This is a corrigendum for the article “Wavelet Fluids” published in ACM Trans. Graph. 44, 6, Article 270 (December 2025), 17 pages.

Electroencephalogram (EEG)-based motor imagery (MI) signals are frequently used in brain-computer interfaces (BCIs) due to their wide applications in the rehabilitation field. However, cross-subject variations often result in a model trained on one participant failing when applied to another. Additionally, privacy concerns regarding sensitive health and mental information in EEG-based MI signals further complicate the situation. Source-free domain adaptation aims to address these cross-subject variations by transferring knowledge from a source domain (i.e., a previous participant) to a target domain (i.e., a new participant) without accessing sensitive source data. However, source-free unsupervised domain adaptation models often face issues with incorrect pseudo-labels, which can lead to unstable and ineffective adaptation. To address this, we propose a source-free semi-supervised domain adaptation algorithm for EEG-based MI signal classification. This algorithm tackles noise accumulation caused by incorrect pseudo-labels while effectively handling data distribution variations and privacy concerns, similar to source-free unsupervised domain adaptation models. Specifically, we train the classifier head using only a limited amount of labeled target data to prevent noise accumulation, and generate pseudo-labels for the unlabeled target data. Furthermore, we introduce an independent self-training head that learns better representations using the generated pseudo-labels, mitigating overfitting caused by the limited labeled target data. Additionally, we design an adversarial head that plays a minimax game to extract more discriminative feature representations from the unlabeled target data. Extensive experiments on three benchmark datasets, compared with eighteen state-of-the-art SFDA methods, demonstrate the superiority of our approach.

Rotation invariance is a crucial requirement for the analysis of 3D point clouds. However, current methods often achieve rotation invariance by employing specific network designs. These networks, though perform well on rotation-aware tasks, is inferior in general tasks such as classification and segmentation. On the other hand, many powerful point processing networks, such as PointNet++, DGCNN, etc., have general point processing abilities, but do not own the property of rotation invariance. In this paper, we propose a standalone rotation-invariant convolution operator called SGGConv (Spherical Geometric Graph-based Convolution) and two ways integrating it with common point-based networks. The networks equipped with SGGConvs are called SGG-Nets which promote the rotation-invariance ability of regular point networks without modifying their network architectures much. Our contributions are three-fold. First, we propose a rotation-invariant feature descriptor, namely Spherical Geometry Descriptor (SGD), which captures point-pair features in a Local Spherical Coordinate System (LSCS). Second, we propose the SGGConv based on SGD and LSCS with an efficient Graph-based Spherical Feature Passing (GSFP) mechanism. Thirdly, we define two modules S-SGGConvMdl and M-SGGConvMdl, which are used to integrate SGGConv into baseline point nets. We test SGG-Nets, such as SGG-PointNet++, SGG-DGCNN, SGG-RIConv++, on representative point cloud datasets. These models, equipped with our SGGConvs, not only enhance the rotation-invariance of the baseline network but also improve its performance on point cloud analysis tasks such as classification and part segmentation, without incurring too much computational overhead.

In today's era of information overload, leveraging data mining techniques to understand and analyze customer behavior has become essential for businesses. Among these techniques, the recency, frequency, and monetary value analysis model serves as a powerful tool for customer segmentation, enabling companies to identify high-value customers. However, traditional recency, frequency, and monetary (RFM) models do not focus on user-specific targets, often struggling to meet the increasing demands for personalization and efficiency. To address this challenge, this article introduces the concept of target RFM patterns, which must satisfy the three dimensions of recency, frequency, and utility while aligning with user interests. Based on this concept, we formulate the problem of mining target RFM patterns. More importantly, we define a mining order, called TaRFM order, and propose an efficient algorithm called TaRFM. This new algorithm is optimized through three pruning strategies based on the TaRFM order, which not only eliminates a significant number of invalid operations, thereby reducing pattern generation, but also accurately extracts all TaRFM patterns without requiring postprocessing techniques. Finally, extensive experiments conducted on multiple datasets demonstrate the accuracy and efficiency of the TaRFM algorithm.

