Dynamics of many complex systems, from weather and climate to spread of infectious diseases, can be described by partial differential equations (PDEs). Such PDEs involve unknown function(s), partial derivatives, and typically multiple independent variables. The traditional numerical methods for solving PDEs assume that the data are observed on a regular grid. However, in many applications, for example, weather and air pollution monitoring delivered by the arbitrary located weather stations of the National Weather Services, data records are irregularly spaced. Furthermore, in problems involving prediction analytics such as forecasting wildfire smoke plumes, the primary focus may be on a set of irregular locations associated with urban development. In recent years, deep learning (DL) methods and, in particular, graph neural networks (GNNs) have emerged as a new promising tool that can complement traditional PDE solvers in scenarios of the irregular spaced data, contributing to the newest research trend of physics informed machine learning (PIML). However, most existing PIML methods tend to be limited in their ability to describe higher dimensional structural properties exhibited by real world phenomena, especially, ones that live on manifolds. To address this fundamental challenge, we bring the elements of the Hodge theory and, in particular, simplicial convolution defined on the Hodge Laplacian to the emerging nexus of DL and PDEs. In contrast to conventional Laplacian and the associated convolution operation, the simplicial convolution allows us to rigorously describe diffusion across higher order structures and to better approximate the complex underlying topology and geometry of the data. The new approach, Simplicial Neural Networks for Partial Differential Equations (SNN PDE) offers a computationally efficient yet effective solution for time dependent PDEs. Our studies of a broad range of synthetic data and wildfire processes demonstrate that SNN PDE improves upon state of the art baselines in handling unstructured grids and irregular time intervals of complex physical systems and offers competitive forecasting capabilities for weather and air quality forecasting.
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Dynamical systems are abstract models of interaction between space and time. They are often used in fields such as physics and engineering to understand complex processes, but due to their general nature, they have found applications for studying computational processes, interaction in multi-agent systems, machine learning algorithms and other computer science related phenomena. In the vast majority of applications, a dynamical system consists of the action of a continuous `transition function' on a metric space. In this work, we consider decidable formal systems for reasoning about such structures. Spatial logics can be traced back to the 1940's, but our work follows a more dynamic turn that these logics have taken due to two recent developments: the study of the topological mu-calculus, and the the integration of linear temporal logic with logics based on the Cantor derivative. In this paper, we combine dynamic topological logics based on the Cantor derivative and the `next point in time' operators with an expressively complete fixed point operator to produce a combination of the topological mu-calculus with linear temporal logic. We show that the resulting logics are decidable and have a natural axiomatisation. Moreover, we prove that these logics are complete for interpretations on the Cantor space, the rational numbers, and subspaces thereof.
Many significant problems involving crystal property prediction from 3D structures have limited labeled data due to expensive and time-consuming physical simulations or lab experiments. To overcome this challenge, we propose a pretrain-finetune framework for the crystal property prediction task named CrysDiff based on diffusion models. In the pre-training phase, CrysDiff learns the latent marginal distribution of crystal structures via the reconstruction task. Subsequently, CrysDiff can be fine-tuned under the guidance of the new sparse labeled data, fitting the conditional distribution of the target property given the crystal structures. To better model the crystal geometry, CrysDiff notably captures the full symmetric properties of the crystals, including the invariance of reflection, rotation, and periodic translation. Extensive experiments demonstrate that CrysDiff can significantly improve the performance of the downstream crystal property prediction task on multiple target properties, outperforming all the SOTA pre-training models for crystals with good margins on the popular JARVIS-DFT dataset.
Modeling continuous-time dynamics constitutes a foundational challenge, and uncovering inter-component correlations within complex systems holds promise for enhancing the efficacy of dynamic modeling. The prevailing approach of integrating graph neural networks with ordinary differential equations has demonstrated promising performance. However, they disregard the crucial signed information potential on graphs, impeding their capacity to accurately capture real-world phenomena and leading to subpar outcomes. In response, we introduce a novel approach: a signed graph neural ordinary differential equation, adeptly addressing the limitations of miscapturing signed information. Our proposed solution boasts both flexibility and efficiency. To substantiate its effectiveness, we seamlessly integrate our devised strategies into three preeminent graph-based dynamic modeling frameworks: graph neural ordinary differential equations, graph neural controlled differential equations, and graph recurrent neural networks. Rigorous assessments encompass three intricate dynamic scenarios from physics and biology, as well as scrutiny across four authentic real-world traffic datasets. Remarkably outperforming the trio of baselines, empirical results underscore the substantial performance enhancements facilitated by our proposed approach. Our code can be found at https://github.com/beautyonce/SGODE.
