UGrid: An Efficient-And-Rigorous Neural Multigrid Solver for Linear PDEs

Numerical solvers of Partial Differential Equations (PDEs) are of fundamental significance to science and engineering. To date, the historical reliance on legacy techniques has circumscribed possible integration of big data knowledge and exhibits sub-optimal efficiency for certain PDE formulations, while data-driven neural methods typically lack mathematical guarantee of convergence and correctness. This paper articulates a mathematically rigorous neural solver for linear PDEs. The proposed UGrid solver, built upon the principled integration of U-Net and MultiGrid, manifests a mathematically rigorous proof of both convergence and correctness, and showcases high numerical accuracy, as well as strong generalization power to various input geometry/values and multiple PDE formulations. In addition, we devise a new residual loss metric, which enables unsupervised training and affords more stability and a larger solution space over the legacy losses.

Details Enhancement in Unsigned Distance Field Learning for High-fidelity 3D Surface Reconstruction

While Signed Distance Fields (SDF) are well-established for modeling watertight surfaces, Unsigned Distance Fields (UDF) broaden the scope to include open surfaces and models with complex inner structures. Despite their flexibility, UDFs encounter significant challenges in high-fidelity 3D reconstruction, such as non-differentiability at the zero level set, difficulty in achieving the exact zero value, numerous local minima, vanishing gradients, and oscillating gradient directions near the zero level set. To address these challenges, we propose Details Enhanced UDF (DEUDF) learning that integrates normal alignment and the SIREN network for capturing fine geometric details, adaptively weighted Eikonal constraints to address vanishing gradients near the target surface, unconditioned MLP-based UDF representation to relax non-negativity constraints, and a UDF-tailored method for extracting iso-surface with non-constant iso-values. These strategies collectively stabilize the learning process from unoriented point clouds and enhance the accuracy of UDFs. Our computational results demonstrate that DEUDF outperforms existing UDF learning methods in both accuracy and the quality of reconstructed surfaces. We will make the source code publicly available.

Robust Zero Level-Set Extraction from Unsigned Distance Fields Based on Double Covering

In this paper, we propose a new method, called DoubleCoverUDF, for extracting the zero level-set from unsigned distance fields (UDFs). DoubleCoverUDF takes a learned UDF and a user-specified parameter $r$ (a small positive real number) as input and extracts an iso-surface with an iso-value $r$ using the conventional marching cubes algorithm. We show that the computed iso-surface is the boundary of the $r$-offset volume of the target zero level-set $S$, which is an orientable manifold, regardless of the topology of $S$. Next, the algorithm computes a covering map to project the boundary mesh onto $S$, preserving the mesh's topology and avoiding folding. If $S$ is an orientable manifold surface, our algorithm separates the double-layered mesh into a single layer using a robust minimum-cut post-processing step. Otherwise, it keeps the double-layered mesh as the output. We validate our algorithm by reconstructing 3D surfaces of open models and demonstrate its efficacy and effectiveness on synthetic models and benchmark datasets. Our experimental results confirm that our method is robust and produces meshes with better quality in terms of both visual evaluation and quantitative measures than existing UDF-based methods. The source code is available at https://github.com/jjjkkyz/DCUDF.

WinDB: HMD-free and Distortion-free Panoptic Video Fixation Learning

To date, the widely-adopted way to perform fixation collection in panoptic video is based on a head-mounted display (HMD), where participants' fixations are collected while wearing an HMD to explore the given panoptic scene freely. However, this widely-used data collection method is insufficient for training deep models to accurately predict which regions in a given panoptic are most important when it contains intermittent salient events. The main reason is that there always exist "blind zooms" when using HMD to collect fixations since the participants cannot keep spinning their heads to explore the entire panoptic scene all the time. Consequently, the collected fixations tend to be trapped in some local views, leaving the remaining areas to be the "blind zooms". Therefore, fixation data collected using HMD-based methods that accumulate local views cannot accurately represent the overall global importance of complex panoramic scenes. This paper introduces the auxiliary Window with a Dynamic Blurring (WinDB) fixation collection approach for panoptic video, which doesn't need HMD and is blind-zoom-free. Thus, the collected fixations can well reflect the regional-wise importance degree. Using our WinDB approach, we have released a new PanopticVideo-300 dataset, containing 300 panoptic clips covering over 225 categories. Besides, we have presented a simple baseline design to take full advantage of PanopticVideo-300 to handle the blind-zoom-free attribute-induced fixation shifting problem. Our WinDB approach, PanopticVideo-300, and tailored fixation prediction model are all publicly available at https://github.com/360submit/WinDB.

Salient Object Detection via Dynamic Scale Routing

Recent research advances in salient object detection (SOD) could largely be attributed to ever-stronger multi-scale feature representation empowered by the deep learning technologies. The existing SOD deep models extract multi-scale features via the off-the-shelf encoders and combine them smartly via various delicate decoders. However, the kernel sizes in this commonly-used thread are usually "fixed". In our new experiments, we have observed that kernels of small size are preferable in scenarios containing tiny salient objects. In contrast, large kernel sizes could perform better for images with large salient objects. Inspired by this observation, we advocate the "dynamic" scale routing (as a brand-new idea) in this paper. It will result in a generic plug-in that could directly fit the existing feature backbone. This paper's key technical innovations are two-fold. First, instead of using the vanilla convolution with fixed kernel sizes for the encoder design, we propose the dynamic pyramid convolution (DPConv), which dynamically selects the best-suited kernel sizes w.r.t. the given input. Second, we provide a self-adaptive bidirectional decoder design to accommodate the DPConv-based encoder best. The most significant highlight is its capability of routing between feature scales and their dynamic collection, making the inference process scale-aware. As a result, this paper continues to enhance the current SOTA performance. Both the code and dataset are publicly available at https://github.com/wuzhenyubuaa/DPNet.