This paper introduces a novel wavelet-based framework for simulating both single-phase (e.g., smoke) and two-phase (e.g., bubbly water) flows, featuring unified boundary condition handling for free surfaces and solid obstacles. In liquid simulations, conventional pressure projection methods enforce zero-pressure Dirichlet conditions at free surfaces by solving a simplified pressure Poisson equation. However, these approaches neglect air-phase incompressibility, leading to artificial bubble collapse. Stream function methods overcome this limitation by solving a density-variable vector potential Poisson equation, ensuring incompressibility in both simulated and unsimulated regions while maintaining divergence-free liquid phases independent of solver accuracy. Yet, they triple the linear system's dimensionality and exhibit poor convergence near solid boundaries. The fundamental limitation of both methods stems from their governing equations: singularities emerge as density approaches extreme values. The pressure Poisson equation becomes ill-conditioned when density nears zero (air phase), compromising air-phase incompressibility, while the vector potential equation degrades as density approaches infinity (solid phase), impeding solid-boundary convergence. To address these singularities, we first propose a novel decomposition where zero and infinite densities are well-defined. We then reformulate this decomposition as a fixed-point iteration using density-agnostic curl-free and divergence-free projections, eliminating the need for linear system solves. The error equation is derived, and a necessary and sufficient convergence condition is established. Building on this, we develop an iterative algorithm that efficiently solves the fixed-point problem through alternating wavelet-based non-orthogonal curl-free and divergence-free projections. Additionally, we investigate orthogonal curl-free projections (e.g., Fourier methods) and their complementary divergence-free counterparts, providing a comprehensive comparison between wavelet and Fourier approaches. Our method simultaneously computes pressure and stream functions, retaining the incompressibility benefits of stream function approaches while resolving their computational inefficiencies and solid-boundary convergence issues. Experiments demonstrate our framework's ability to efficiently simulate complex two-phase phenomena, such as the glugging effect during water pouring and multi-liquid-region interactions across zero-density air.

Human Mesh Recovery (HMR) is the task of estimating a parameterized 3D human mesh from an image. There is a kind of methods first training a regression model for this problem, then further optimizing the pretrained regression model for any specific sample individually at test time. However, the pretrained model may not provide an ideal optimization starting point for the test-time optimization. Inspired by meta-learning, we incorporate the test-time optimization into training, performing a step of test-time optimization for each sample in the training batch before really conducting the training optimization over all the training samples. In this way, we obtain a meta-model, the meta-parameter of which is friendly to the test-time optimization. At test time, after several test-time optimization steps starting from the meta-parameter, we obtain much higher HMR accuracy than the test-time optimization starting from the simply pretrained regression model. Furthermore, we find test-time HMR objectives are different from training-time objectives, which reduces the effectiveness of the learning of the meta-model. To solve this problem, we propose a dual-network architecture that unifies the training-time and test-time objectives. Our method, armed with meta-learning and the dual networks, outperforms state-of-the-art regression-based and optimization-based HMR approaches, as validated by the extensive experiments. The codes are available at https://github.com/fmx789/Meta-HMR.

Abstract We introduce an efficient technique for recovering the vector potential in wavelet space to simulate pointwise incompressible fluids. This technique ensures that fluid velocities remain divergence‐free at any point within the fluid domain and preserves local volume during the simulation. Divergence‐free wavelets are utilized to calculate the wavelet coefficients of the vector potential, resulting in a smooth vector potential with enhanced accuracy, even when the input velocities exhibit some degree of divergence. This enhanced accuracy eliminates the need for additional computational time to achieve a specific accuracy threshold, as fewer iterations are required for the pressure Poisson solver. Additionally, in 3D, since the wavelet transform is taken in‐place, only the memory for storing the vector potential is required. These two features make the method remarkably efficient for recovering vector potential for fluid simulation. Furthermore, the method can handle various boundary conditions during the wavelet transform, making it adaptable for simulating fluids with Neumann and Dirichlet boundary conditions. Our approach is highly parallelizable and features a time complexity of O(n), allowing for seamless deployment on GPUs and yielding remarkable computational efficiency. Experiments demonstrate that, taking into account the time consumed by the pressure Poisson solver, the method achieves an approximate 2x speedup on GPUs compared to state‐of‐the‐art vector potential recovery techniques while maintaining a precision level of 10−6 when single float precision is employed. The source code of ‘Wavelet Potentials’ can be found in https://github.com/yours321dog/WaveletPotentials .