Recent advances in implicit neural representation have demonstrated the ability to recover detailed geometry and material from multi-view images. However, the use of simplified lighting models such as environment maps to represent non-distant illumination, or using a network to fit indirect light modeling without a solid basis, can lead to an undesirable decomposition between lighting and material. To address this, we propose a fully differentiable framework named Neural Illumination Fields (NeIF) that uses radiance fields as a lighting model to handle complex lighting in a physically based way. Together with integral lobe encoding for roughness-adaptive specular lobe and leveraging the pre-convolved background for accurate decomposition, the proposed method represents a significant step towards integrating physically based rendering into the NeRF representation. The experiments demonstrate the superior performance of novel-view rendering compared to previous works, and the capability to re-render objects under arbitrary NeRF-style environments opens up exciting possibilities for bridging the gap between virtual and real-world scenes.
In the field of autonomous driving, accurate and comprehensive perception of the 3D environment is crucial. Bird's Eye View (BEV) based methods have emerged as a promising solution for 3D object detection using multi-view images as input. However, existing 3D object detection methods often ignore the physical context in the environment, such as sidewalk and vegetation, resulting in sub-optimal performance. In this paper, we propose a novel approach called SOGDet (Semantic-Occupancy Guided Multi-view 3D Object Detection), that leverages a 3D semantic-occupancy branch to improve the accuracy of 3D object detection. In particular, the physical context modeled by semantic occupancy helps the detector to perceive the scenes in a more holistic view. Our SOGDet is flexible to use and can be seamlessly integrated with most existing BEV-based methods. To evaluate its effectiveness, we apply this approach to several state-of-the-art baselines and conduct extensive experiments on the exclusive nuScenes dataset. Our results show that SOGDet consistently enhance the performance of three baseline methods in terms of nuScenes Detection Score (NDS) and mean Average Precision (mAP). This indicates that the combination of 3D object detection and 3D semantic occupancy leads to a more comprehensive perception of the 3D environment, thereby aiding build more robust autonomous driving systems. The codes are available at: https://github.com/zhouqiu/SOGDet.
Bio-inspired spike camera mimics the sampling principle of primate fovea. It presents high temporal resolution and dynamic range, showing great promise in fast-moving object recognition. However, the physical limit of CMOS technology in spike cameras still hinders their capability of recognizing ultra-high-speed moving objects, e.g., extremely fast motions cause blur during the imaging process of spike cameras. This paper presents the first theoretical analysis for the causes of spiking motion blur and proposes a robust representation that addresses this issue through temporal-spatial context learning. The proposed method leverages multi-span feature aggregation to capture temporal cues and employs residual deformable convolution to model spatial correlation among neighbouring pixels. Additionally, this paper contributes an original real-captured spiking recognition dataset consisting of 12,000 ultra-high-speed (equivalent speed > 500 km/h) moving objects. Experimental results show that the proposed method achieves 73.2% accuracy in recognizing 10 classes of ultra-high-speed moving objects, outperforming all existing spike-based recognition methods. Resources will be available at https://github.com/Evin-X/UHSR.
Neighborhood-Enhanced 3D Human Pose Estimation with Monocular LiDAR in Long-Range Outdoor Scenes
PDF ↗3D human pose estimation (3HPE) in large-scale outdoor scenes using commercial LiDAR has attracted significant attention due to its potential for real-life applications. However, existing LiDAR-based methods for 3HPE primarily rely on recovering 3D human poses from individual point clouds, and the coherence cues present in the neighborhood are not sufficiently harnessed. In this work, we explore spatial and contexture coherence cues contained in the neighborhood that lead to great performance improvements in 3HPE. Specifically, firstly, we deeply investigate the 3D neighbor in the background (3BN) which serves as a spatial coherence cue for inferring reliable motion since it provides physical laws to limit motion targets. Secondly, we introduce a novel 3D scanning neighbor (3SN) generated during the data collection and 3SN implies structural edge coherence cues. We use 3SN to overcome the degradation of performance and data quality caused by the sparsity-varying properties of LiDAR point clouds. In order to effectively model the complementation between these distinct cues and build consistent temporal relationships across human motions, we propose a new transformer-based module called the CoherenceFuse module. Extensive experiments were conducted on publicly available datasets, namely LidarHuman26M, CIMI4D, SLOPER4D and Waymo Open Dataset v2.0, showcase the superiority and effectiveness of our proposed method. In particular, when compared with LidarCap on the LidarHuman26M dataset, our method demonstrates a reduction of 7.08mm in the average MPJPE metric, along with a decrease of 16.55mm in the MPJPE metric for distances exceeding 25 meters. The code and models are available at https://github.com/jingyi-zhang/Neighborhood-enhanced-LidarCap.
