Spatial Domain Research Articles

An illumination-guided dual-domain network for image exposure correction

Exposure problems, including underexposure and overexposure, can significantly degrade image quality. Poorly exposed images often suffer from coupled illumination degradation and detail degradation, aggravating the difficulty of recovery. These necessitate a spatial discriminating exposure correction, making achieving uniformly exposed and visually consistent images challenging. To address these issues, we propose an Illumination-guided Dual-domain Network (IDNet), which employs a Dual-Domain Module (DDM) to simultaneously recover illumination and details from the frequency and spatial domains, respectively. The DDM also integrates a structural re-parameterization technique to enhance the detail-aware capabilities with reduced computational cost. An Illumination Mask Predictor (IMP) is introduced to guide exposure correction by estimating the optimal illumination mask. The comparison with 26 methods on three benchmark datasets shows that IDNet achieves superior performance with fewer parameters and lower computational complexity. These results confirm the effectiveness and efficiency of our approach in enhancing image quality across various exposure scenarios.

EENet: An effective and efficient network for single image dehazing

While numerous solutions leveraging convolutional neural networks and Transformers have been proposed for image dehazing, there remains significant potential to improve the balance between efficiency and reconstruction performance. In this paper, we introduce an efficient and effective network named EENet, designed for image dehazing through enhanced spatial–spectral learning. EENet comprises three primary modules: the frequency processing module, the spatial processing module, and the dual-domain interaction module. Specifically, the frequency processing module handles Fourier components individually based on their distinct properties for image dehazing while also modeling global dependencies according to the convolution theorem. Additionally, the spatial processing module is designed to enable multi-scale learning. Finally, the dual-domain interaction module promotes information exchange between the frequency and spatial domains. Extensive experiments demonstrate that EENet achieves state-of-the-art performance on seven synthetic and real-world datasets for image dehazing. Moreover, the network’s generalization ability is validated by extending it to image desnowing, image defocus deblurring, and low-light image enhancement.

DBSF-Net: Infrared Image Colorization Based on the Generative Adversarial Model with Dual-Branch Feature Extraction and Spatial-Frequency-Domain Discrimination

Thermal infrared cameras can image stably in complex scenes such as night, rain, snow, and dense fog. Still, humans are more sensitive to visual colors, so there is an urgent need to convert infrared images into color images in areas such as assisted driving. This paper studies a colorization method for infrared images based on a generative adversarial model. The proposed dual-branch feature extraction network ensures the stability of the content and structure of the generated visible light image; the proposed discrimination strategy combining spatial and frequency domain hybrid constraints effectively improves the problem of undersaturated coloring and the loss of texture details in the edge area of the generated visible light image. The comparative experiment of the public infrared visible light paired data set shows that the algorithm proposed in this paper has achieved the best performance in maintaining the consistency of the content structure of the generated image, restoring the image color distribution, and restoring the image texture details.

Parallel Channel Feature Weighted Seizure Prediction Based on Multi-Scale Spatial and Temporal Factorization

Epileptic seizure prediction based on electroencephalography (EEG) plays an important role in the field. However, the existing epilepsy prediction methods have little modeling ability to capture the interaction between features, and the high redundancy of features leads to the limitations of model performance. In addition, the feature information guided by the multi-channel spatial location of the brain region is ignored. To solve these problems, this paper proposes a parallel channel feature-weighted seizure prediction network based on multi-scale temporal and spatial factorization (MS-STFM-PCFWNet). Specifically, the feature information of time domain and multi-channel spatial domain of brain region can be extracted by using feature matrix to fully learn the correlation between channels. Secondly, the multi-scale spatiotemporal Factorizer (MS-STFM) is utilized to combine and interact the features, and the correlation information between the features is captured. Finally, by combining the multi-scale Inception module with an efficient channel attention mechanism, a parallel channel feature weighted network (PCFWNet) is constructed to effectively learn multi-domain features and map the discriminant representation of epilepsy prediction. The proposed MS-STFM-PCFWNet is evaluated on public CHB-MIT and BONN datasets. The experimental results show that compared with the most advanced methods, the proposed method achieves excellent predictive performance, which can be used for early warning of epileptic seizures in specific patients.