This paper addresses the problem of animating a person in static images, the core task of which is to infer future poses for the person. Existing approaches predict future poses in the 2D space, suffering from entanglement of pose action and shape. We propose a method that generates actions in the 3D space and then transfers them to the 2D person. We first lift the 2D pose of the person to a 3D skeleton, then propose a 3D action synthesis network predicting future skeletons, and finally devise a self-supervised action transfer network that transfers the actions of 3D skeletons to the 2D person. Actions generated in the 3D space look plausible and vivid. More importantly, self-supervised action transfer allows our method to be trained only on a 3D MoCap dataset while being able to process images in different domains. Experiments on three image datasets validate the effectiveness of our method.

Recently, Point-MAE has extended Masked Autoencoders (MAE) to point clouds for 3D self-supervised learning, which however faces two problems: (1) the shape similarity between the masked point cloud and original point cloud is high, and (2) the pretext task of reconstructing the original point cloud is straightforward which fails to compel the network to learn deep representative features. In this paper, we tackle these problems by proposing a PatchMixing strategy and a teacher-student training framework. First, with PatchMixing, we mix selected point patches of multiple point clouds and attempt to infer the object information from the resulting mixed point cloud. Due to the interference of other objects, the task is challenging but facilitates representation learning. Second, rather than directly restoring the original point cloud, we propose a novel pretext task that involves a two-branch teacher model and a student model. These models process the multiple input point clouds in different ways (no mixing, mixing + unmixing, mixing + masking), but are expected to output similar features, thereby compelling the network to extract essential features from the input. Extensive experiments show that our well-designed PatchMixing strategy and effective teacher-student learning architecture yield impressive results. Specifically, our model achieves a remarkable 92.9% classification accuracy in the Linear SVM task on the ModelNet40 dataset. Through pre-training and fine-tuning on downstream tasks, our method achieves an 89.8% classification accuracy on the most challenging split of ScanObjectNN and an outstanding 94.0% on ModelNet40.

Recently, the Deep Neural Networks (DNNs) have had a large impact on imaging process including medical image segmentation, and the real-valued convolution of DNN has been extensively utilized in multi-modal medical image segmentation to accurately segment lesions via learning data information. However, the weighted summation operation in such convolution limits the ability to maintain spatial dependence that is crucial for identifying different lesion distributions. In this paper, we propose a novel Quaternion Cross-modality Spatial Learning (Q-CSL) which explores the spatial information while considering the linkage between multi-modal images. Specifically, we introduce to quaternion to represent data and coordinates that contain spatial information. Additionally, we propose Quaternion Spatial-association Convolution to learn the spatial information. Subsequently, the proposed De-level Quaternion Cross-modality Fusion (De-QCF) module excavates inner space features and fuses cross-modality spatial dependency. Our experimental results demonstrate that our approach compared to the competitive methods perform well with only 0.01061 M parameters and 9.95G FLOPs.

Making available a large size of training data for deep learning models and preserving data privacy are two ever-growing concerns in the machine learning community.Multi-source domain adaptation(MDA) leverages the data information from different domains and aggregates them to improve the performance in the target task, while the privacy leakage risk of publishing models under malicious attacker for membership or attribute inference is even more complicated than the one faced by single-source domain adaptation. In this paper, we tackle the problem of effectively protecting data privacy while training and aggregating multi-source information, where each source domain enjoys an independent privacy budget. Specifically, we develop adifferentially private MDA(DPMDA) algorithm to provide domain-wise privacy protection with adaptive weighting scheme based on task similarity and task-specific privacy budget. We evaluate our algorithm on three benchmark tasks and show that DPMDA can effectively leverage different private budgets from source domains and consistently outperforms the existing private baselines with a reasonable gap with non-private state-of-the-art.