Generating high-quality, realistic rendering images for real-time applications generally requires tracing a few samples-per-pixel (spp) and using deep learning-based approaches to denoise the resulting low-spp images. Existing denoising methods necessitate a substantial time expenditure when rendering at high resolutions due to the physically-based sampling and network inference time burdens. In this paper, we propose a novel Monte Carlo sampling strategy to accelerate the sampling process and a corresponding denoiser, subpixel sampling reconstruction (SSR), to obtain high-quality images. Extensive experiments demonstrate that our method significantly outperforms previous approaches in denoising quality and reduces overall time costs, enabling real-time rendering capabilities at 2K resolution.
Moiré patterns occur when capturing images or videos on screens, severely degrading the quality of the captured images or videos. Despite the recent progresses, existing video demoiréing methods neglect the physical characteristics and formation process of moiré patterns, significantly limiting the effectiveness of video recovery. This paper presents a unified framework, DTNet, a direction-aware and temporal-guided bilateral learning network for video demoiréing. DTNet effectively incorporates the process of moiré pattern removal, alignment, color correction, and detail refinement. Our proposed DTNet comprises two primary stages: Frame-level Direction-aware Demoiréing and Alignment (FDDA) and Tone and Detail Refinement (TDR). In FDDA, we employ multiple directional DCT modes to perform the moiré pattern removal process in the frequency domain, effectively detecting the prominent moiré edges. Then, the coarse and fine-grained alignment is applied on the demoiréd features for facilitating the utilization of neighboring information. In TDR, we propose a temporal-guided bilateral learning pipeline to mitigate the degradation of color and details caused by the moiré patterns while preserving the restored frequency information in FDDA. Guided by the aligned temporal features from FDDA, the affine transformations for the recovery of the ultimate clean frames are learned in TDR. Extensive experiments demonstrate that our video demoiréing method outperforms state-of-the-art approaches by 2.3 dB in PSNR, and also delivers a superior visual experience.
Existing deep pan-sharpening methods lack the learning of complementary information between PAN and MS modalities in the intermediate layers, and exhibit low interpretability due to their black-box designs. To this end, an interpretable deep unfolded network with intrinsic supervision for pan-sharpening is proposed. Building upon the observation degradation process, it formulates the pan-sharpening task as a variational model minimization with spatial consistency prior and spectral projection prior. The former prior requires a joint component decomposition of PAN and MS images to extract intrinsic features. By being supervised in the intermediate layers, it can selectively provide high-frequency information for spatial enhancement. The latter prior constrains the intensity correlation between MS and PAN images derived from physical observations, so as to improve spectral fidelity. To further enhance the transparency of network design, we develop an iterative solution algorithm following the half-quadratic splitting to unfold the deep model. It rigorously adheres to the variational model, significantly enhancing the interpretability behind network design and efficiently alternating the optimization of the network. Extensive experiments demonstrate the advantages of our method compared to state-of-the-arts, showcasing its remarkable generalization capability to real-world scenes. Our code is publicly available at https://github.com/Baixuzx7/DISPNet.
We explore the generalization of the implicit representation in the physical simulation task. Traditional time-dependent partial differential equations (PDEs) solvers for physical simulation often adopt the grid or mesh for spatial discretization, which is memory-consuming for high resolution and lack of adaptivity. Many implicit representations like local extreme machine or Siren are proposed but they are still too compact to suffer from limited accuracy in handling local details and a long time of convergence. We contribute a neural simulation framework based on multi-resolution hash grid representation to introduce hierarchical consideration of global and local information, simultaneously. Furthermore, we propose two key strategies: 1) a numerical gradient method for computing high-order derivatives with boundary conditions; 2) a range analysis sample method for fast neural geometry boundary sampling with dynamic topologies. Our method shows much higher accuracy and strong flexibility for various simulation problems: e.g., large elastic deformations, complex fluid dynamics, and multi-scale phenomena which remain challenging for existing neural physical solvers.
