structural SIMilarity (S3IM) loss
that processes multiple data points as a whole set instead of process multiple
inputs independently. Our extensive experiments demonstrate the unreasonable
effectiveness of S3IM in improving NeRF and neural surface representation for
nearly free. The improvements of quality metrics can be particularly
significant for those relatively difficult tasks: e.g., the test MSE loss
unexpectedly drops by more than 90% for TensoRF and DVGO over eight novel view
synthesis tasks; a 198% F-score gain and a 64% Chamfer $L_{1}$ distance
reduction for NeuS over eight surface reconstruction tasks. Moreover, S3IM is
consistently robust even with sparse inputs, corrupted images, and dynamic
scenes.

我们设计了一个非局部多路训练范式，通过一种新颖的随机结构相似度 (S3IM) 损失方法，将多个数据点作为一个整体集合处理而不是独立处理多个输入，从而改进了 NeRF 和神经表面表示，而且在稀疏输入、受损图像和动态场景下具有稳健性。