Deep learning approaches for multi-label Chest X-ray (CXR) images classification usually require large-scale datasets. However, acquiring such datasets with full annotations is costly, time-consuming, and prone to noisy labels. Therefore, we introduce a weakly supervised learning problem called Single Positive Multi-label Learning (SPML) into CXR images classification (abbreviated as SPML-CXR), in which only one positive label is annotated per image. A simple solution to SPML-CXR problem is to assume that all the unannotated pathological labels are negative, however, it might introduce false negative labels and decrease the model performance. To this end, we present a Multi-level Pseudo-label Consistency (MPC) framework for SPML-CXR. First, inspired by the pseudo-labeling and consistency regularization in semi-supervised learning, we construct a weak-to-strong consistency framework, where the model prediction on weakly-augmented image is treated as the pseudo label for supervising the model prediction on a strongly-augmented version of the same image, and define an Image-level Perturbation-based Consistency (IPC) regularization to recover the potential mislabeled positive labels. Besides, we incorporate Random Elastic Deformation (RED) as an additional strong augmentation to enhance the perturbation. Second, aiming to expand the perturbation space, we design a perturbation stream to the consistency framework at the feature-level and introduce a Feature-level Perturbation-based Consistency (FPC) regularization as a supplement. Third, we design a Transformer-based encoder module to explore the sample relationship within each mini-batch by a Batch-level Transformer-based Correlation (BTC) regularization. Extensive experiments on the CheXpert and MIMIC-CXR datasets have shown the effectiveness of our MPC framework for solving the SPML-CXR problem.

Despite the significant progress in unsupervised domain adaptation (UDA), the performance of UDA methods is still far inferior to that of the fully supervised ones. In practical scenarios, it is usually feasible to acquire labels on a small portion of the target data through active learning (AL), which aims to train an effective model with as few queried instances as possible. However, due to the domain shift, the instances selected by existing AL algorithms can be uninformative, redundant, or outlying. To address this issue, we propose a novel approach, namely, clustering environment-aware learning (CEAL), for active domain adaptation (ADA). CEAL selects potentially the most valuable instances under domain shift by exploring the informativeness and representativeness of target samples in a clustering environment-aware manner. Specifically, for the informativeness, we not only leverage the knowledge of individual points but also their nearby neighbors, by measuring the proposed clustering environment aware informativeness score (CEAIS), thus ensuring that the selected samples are highly informative. For the representativeness, we design two schemes called point distance release (PDR) and informativeness score difference exclusion (ISDE) to guarantee the diversity and validity of the selected samples. Furthermore, we fully utilize the large amount of unlabeled data from target domain via pseudo labeling and adopt information maximization to improve the reliability of the target pseudo labels, thereby further improving the performance of the model. The effectiveness of our method is empirically verified on various benchmark datasets against recent state-of-the-art algorithms.

Video super-resolution (VSR) is a fundamental and challenging task in computer vision. Many of the existing VSR works focus on how to effectively align neighboring frames to better incorporate temporal information, while little work is devoted to the important subsequent step of inter-frame information fusion, and the existing methods on frame fusion have shortcomings such as not being able to make full use of spatio-temporal information. In this work, we propose a Frame-by-frame Feedback Fusion Network (FFFN) for VSR tasks. By applying the feedback learning mechanism commonly existing in the human cognitive system to the frame fusion stage, FFFN can refine low-level representation of the fused frames with high-level information in a coarse-to-fine manner. Specifically, after the neighboring frames are aligned, we first rearrange them from near to far according to the distance from the reference frame in the temporal space, and then feed them one-by-one into a proposed recurrent structure called Feedback Fusion Module (FFM), which is then able to iteratively generate high-level representation of the fused frames with several Feature Refinement Groups (FRGs) and feedback connections. Finally, we design a Dual-path Residual Reconstruction Module (DRRM) to reconstruct the final high-resolution image. The proposed FFFN comes with a strong frame fusion and reconstruction ability, and extensive experiments on several benchmark data sets show that it achieves favorable performance against state-of-the-art methods.