Devignet: High-Resolution Vignetting Removal via a Dual Aggregated Fusion Transformer with Adaptive Channel Expansion
PDF ↗Vignetting commonly occurs as a degradation in images resulting from factors such as lens design, improper lens hood usage, and limitations in camera sensors. This degradation affects image details, color accuracy, and presents challenges in computational photography. Existing vignetting removal algorithms predominantly rely on ideal physics assumptions and hand-crafted parameters, resulting in the ineffective removal of irregular vignetting and suboptimal results. Moreover, the substantial lack of real-world vignetting datasets hinders the objective and comprehensive evaluation of vignetting removal. To address these challenges, we present VigSet, a pioneering dataset for vignetting removal. VigSet includes 983 pairs of both vignetting and vignetting-free high-resolution (over 4k) real-world images under various conditions. In addition, We introduce DeVigNet, a novel frequency-aware Transformer architecture designed for vignetting removal. Through the Laplacian Pyramid decomposition, we propose the Dual Aggregated Fusion Transformer to handle global features and remove vignetting in the low-frequency domain. Additionally, we propose the Adaptive Channel Expansion Module to enhance details in the high-frequency domain. The experiments demonstrate that the proposed model outperforms existing state-of-the-art methods. The code, models, and dataset are available at https://github.com/CXH-Research/DeVigNet.
Reconstructing a dynamic human with loose clothing is an important but difficult task. To address this challenge, we propose a method named DLCA-Recon to create human avatars from monocular videos. The distance from loose clothing to the underlying body rapidly changes in every frame when the human freely moves and acts. Previous methods lack effective geometric initialization and constraints for guiding the optimization of deformation to explain this dramatic change, resulting in the discontinuous and incomplete reconstruction surface.To model the deformation more accurately, we propose to initialize an estimated 3D clothed human in the canonical space, as it is easier for deformation fields to learn from the clothed human than from SMPL.With both representations of explicit mesh and implicit SDF, we utilize the physical connection information between consecutive frames and propose a dynamic deformation field (DDF) to optimize deformation fields. DDF accounts for contributive forces on loose clothing to enhance the interpretability of deformations and effectively capture the free movement of loose clothing. Moreover, we propagate SMPL skinning weights to each individual and refine pose and skinning weights during the optimization to improve skinning transformation. Based on more reasonable initialization and DDF, we can simulate real-world physics more accurately. Extensive experiments on public and our own datasets validate that our method can produce superior results for humans with loose clothing compared to the SOTA methods.
Focus stacking is a technique in computational photography, and it synthesizes a single all-in-focus image from different focal plane images. It is difficult for previous works to produce a high-quality all-in-focus image that meets two goals: high-fidelity to its source images and good visual effects without defects or abnormalities. This paper proposes a novel method based on optical imaging process analysis and modeling. Based on a foreground segmentation - diffusion elimination architecture, the foreground segmentation makes most of the areas in full-focus images heritage information from the source images to achieve high fidelity; diffusion elimination models the physical imaging process and is specially used to solve the transition region (TR) problem that is a long-term neglected issue and degrades visual effects of synthesized images. Based on extensive experiments on simulated dataset, existing realistic dataset and our proposed BetaFusion dataset, the results show that our proposed method can generate high-quality all-in-focus images by achieving two goals simultaneously, especially can successfully solve the TR problem and eliminate the visual effect degradation of synthesized images caused by the TR problem.
Recent years have witnessed the substantial progress of large-scale models across various domains, such as natural language processing and computer vision, facilitating the expression of concrete concepts. Unlike concrete concepts that are usually directly associated with physical objects, expressing abstract concepts through natural language requires considerable effort since they are characterized by intricate semantics and connotations. An alternative approach is to leverage images to convey rich visual information as a supplement. Nevertheless, existing Text-to-Image (T2I) models are primarily trained on concrete physical objects and often struggle to visualize abstract concepts. Inspired by the three-layer artwork theory that identifies critical factors, intent, object and form during artistic creation, we propose a framework of Text-to-Image generation for Abstract Concepts (TIAC). The abstract concept is clarified into a clear intent with a detailed definition to avoid ambiguity. LLMs then transform it into semantic-related physical objects, and the concept-dependent form is retrieved from an LLM-extracted form pattern set. Information from these three aspects will be integrated to generate prompts for T2I models via LLM. Evaluation results from human assessments and our newly designed metric concept score demonstrate the effectiveness of our framework in creating images that can sufficiently express abstract concepts.
