NeuRBF：具有自適應徑向基函數的神經場表示形式

摘要

我們提出一種新型的神經場，使用一般的基於徑向基的信號表示。最先進的神經場通常依賴基於網格的表示來存儲本地神經特徵和N維線性核心，以在連續查詢點上插值特徵。它們的神經特徵的空間位置固定在網格節點上，無法很好地適應目標信號。相反，我們的方法建立在具有靈活核心位置和形狀的一般徑向基之上，這些基具有更高的空間適應性，可以更緊密地擬合目標信號。為了進一步提高徑向基函數的通道容量，我們建議將它們與多頻率正弦函數組合。這種技術將一個徑向基擴展到不同頻率帶的多個傅立葉徑向基，而無需額外的參數，有助於表示細節。此外，通過將自適應徑向基與基於網格的基結合，我們的混合組合繼承了適應性和插值平滑性。我們精心設計了加權方案，讓徑向基能夠有效地適應不同類型的信號。我們在2D圖像和3D符號距離場表示上的實驗證明了我們的方法比先前方法具有更高的準確性和緊湊性。當應用於神經輻射場重建時，我們的方法實現了最先進的渲染質量，具有較小的模型尺寸和可比較的訓練速度。

English

We present a novel type of neural fields that uses general radial bases for signal representation. State-of-the-art neural fields typically rely on grid-based representations for storing local neural features and N-dimensional linear kernels for interpolating features at continuous query points. The spatial positions of their neural features are fixed on grid nodes and cannot well adapt to target signals. Our method instead builds upon general radial bases with flexible kernel position and shape, which have higher spatial adaptivity and can more closely fit target signals. To further improve the channel-wise capacity of radial basis functions, we propose to compose them with multi-frequency sinusoid functions. This technique extends a radial basis to multiple Fourier radial bases of different frequency bands without requiring extra parameters, facilitating the representation of details. Moreover, by marrying adaptive radial bases with grid-based ones, our hybrid combination inherits both adaptivity and interpolation smoothness. We carefully designed weighting schemes to let radial bases adapt to different types of signals effectively. Our experiments on 2D image and 3D signed distance field representation demonstrate the higher accuracy and compactness of our method than prior arts. When applied to neural radiance field reconstruction, our method achieves state-of-the-art rendering quality, with small model size and comparable training speed.

NeuRBF：具有自適應徑向基函數的神經場表示形式

NeuRBF: A Neural Fields Representation with Adaptive Radial Basis Functions

摘要

Support