A fast H3N3‐2σ$_\sigma$‐based compact ADI difference method for time fractional wave equations

AbstractIn the present paper, we derive a fast H3N3‐2‐based compact alternating direction implicit (ADI) scheme for the time fractional wave equation in two‐dimensional spatial domains. The time fractional derivative involved in the equation is discretized by the H3N3‐2 formula combined with sum‐of‐exponential technique. The former was first proposed by Du et al., while the latter has become a widely used technique to reduce the computational cost in the processing of convolution integrals. The spatial discretization adopts the standard compact ADI method, which can ensure that the space can reach the fourth‐order accuracy without increasing the amount of computation. The numerical stability and convergence of the difference scheme are analyzed rigorously. As an auxiliary illustration, a numerical example is given to verify the validity of the theoretical findings.

Next-Generation Secure and Reversible Watermarking for Medical Images using Hybrid Radon-Slantlet Transform

This research article proposes a security-enhanced watermarking method for medical images using the Radon and Slantlet transforms. The first step involves transforming the cover image from the spatial domain to the Radon domain. This transformation involves rotation, scaling, and translation through the Radon transform, which alters the locations of concealed bits. As a result, identifying the embedded data poses a considerable challenge. The embedded data cannot be identified without employing the inverse Radon transform. Subsequently, the Radon-transformed image is converted to the frequency domain using the Slantlet transform. Secret bits are incorporated into frequency coefficients during this phase through the pixel pair mapping approach. The final watermarked image is generated by inserting side information into the robust watermarked image. Simulation experiments are carried out to evaluate the imperceptibility of watermarks in medical images, employing metrics such as PSNR and SSIM. The results indicate high imperceptibility, with PSNR values exceeding 45 dB and SSIM values surpassing 0.95 for all tested images. Furthermore, the proposed method's robustness and reversibility are assessed by exposing watermarked images to various attacks. Performance is measured through the BER and NCC. Experimental findings reveal a BER of 0.2 % for the watermarked information, indicating strong resilience against attacks. Additionally, the NCC is determined to be 0.96, highlighting a high level of reversibility in extracting embedded data.

EEG spatial inter-channel connectivity analysis: A GCN-based dual stream approach to distinguish mental fatigue status

Mental fatigue is defined as a decline in the ability and efficiency of mental activities. A lot of research suggests that the transition from alertness to fatigue is accompanied by alterations in correlation patterns among various brain regions. However, conventional methods for detecting mental fatigue seldom emphases inter-channel connectivity in the spatial domain. To fill this gap, this paper explores the spatial inter-channel connectivity in alertness and fatigue, employing spectral graph convolutional networks (GCN) for mental fatigue detection. We utilized Pearson correlation coefficients (PCC) to establish temporal connections and magnitude-squared coherence (MSC) for spectral connections. Topological features of the brain network were then analysed. To enhance the learning of spatial inter-channel connectivity, a dual-graph strategy transforms edge features into node features, serving as inputs to the spectral GCN. By simultaneously learning PCC and MSC features, the model results indicate significant differences in some brain network characteristics between alert and fatigue states. It confirms that the synchronicity of brain operations differs in the alert state compared to mental fatigue, and indicates that fatigue states can influence correlation patterns among different brain regions. Our approach is evaluated on a self-designed experimental dataset containing 7 subjects, demonstrating a classification accuracy of 89.59 % in group-level experiments and 95.24 % at the subject level. Additionally, on the public dataset SEED-VIG containing 23 subjects, our method achieves an accuracy of 86.58 %. In summary, this paper proposes a neural network approach based on a dynamic functional connectivity network. The network integrates both temporal and spectral connections with the goal of simultaneously learning spatial inter-channel connectivity in time and frequency domains. This effectively accomplishes fatigue state detection, highlighting that fatigue significantly influences correlations among different brain regions.