Existing causal representation learning methods are based on the causal graph they build. However, due to the omission of bias within the causal graph, they essentially encourage models to learn biased causal effects in latent space. In this paper, we propose a novel causally disentangling framework that aims to learn unbiased causal effects. We first introduce inductive and dataset biases into traditional causal graph for the physical concepts of interest. Then, we eliminate the negative effects from these two biases by counterfactual intervention with reweighted loss function for learning unbiased causal effects. Finally, we employ the causal effects into the VAE to endow the latent representations with causality. In particular, we highlight that removing biases in this paper is regarded as a part of learning process for unbiased causal effects, which is crucial for causal disentanglement performance improvement. Through extensive experiments on real-world and synthetic datasets, we show that our method outperforms different baselines and obtains the state-of-the-art results for achieving causal representation learning.
In this paper, we propose SpectralNeRF, an end-to-end Neural Radiance Field (NeRF)-based architecture for high-quality physically based rendering from a novel spectral perspective. We modify the classical spectral rendering into two main steps, 1) the generation of a series of spectrum maps spanning different wavelengths, 2) the combination of these spectrum maps for the RGB output. Our SpectralNeRF follows these two steps through the proposed multi-layer perceptron (MLP)-based architecture (SpectralMLP) and Spectrum Attention UNet (SAUNet). Given the ray origin and the ray direction, the SpectralMLP constructs the spectral radiance field to obtain spectrum maps of novel views, which are then sent to the SAUNet to produce RGB images of white-light illumination. Applying NeRF to build up the spectral rendering is a more physically-based way from the perspective of ray-tracing. Further, the spectral radiance fields decompose difficult scenes and improve the performance of NeRF-based methods. Comprehensive experimental results demonstrate the proposed SpectralNeRF is superior to recent NeRF-based methods when synthesizing new views on synthetic and real datasets. The codes and datasets are available at https://github.com/liru0126/SpectralNeRF.
Our work aims to reconstruct a 3D object that is held and rotated by a hand in front of a static RGB camera. Previous methods that use implicit neural representations to recover the geometry of a generic hand-held object from multi-view images achieved compelling results in the visible part of the object. However, these methods falter in accurately capturing the shape within the hand-object contact region due to occlusion. In this paper, we propose a novel method that deals with surface reconstruction under occlusion by incorporating priors of 2D occlusion elucidation and physical contact constraints. For the former, we introduce an object amodal completion network to infer the 2D complete mask of objects under occlusion. To ensure the accuracy and view consistency of the predicted 2D amodal masks, we devise a joint optimization method for both amodal mask refinement and 3D reconstruction. For the latter, we impose penetration and attraction constraints on the local geometry in contact regions. We evaluate our approach on HO3D and HOD datasets and demonstrate that it outperforms the state-of-the-art methods in terms of reconstruction surface quality, with an improvement of 52% on HO3D and 20% on HOD. Project webpage: https://east-j.github.io/ihor.
Among various interactions between humans, such as eye contact and gestures, physical interactions by contact can act as an essential moment in understanding human behaviors. Inspired by this fact, given a 3D partner human with the desired interaction label, we introduce a new task of 3D human generation in terms of physical contact. Unlike previous works of interacting with static objects or scenes, a given partner human can have diverse poses and different contact regions according to the type of interaction. To handle this challenge, we propose a novel method of generating interactive 3D humans for a given partner human based on a guided diffusion framework (ContactGen in short). Specifically, we newly present a contact prediction module that adaptively estimates potential contact regions between two input humans according to the interaction label. Using the estimated potential contact regions as complementary guidances, we dynamically enforce ContactGen to generate interactive 3D humans for a given partner human within a guided diffusion model. We demonstrate ContactGen on the CHI3D dataset, where our method generates physically plausible and diverse poses compared to comparison methods.