Palmprint recognition provides a potential solution for noninvasive personal authentication due to its excellent contactless property and user-security, and it has attracted tremendous research interest in recent years. However, most existing methods focus on intraspectral palmprint recognition, which requires gallery and probe images to be captured under similar illumination, and thus significantly limit its practical applications in open environments with variant illuminations. In this study, we present a spectrum-invariant feature learning method for cross-spectral palmprint recognition to address the problem that gallery and probe samples are captured under different spectra. First, the blockwise direction-based ordinal measure vectors are formed to represent the intrinsic information of palmprint images. Then, a unified feature projection is jointly learned to map two different spectra of palmprint images into a common feature space, in which the different spectral features have enhanced discriminative power by enlarging their variances while the intraclass features learned from different spectral images are similar. The proposed method can be easily extended to seek the unified spectrum-invariant representation of multiple spectral palmprint images, making it feasible to perform palmprint recognition crossing one spectrum to multiple spectra. Experimental results on two multispectral palmprint image databases demonstrate the promising effectiveness of the proposed method on cross-spectral palmprint recognition.

Cross-modal hashing has received increasing research attentions due to its less storage and efficient retrieval. However, most existing cross-modal hashing methods focus only on exploring multi-modal information, while underestimate the significance of local and Euclidean structure information on the hashing learning procedure. In this paper, we propose a supervised discrete-based cross-modal hashing method, named Scalable Discriminative Discrete Hashing (SDDH), for cross-modal retrieval, where 1) the discrete hash codes are directly obtained by multi-modal features and semantic labels so that the quantization errors are dramatically reduced, and 2) the discrete hash codes simultaneously preserve the heterogeneous similarity and manifold information in the original space by employing matrix factoring with orthogonal and balanced constraints. Moreover, an efficient optimization is introduced to tackle the discrete solution, which makes the SDDH scalable to large-scale cross-modal retrieval. Empirical results on three widely-used benchmark databases clearly demonstrate the effectiveness and efficiency of the proposed method in comparison with state-of-the-arts.

Abstract Compared with video de‐raining, single image de‐raining is more technically difficult due to the lack of temporally redundant information. This paper proposes a new two‐stage method for single image de‐raining. In the first stage, the authors develop an effective two‐step model to detect the rain streaks by taking pixel intensity, and direction of rain streaks as priors. In the second stage, the rain repair process is performed at the patch level. The authors first define a way to search for similar patches of each patch, and then group the similar patches together to form a matrix. Finally, a low‐rank matrix completion technique is utilized to recover the rain‐stained pixels based on the rain map obtained from the first stage. Compared with several state‐of‐the‐art methods, authors' proposed method is competitive in terms of the abilities of removing rain streaks, and preserving image details.

Abstract The advection step in grid‐based fluid simulation is prone to numerical dissipation, which results in loss of detail. How to improve the advection accuracy to preserve more fluid details is still challenging. On the other hand, a common way to enhance smoke details is to use vorticity confinement. However, most of the previous methods simply used a fine‐tuned scale factor ε to adjust the strength of the confinement force, which can only amplify existing vortex details and is easy to cause instability when ε is large. In this article, we proposed an adaptive vorticity confinement method, which does not suffer from the above problems, to compensate the vorticity loss during advection with little extra cost. The main idea is to first calculate a scale factor whose value depends on the vorticity loss during advection, and then use it to adaptively control the vorticity confinement force for vorticity compensation with high stability. The experiment results show the effectiveness and efficiency of our method.

In the smoothed particle hydrodynamics (SPH) fluid simulation method, thesmoothing length affects not only the process of neighbor search but also the calculation accuracy of the pressure solver. Therefore, it plays a crucial role in ensuring the accuracy and stability of SPH. In this study, an adaptive SPH fluid simulation method with a variable smoothing length is designed. In this method, the smoothing length is adaptively adjusted according to the ratio of the particle density to the weighted average of the density of the neighboring particles. Additionally, a neighbor search scheme and kernel function scheme are designed to solve the asymmetry problems caused by the variable smoothing length. The simulation efficiency of the proposed algorithm is comparable to that of some classical methods, and the variance of the number of neighboring particles is reduced. Thus, the visual effect is more similar to the corresponding physical reality. The precision of the interpolation calculation performed in the SPH algorithm is improved using the adaptive-smoothing length scheme; thus, the stability of the algorithm is enhanced, and a larger timestep is possible.