HyperDehazing: A hyperspectral image dehazing benchmark dataset and a deep learning model for haze removal

Haze contamination severely degrades the quality and accuracy of optical remote sensing (RS) images, including hyperspectral images (HSIs). Currently, there are no paired benchmark datasets containing hazy and haze-free scenes in HSI dehazing, and few studies have analyzed the distributional properties of haze in the spatial and spectral domains. In this paper, we developed a new hazy synthesis strategy and constructed the first hyperspectral dehazing benchmark dataset (HyperDehazing), which contains 2000 pairs synthetic HSIs covering 100 scenes and another 70 real hazy HSIs. By analyzing the distribution characteristics of haze, we further proposed a deep learning model called HyperDehazeNet for haze removal from HSIs. Haze-insensitive longwave information injection, novel attention mechanisms, spectral loss function, and residual learning are used to improve dehazing and scene reconstruction capability. Comprehensive experimental results demonstrate that the HyperDehazing dataset effectively represents complex haze in real scenes with synthetic authenticity and scene diversity, establishing itself as a new benchmark for training and assessment of HSI dehazing methods. Experimental results on the HyperDehazing dataset demonstrate that our proposed HyperDehazeNet effectively removes complex haze from HSIs, with outstanding spectral reconstruction and feature differentiation capabilities. Furthermore, additional experiments conducted on real HSIs as well as the widely used Landsat-8 and Sentinel-2 datasets showcase the exceptional dehazing performance and robust generalization capabilities of HyperDehazeNet. Our method surpasses other state-of-the-art methods with high computational efficiency and a low number of parameters.

Damage evolution simulation and lifetime prediction for composite blades under continuous droplet impacts

Offshore wind power generation is a promising technology in renewable energy applications due to its high reserves of wind energy in sea areas. To improve the energy transformation efficiency, the blade length of the offshore wind turbines has become larger and larger, and it has made rain erosion be one of the most frequent failures during the turbine operation. As the natural rainfall is stochastic in spatial and time domains, it is difficult to depict the damage evolution process caused by rain impact exactly. Therefore, regular and continuous droplet impact simulation and experiments present an alternative methodology for this issue. With the composite structure of the blade and deformability of the liquid droplet in consideration, a fluid solid interaction model will be established to investigate the impact response and subsequent damage evolution. In which, the Smooth Particle Hydrodynamics (SPH) model is utilized to depict the constitutive relationship within the droplet, and Finite Element Method (FEM) is used to construct the Representative Volume Element (RVE) model of the blade leading edge. The impact process is simulated first to obtain the impact pressure distribution at the contact center and velocity field in the droplet. Furthermore, the stress wave propagation in the blade multilayer structure can be analyzed. Owing to the multiaxial fatigue feature of the continuous droplet impact, the continuum damage mechanics is integrated with the fatigue criterion and the Jump-in-Cycle procedure is used to simulate the high-cycle fatigue process. The damage factor distribution on the blade coating surface and its influence on mechanical properties are analyzed. Thereafter, the droplet impact fatigue life can be accumulated based on Miner’s linear rules. The theoretical achievements are validated by experimental data provided by Rain Erosion Testing (RET), which shows a good agreement between each other. As a result, V-N curves and D-N curves, i.e. quantitative relationship between droplet falling conditions and impact fatigue life, are established. The achievements in this study can provide an effective tool for rain erosion mechanism analysis and life prediction in industrial applications.

Acoustic beamforming using maximum likelihood criteria with Laplacian model of the desired signal

Acoustic beamforming is a technique used in audio engineering and signal processing to filter sound waves in the spatial domain. Usually, an array of microphones is used to capture sound from different directions. These array signals are then combined to reinforce each other in the desired direction while cancelling the noise or interference from other directions. An important application of acoustic beamforming is the cocktail party scenario where multiple people speak simultaneously in a noisy room. To capture the speech of only the desired speaker, acoustic beamforming is used. Usually, in such cases, the target speech is modelled as a zero-mean complex Gaussian distributed random variable. However, the target speech coefficients are sparse in the time-frequency domain. Hence, in our work, we model the speech coefficients using a zero-mean circular Laplacian distribution. After modelling the target speech, we formulate a beamformer based on the maximum likelihood criteria. We add a distortionless constraint to the proposed beamformer to further improve performance. The final solution of the proposed beamformer encourages sparsity, indicating that it models the target speech better than the complex Gaussian distribution. Simulations show the effectiveness of the proposed beamformer in capturing the target speech and rejecting interfering speakers.