Shifting Trends of COVID-19 Tweet Sentiment with Respect to Voting Preferences in the 2020 Election Year of the United States

COVID-19 related policies were extensively politicized during the 2020 election year of the United States, resulting in polarizing viewpoints. Twitter users were particularly engaged during the 2020 election year. Here we investigated whether COVID-19 related tweets were associated with the overall election results at the state level during the period leading up to the election day. We observed weak correlations between the average sentiment of COVID-19 related tweets and popular votes in two-week intervals, and the trends gradually become opposite. We then compared the average sentiments of COVID-19 related tweets between states called in favor of Republican (red states) or Democratic parties (blue states). We found that at the beginning of lockdowns sentiments in the blue states were much more positive than those in the red states. However, sentiments in the red states gradually become more positive during the summer of 2020 and persisted until the election day.

Weakly Supervised Visual-Auditory Saliency Detection with Multigranularity Perception

Thanks to the rapid advances in deep learning techniques and the wide availability of large-scale training sets, the performance of video saliency detection models has been improving steadily and significantly. However, deep learning-based visualaudio fixation prediction is still in its infancy. At present, only a few visual-audio sequences have been furnished, with real fixations being recorded in real visual-audio environments. Hence, it would be neither efficient nor necessary to recollect real fixations under the same visual-audio circumstances. To address this problem, this paper promotes a novel approach in a weakly supervised manner to alleviate the demand of large-scale training sets for visual-audio model training. By using only the video category tags, we propose the selective class activation mapping (SCAM) and its upgrade (SCAM+). In the spatial-temporal-audio circumstance, the former follows a coarse-to-fine strategy to select the most discriminative regions, and these regions are usually capable of exhibiting high consistency with the real human-eye fixations. The latter equips the SCAM with an additional multi-granularity perception mechanism, making the whole process more consistent with that of the real human visual system. Moreover, we distill knowledge from these regions to obtain complete new spatial-temporal-audio (STA) fixation prediction (FP) networks, enabling broad applications in cases where video tags are not available. Without resorting to any real human-eye fixation, the performances of these STA FP networks are comparable to those of fully supervised networks. The code and results are publicly available at https://github.com/guotaowang/STANet.

Learning Continuous Face Representation with Explicit Functions

How to represent a face pattern? While it is presented in a continuous way in our visual system, computers often store and process the face image in a discrete manner with 2D arrays of pixels. In this study, we attempt to learn a continuous representation for face images with explicit functions. First, we propose an explicit model (EmFace) for human face representation in the form of a finite sum of mathematical terms, where each term is an analytic function element. Further, to estimate the unknown parameters of EmFace, a novel neural network, EmNet, is designed with an encoder-decoder structure and trained using the backpropagation algorithm, where the encoder is defined by a deep convolutional neural network and the decoder is an explicit mathematical expression of EmFace. Experimental results show that EmFace has a higher representation performance on faces with various expressions, postures, and other factors, compared to that of other methods. Furthermore, EmFace achieves reasonable performance on several face image processing tasks, including face image restoration, denoising, and transformation.

Rethinking of the Image Salient Object Detection: Object-level Semantic Saliency Re-ranking First, Pixel-wise Saliency Refinement Latter

The real human attention is an interactive activity between our visual system and our brain, using both low-level visual stimulus and high-level semantic information. Previous image salient object detection (SOD) works conduct their saliency predictions in a multi-task manner, i.e., performing pixel-wise saliency regression and segmentation-like saliency refinement at the same time, which degenerates their feature backbones in revealing semantic information. However, given an image, we tend to pay more attention to those regions which are semantically salient even in the case that these regions are perceptually not the most salient ones at first glance. In this paper, we divide the SOD problem into two sequential tasks: 1) we propose a lightweight, weakly supervised deep network to coarsely locate those semantically salient regions first; 2) then, as a post-processing procedure, we selectively fuse multiple off-the-shelf deep models on these semantically salient regions as the pixel-wise saliency refinement. In sharp contrast to the state-of-the-art (SOTA) methods that focus on learning pixel-wise saliency in "single image" using perceptual clues mainly, our method has investigated the "object-level semantic ranks between multiple images", of which the methodology is more consistent with the real human attention mechanism. Our method is simple yet effective, which is the first attempt to consider the salient object detection mainly as an object-level semantic re-ranking problem.

Knowing Depth Quality In Advance: A Depth Quality Assessment Method For RGB-D Salient Object Detection

Previous RGB-D salient object detection (SOD) methods have widely adopted deep learning tools to automatically strike a trade-off between RGB and D (depth), whose key rationale is to take full advantage of their complementary nature, aiming for a much-improved SOD performance than that of using either of them solely. However, such fully automatic fusions may not always be helpful for the SOD task because the D quality itself usually varies from scene to scene. It may easily lead to a suboptimal fusion result if the D quality is not considered beforehand. Moreover, as an objective factor, the D quality has long been overlooked by previous work. As a result, it is becoming a clear performance bottleneck. Thus, we propose a simple yet effective scheme to measure D quality in advance, the key idea of which is to devise a series of features in accordance with the common attributes of high-quality D regions. To be more concrete, we conduct D quality assessments for each image region, following a multi-scale methodology that includes low-level edge consistency, mid-level regional uncertainty and high-level model variance. All these components will be computed independently and then be assembled with RGB and D features, applied as implicit indicators, to guide the selective fusion. Compared with the state-of-the-art fusion schemes, our method can achieve a more reasonable fusion status between RGB and D. Specifically, the proposed D quality measurement method achieves steady performance improvements for almost 2.0\% in general.