Abstract The accuracy of advection has a great influence on the visual effect of fluid simulation. Constrained interpolation profile (CIP) method has been an important advection scheme because of its third‐order accuracy and the fact that it only needs to be performed over a compact stencil, but extending it to high‐dimensional advection equations is not easy, because it involves complex calculations and large memory overheads, and is usually unstable. In this article, we propose a stable and efficient three‐dimensional (3D) CIP scheme which can maintain high accuracy but requires low computation and memory cost. We first construct an efficient two‐dimensional (2D) CIP scheme based on dimensional splitting and local Taylor expansions, and then propose an effective way to extend it for 3D applications without decreasing the computational accuracy or affecting the stability. The experimental results show the advantages of our method over the state‐of‐the‐art advection schemes.

Abstract In this paper, a novel method with good numerical stability is proposed from the perspective of energy preserving to alleviate the numerical dissipations in the advection step of Eulerian fluid simulation. The main idea is to measure the vorticity loss during advection, calculate the lost angular kinetic energy with a proposed scheme, and then synthesize a high‐frequency incompressible details field to compensate the lost energy in a way that is consistent with Kolmogorov's theory, which prevents the synthetic details from interfering with the existing fluid flow. The method works independently of the advection scheme and can be easily combined with other advection schemes to enhance the effect. It adds only 5% to 10% of the computational overhead while producing convincing fluid details without changing the overall behavior of the original flow.

Abstract In virtual environments, real‐time simulation and rendering of dynamic fluids have always been the pursuit for virtual reality research. In this paper, we present a real‐time framework for realistic fluid simulation and rendering on graphics processing unit. Because of the high demand for interactive fluids with larger particle set, the computational need is becoming higher. The proposed framework can effectively reduce the computational burden through avoiding the computation in inactive areas, where many particles with similar properties and low local pressure cluster together. While in active areas, the computation is fully carried out; thus, the fluid dynamics are largely preserved. Here, a robust particle classification technique is introduced to classify particles into either active or inactive. The test results have shown that the technique improves the time performance of fluid simulation largely. We then incorporate parallel surface reconstruction technique using marching cubes to extract the surfaces of the fluid. The introduced histogram pyramid‐based marching cubes technique is fast and memory efficiency. As a result, we are able to produce plausible and interactive fluids with the proposed framework for large‐scale virtual environments. Copyright © 2013 John Wiley & Sons, Ltd.

Abstract We present a realistic, fast, and controllable model to simulate fire propagation on solid objects with the object decomposition process involved. A hybrid structure of grids is employed to simulate the whole process efficiently. An improved burning surface update scheme based on level set and a novel method for visualizing the burning surface are proposed to produce convincing results. To achieve interactive simulation speed, a few acceleration techniques are employed, including a moving grid generated to dynamically track the fire propagation, a refined Marching Cubes method to reconstruct the burning surface, and a hardware‐implemented fluid solver. By controlling a few physical and geometric parameters, we are able to simulate various solid combustion phenomena. Copyright © 2011 John Wiley & Sons, Ltd.

We present a particle-based method for viscoelastic fluids simulation. In the method, based on the traditional Navier-Stokes equation, an additional elastic stress term is introduced to achieve viscoelastic flow behaviors, which have both fluid and solid features. Benefiting from the Lagrangian nature of Smoothed Particle Hydrodynamics, large flow deformation can be handled more easily and naturally. And also, by changing the viscosity and elastic stress coefficient of the particles according to the temperature variation, the melting and flowing phenomena, such as lava flow and wax melting, are achieved. The temperature evolution is determined with the heat diffusion equation. The method is effective and efficient, and has good controllability. Different kinds of viscoelastic fluid behaviors can be obtained easily by adjusting the very few experimental parameters.