Utilizing porous dielectric material to enhance the performance of capacitive MEMS accelerometers for shaft monitoring

This research investigates the optimization of the performance of a capacitive-based microelectromechanical systems (MEMS) shaft monitoring accelerometer using a porous soft dielectric material with high polarization capability and low Young’s modulus. The nonlinear governing equations of a microbeam with a proof mass coupled with the squeeze motion equation of the polymeric dielectric material excited by shaft vibrations are extracted and solved in both the spatial and temporal domains. The studied model considers the stiffness, dissipative, and inertial effects of the polymeric material and incorporates porosity as a displacement-dependent variable, which introduces an additional nonlinearity. After discretizing the coupled nonlinear differential equations using the Galerkin method, the response in the frequency domain is obtained by applying an energy balance method, where the coefficients of the Fourier expansion of the response are found by arc-length continuation through a physical gradient descent learning-based approach method. The occurrence of secondary and primary resonances in different harmonic responses is studied for different harmonic acceleration inputs. The equivalent rigidity of the design is investigated for different shaft frequency magnitudes and different proof mass geometries. The effect of the initial porosity volume fraction of the elastomeric dielectric material on the dynamic response of the accelerometer is also examined. The sensor’s sensitivity is dependent on its geometry and properties and can vary based on the structure’s material parameters. Consequently, the selection of different geometries and materials may result in either an improvement or a deterioration of the sensor’s performance.

Low-light image enhancement guided by multi-domain features for detail and texture enhancement

Low-light image enhancement holds significant value in the fields of computer vision and image processing, such as in applications like surveillance photography and medical imaging. Images captured in low-light environments typically suffer from significant noise levels, low contrast, and color distortion. Although existing low-light image enhancement techniques can improve image brightness and contrast to some extent, they often introduce noise or result in over-enhancement, leading to the loss of detail and texture. This paper introduces an innovative approach to low-light image enhancement by fusing spatial and frequency domain features while optimizing them with multiple loss functions. The core of the algorithm lies in its multi-branch feature extraction, multi-loss function constraints, and a carefully designed model structure. In particular, the model employs an encoder-decoder architecture, where the encoder extracts spatial features from the image, the Fourier feature extraction module captures frequency domain information, and the histogram feature encoder-decoder module processes global brightness distribution. These extracted features are then fused and reconstructed in the decoder to produce the enhanced image. In terms of loss functions, the algorithm combines perceptual loss, structural similarity loss, Fourier loss, and histogram loss to ensure comprehensive and natural enhancement effects. The novelty of this algorithm lies not only in its multi-branch feature extraction design but also in its unique model structure, which synergistically improves image quality across different domains, effectively preventing over-enhancement, and ultimately achieving a balanced enhancement of brightness, details, and texture. Experimental results on multiple datasets, including SIDD, LOL, MIT-Adobe-FiveK, and LOL-v2-synthetic, demonstrate that the proposed method outperforms existing techniques in terms of image detail, texture, and brightness. Specifically, it achieves a PSNR of 27.52 dB on the LOL dataset, surpassing Wavelet Diffusion by 1.19 dB. Additionally, on the LOL-v2-synthetic dataset, it achieves a PSNR of 29.56 dB, exceeding Wavelet Diffusion by 3.06 dB. These results demonstrate a significant enhancement in the visual quality of low-light images.

Coastline target detection based on UAV hyperspectral remote sensing images

Timely and accurate monitoring of typical coastal targets using remote sensing technology is crucial for maintaining marine ecological stability. Hyperspectral target detection technology proves to be an effective tool in extracting various typical materials along the coastline. Traditional target detection methods using spectral domain information can effectively retain the intrinsic properties of the material. However, it is difficult to effectively recognize targets in homogeneous regions by using only spectral domain information, which may lead to insufficient utilization of spatial information. In this study, a detector based on signal-to-noise ratio fusion constrained energy minimization with low-rank sparse decomposition (SFLRSD) is proposed. This detector improves the separability of background and target by obtaining spatial domain information from hyperspectral images and fusing spectral domain information. First, total variation regularization and fractional Fourier transform are applied to process spatial and spectral domain information, respectively. The constrained energy minimization (CEM) detector is used to improve the separability between the target and background of the processed data. Then, the background and anomalies are represented as low-rank and sparse components, respectively, using low-rank sparse matrix factorization. This transforms the model solution into a covariance matrix problem, which is then solved using marginal distance difference (MDD) to isolate anomalous parts. Subsequently, the anomaly parts are fused with CEM detector results, weighted by their respective signal-to-noise ratios. This detection model leverages unified hyperspectral image features, enhancing spectral discreteness of anomalous targets and backgrounds. Finally, experiments on custom created hyperspectral dataset show that the proposed method outperforms other baseline methods in terms of visualization and quantitative performance. In this paper, we not only propose a new hyperspectral target detection method, but we also collect three typical marine litter of different materials by means of airborne hyperspectral remote sensing and construct four hyperspectral datasets in a real environment. All the simulation experiments in this paper are conducted in these four datasets.

