360-Degree Panorama Generation from Few Unregistered NFoV Images

360$^\circ$ panoramas are extensively utilized as environmental light sources in computer graphics. However, capturing a 360$^\circ$ $\times$ 180$^\circ$ panorama poses challenges due to the necessity of specialized and costly equipment, and additional human resources. Prior studies develop various learning-based generative methods to synthesize panoramas from a single Narrow Field-of-View (NFoV) image, but they are limited in alterable input patterns, generation quality, and controllability. To address these issues, we propose a novel pipeline called PanoDiff, which efficiently generates complete 360$^\circ$ panoramas using one or more unregistered NFoV images captured from arbitrary angles. Our approach has two primary components to overcome the limitations. Firstly, a two-stage angle prediction module to handle various numbers of NFoV inputs. Secondly, a novel latent diffusion-based panorama generation model uses incomplete panorama and text prompts as control signals and utilizes several geometric augmentation schemes to ensure geometric properties in generated panoramas. Experiments show that PanoDiff achieves state-of-the-art panoramic generation quality and high controllability, making it suitable for applications such as content editing.

Statistical Guarantees of Group-Invariant GANs

Group-invariant generative adversarial networks (GANs) are a type of GANs in which the generators and discriminators are hardwired with group symmetries. Empirical studies have shown that these networks are capable of learning group-invariant distributions with significantly improved data efficiency. In this study, we aim to rigorously quantify this improvement by analyzing the reduction in sample complexity for group-invariant GANs. Our findings indicate that when learning group-invariant distributions, the number of samples required for group-invariant GANs decreases proportionally with a power of the group size, and this power depends on the intrinsic dimension of the distribution's support. To our knowledge, this work presents the first statistical estimation for group-invariant generative models, specifically for GANs, and it may shed light on the study of other group-invariant generative models.

On the Implicit Bias of Linear Equivariant Steerable Networks: Margin, Generalization, and Their Equivalence to Data Augmentation

We study the implicit bias of gradient flow on linear equivariant steerable networks in group-invariant binary classification. Our findings reveal that the parameterized predictor converges in direction to the unique group-invariant classifier with a maximum margin defined by the input group action. Under a unitary assumption on the input representation, we establish the equivalence between steerable networks and data augmentation. Furthermore, we demonstrate the improved margin and generalization bound of steerable networks over their non-invariant counterparts.

Sample Complexity of Probability Divergences under Group Symmetry

We rigorously quantify the improvement in the sample complexity of variational divergence estimations for group-invariant distributions. In the cases of the Wasserstein-1 metric and the Lipschitz-regularized $\alpha$-divergences, the reduction of sample complexity is proportional to an ambient-dimension-dependent power of the group size. For the maximum mean discrepancy (MMD), the improvement of sample complexity is more nuanced, as it depends on not only the group size but also the choice of kernel. Numerical simulations verify our theories.

SpecNet2: Orthogonalization-free spectral embedding by neural networks

Spectral methods which represent data points by eigenvectors of kernel matrices or graph Laplacian matrices have been a primary tool in unsupervised data analysis. In many application scenarios, parametrizing the spectral embedding by a neural network that can be trained over batches of data samples gives a promising way to achieve automatic out-of-sample extension as well as computational scalability. Such an approach was taken in the original paper of SpectralNet (Shaham et al. 2018), which we call SpecNet1. The current paper introduces a new neural network approach, named SpecNet2, to compute spectral embedding which optimizes an equivalent objective of the eigen-problem and removes the orthogonalization layer in SpecNet1. SpecNet2 also allows separating the sampling of rows and columns of the graph affinity matrix by tracking the neighbors of each data point through the gradient formula. Theoretically, we show that any local minimizer of the new orthogonalization-free objective reveals the leading eigenvectors. Furthermore, global convergence for this new orthogonalization-free objective using a batch-based gradient descent method is proved. Numerical experiments demonstrate the improved performance and computational efficiency of SpecNet2 on simulated data and image datasets.

Representation-Agnostic Shape Fields

3D shape analysis has been widely explored in the era of deep learning. Numerous models have been developed for various 3D data representation formats, e.g., MeshCNN for meshes, PointNet for point clouds and VoxNet for voxels. In this study, we present Representation-Agnostic Shape Fields (RASF), a generalizable and computation-efficient shape embedding module for 3D deep learning. RASF is implemented with a learnable 3D grid with multiple channels to store local geometry. Based on RASF, shape embeddings for various 3D shape representations (point clouds, meshes and voxels) are retrieved by coordinate indexing. While there are multiple ways to optimize the learnable parameters of RASF, we provide two effective schemes among all in this paper for RASF pre-training: shape reconstruction and normal estimation. Once trained, RASF becomes a plug-and-play performance booster with negligible cost. Extensive experiments on diverse 3D representation formats, networks and applications, validate the universal effectiveness of the proposed RASF. Code and pre-trained models are publicly available https://github.com/seanywang0408/RASF

Disentangling modes with crossover instantaneous frequencies by synchrosqueezed chirplet transforms, from theory to application

Analysis of signals with oscillatory modes with crossover instantaneous frequencies is a challenging problem in time series analysis. One way to handle this problem is lifting the 2-dimensional time-frequency representation to a 3-dimensional representation, called time-frequency-chirp rate (TFC) representation, by adding one extra chirp rate parameter so that crossover frequencies are disentangles in higher dimension. The chirplet transform is an algorithm for this lifting idea. However, in practice we found that it has a stronger "blurring" effect in the chirp rate axis, which limits its application in real world data. Moreover, to our knowledge, we have limited mathematical understanding of the chirplet transform in the literature. Motivated by real world data challenges, in this paper, we propose the synchrosqueezed chirplet transform (SCT) that gives a concentrated TFC representation that the contrast is enhanced so that one can distinguish different modes even with crossover instantaneous frequencies. We also analyze chirplet transform and provide theoretical guarantee of SCT.

FHEDN: A based on context modeling Feature Hierarchy Encoder-Decoder Network for face detection

Because of affected by weather conditions, camera pose and range, etc. Objects are usually small, blur, occluded and diverse pose in the images gathered from outdoor surveillance cameras or access control system. It is challenging and important to detect faces precisely for face recognition system in the field of public security. In this paper, we design a based on context modeling structure named Feature Hierarchy Encoder-Decoder Network for face detection(FHEDN), which can detect small, blur and occluded face with hierarchy by hierarchy from the end to the beginning likes encoder-decoder in a single network. The proposed network is consist of multiple context modeling and prediction modules, which are in order to detect small, blur, occluded and diverse pose faces. In addition, we analyse the influence of distribution of training set, scale of default box and receipt field size to detection performance in implement stage. Demonstrated by experiments, Our network achieves promising performance on WIDER FACE and FDDB benchmarks.