Implicit Neural Representation (INR) has shown great potential in constructing the complex nature signal as a continuous implicit function. However, the representation results are incomplete since different components of the signal correspond to different frequencies and neural network inherently tends to low-frequency convergence. In this paper, we propose the adaptive Wavelet-Positional Encoding (WPE) to precisely represent content under different frequency distributions for coordinate-based implicit representations. The High-Frequency Perception (HFP) method is first proposed to query locations of high-frequency components from input signals, which can be indicated as local centers of WPE. Then, motivated by wavelet series regression, we present to embed these queried low-dimensional coordinate inputs into wavelet-frequency space by WPE to represent fine details of target signals. Experiments demonstrate that the proposed method can be integrated into various INR methods without modifying training frameworks while significantly improving their performance in 1D signal fitting, 2D image regression, and even 3D scene representation.

Humans can infer 3D structure from 2D images of an object based on past experience and improve their 3D understanding as they see more images. Inspired by this be-havior, we introduce SAP3D, a system for 3D reconstruction and novel view synthesis from an arbitrary number of un-posed images. Given a few unposed images of an object, we adapt a pre-trained view-conditioned diffusion model together with the camera poses of the images via test-time fine-tuning. The adapted diffusion model and the obtained camera poses are then utilized as instance-specific priors for 3D reconstruction and novel view synthesis. We show that as the number of input images increases, the performance of our approach improves, bridging the gap between optimization-based prior-less 3D reconstruction methods and single-image-to-3D diffusion-based methods. We demon-strate our system on real images as well as standard synthetic benchmarks. Our ablation studies confirm that this adaption behavior is key for more accurate 3D understanding.1

Neural Radiance Fields have shown great potential to synthesize novel views with only a few discrete image observations of the world. However, the requirement of accurate camera parameters to learn scene representations limits its further application. In this paper, we present adaptive positional encoding (APE) for bundle-adjusting neural radiance fields to reconstruct the neural radiance fields from unknown camera poses (or even intrinsics). Inspired by Fourier series regression, we investigate its relationship with the positional encoding method and therefore propose APE where all frequency bands are trainable. Furthermore, we introduce period-activated multilayer perceptrons (PMLPs) to construct the implicit network for the high-order scene representations and fine-grained gradients during backpropagation. Experimental results on public datasets demonstrate that the proposed method with APE and PMLPs can outperform the state-of-the-art methods in accurate camera poses and high-fidelity view synthesis.