Dynamic buckling active control of FGM spherical shell with piezoelectric sensor and actuator layers

The mechanical snap-through phenomenon represents one of the buckling modes inherent in shallow shells, exemplifying the shell's reaction to external loads, which can potentially have detrimental effects on structural performance. This article delves into the study of this phenomenon within the context of spherical shells. Leveraging functionally graded material (FGM) in the main layer of this structure proves instrumental in enhancing the shell's performance against rapid mechanical loads. Furthermore, the strategic placement of piezoelectric layers, both symmetrically and asymmetrically, coupled with the implementation of a proportional and derivative control system, facilitates the control of the shell's response. The formulation of displacement field and electric potential is grounded in the first-order shear deformation theory (FSDT) and second-order distribution, respectively. The strong form of nonlinear dynamic and electrostatic equations is derived using Hamilton's principle. Solving these equations is achieved through the implementation of the generalized differential quadrature (GDQ) method in the spatial domain and Newmark in the time domain. Additionally, the Newton-Raphson method is employed to tackle the inherent nonlinearity of the problem. The Budiansky's criterion is employed for the assessment of the load necessary for the buckling of the shell. Following the validation of results against numerical, analytical, and laboratory outcomes, a set of parametric results is presented. These results underscore the remarkable impact of the control system in mitigating shell deformation under time-dependent mechanical loads, as well as in postponing the occurrence of the snap-through phenomenon and damping the vibrations.

Integrating angular and domain decomposition with space-angle discontinuous Galerkin methods in 2D radiative transfer

A space-angle discontinuous Galerkin (saDG) method is used to solve the steady-state radiative transfer equation (RTE) for 2D problems involving absorption, emission, and scattering for a semitransparent medium. This approach discretizes both spatial and angular domains. Parallel computing is based on angular decomposition (AD), and domain decomposition (DD) techniques. The DD technique directly solves the entire domain using the MUMPS library, whereas the AD technique results in an iterative approach for scattering media. This study proposes a novel hybrid AD-DD method, combining the best aspects of both techniques. Numerical results investigate the scalability, performance, and efficiency of AD and DD techniques. It is shown that a hybrid AD-DD technique is superior to these individual techniques by taking advantage of their strengths. Numerical methods demonstrate the applicability of the method of the best combination of hybrid AD-DD to 2D scattering gray media with complex geometries or enclosures with circular and square obstacles.

PDE-regularised spatial quantile regression

We consider the problem of estimating the conditional quantiles of an unknown distribution from data gathered on a spatial domain. We propose a spatial quantile regression model with differential regularisation. The penalisation involves a partial differential equation defined over the considered spatial domain, that can display a complex geometry. Such regularisation permits, on one hand, to model complex anisotropy and non-stationarity patterns, possibly on the basis of problem-specific knowledge, and, on the other hand, to comply with the complex conformation of the spatial domain. We define an innovative functional Expectation-Maximisation algorithm, to estimate the unknown quantile surface. We moreover describe a suitable discretisation of the estimation problem, and investigate the theoretical properties of the resulting estimator. The performance of the proposed method is assessed by simulation studies, comparing with state-of-the-art techniques for spatial quantile regression. Finally, the considered model is applied to two real data analyses, the first concerning rainfall measurements in Switzerland and the second concerning sea surface conductivity data in the Gulf of Mexico.

A fast impact force identification method via constructing a dynamic reduced dictionary

Impact force identification is an important aspect of structural health monitoring for online assessment of the integrity of engineering structures. Increasing the number of monitoring positions is undoubtedly beneficial to accurate force localization, however, it may increase sharply the dimension of the transfer matrix and thus lead to a large-scale inverse problem. In this case, traditional methods, such as the Iterative Shrinkage Threshold algorithm (IST) and the Two-Step Iterative Shrinkage Thresholding algorithm (TwIST), suffer from low solving efficiency. In this paper, the dynamic reduced dictionary is firstly introduced according to the sparsity of impact force in both time and spatial domains so as to lower significantly the dimension of the transfer matrix. Then, a new reduced unconstrained optimization problem is established via the dynamic reduced dictionary for impact force identification. By integrating the reduced unconstrained optimization problem into each iteration step of IST/TwIST, two novel algorithms, which are the reduced Newton iteration shrinkage threshold algorithm (rNIST) and the reduced Newton two-step iteration shrinkage threshold algorithm (rNTwIST), are proposed to solve quickly the large-scale impact force identification problem using ℓ1-norm sparse regularization. Meanwhile, the adaptive setting of regularization parameters strategy is used to construct force more fast and accurately. The proposed algorithms are numerically and experimentally demonstrated through identifying impact forces at 16-point and 81-point distributions of a plate using one sensor response. The results show that rNIST/rNTwIST can more quickly and accurately identify impact forces under numerous monitoring points compared with other ℓ1-norm regularization methods and nonconvex sparse regularization methods. Moreover, the more the number of monitoring points, the more obvious the efficiency improvement of the impact force identification by rNIST/rNTwIST method.

Frequency domain attention network for copper chain defect detection in tobacco cutting machine

AbstractThe detection of defects on the copper chain in the production process of tobacco cutters is crucial for ensuring product quality. Traditional defect detection methods often rely on spatial domain image analysis, which not only has a large computational load but also performs poorly in handling high‐frequency noise and complex backgrounds. To address this issue, this paper proposes a novel neural network model based on frequency domain analysis, called frequency domain attention network. This network first utilizes discrete cosine transform to transform the image from the spatial domain to the frequency domain, effectively reducing computational complexity and improving processing speed. Subsequently, through the innovative frequency domain attention module, the network automatically identifies and enhances key discriminative features in the frequency domain, thereby strengthening the model's ability to identify defects. Finally, the frequency domain attention map, after feature extraction and integration, is inputted into the coupling detection head to achieve high‐precision defect detection. The experimental results show that our method outperforms the SOTA method with an increase of 0.03 in AP and 21 in FPS.

Array infrared thermography for visualization of defects in bonded fiber reinforced polymer joints

Fiber reinforced polymer (FRP) is widely used in new and existing structures, however, interfacial defects in the bonded joints pose a significant threat to structural integrity. Therefore, detection of interfacial defects is imperative for ensuring structural safety. This study proposes array infrared thermography (IRT) as a novel non-destructive evaluation method to visualize interfacial defects. Array IRT provides uniform heat excitation within the spatial domain, which overcomes the problem of heat concentration by conventional IRT. Forty-five bonded FRP plate specimens were tested using array IRT, results of which show that interfacial defects can be accurately detected within (8h+8) s (where h is the thickness of the upper layer of FRP in mm). Array IRT achieves high accuracy in detecting shapes, particularly sharp corners of defects. A pre-processing method was proposed to eliminate the twisted angles of thermal camera and to more clearly show the defects in the thermograms. A database containing tested thermograms and the corresponding predefined defects was established. Intelligent algorithms - UNet, Deeplabv3, and YOLOv8 - were used to segment the defected regions for array IRT analysis, results of which show a precision of 95.8%, 94.4%, and 94.1%, respectively.

Statistical batch-aware embedded integration, dimension reduction, and alignment for spatial transcriptomics.

Spatial transcriptomics (ST) technologies provide richer insights into the molecular characteristics of cells by simultaneously measuring gene expression profiles and their relative locations. However, each slice can only contain limited biological variation, and since there are almost always non-negligible batch effects across different slices, integrating numerous slices to account for batch effects and locations is not straightforward. Performing multi-slice integration, dimensionality reduction, and other downstream analyses separately often results in suboptimal embeddings for technical artifacts and biological variations. Joint modeling integrating these steps can enhance our understanding of the complex interplay between technical artifacts and biological signals, leading to more accurate and insightful results. In this context, we propose a hierarchical hidden Markov random field model STADIA to reduce batch effects, extract common biological patterns across multiple ST slices, and simultaneously identify spatial domains. We demonstrate the effectiveness of STADIA using five datasets from different species (human and mouse), various organs (brain, skin, and liver), and diverse platforms (10x Visium, ST, and Slice-seqV2). STADIA can capture common tissue structures across multiple slices and preserve slice-specific biological signals. In addition, STADIA outperforms the other three competing methods (PRECAST, fastMNN, and Harmony) in terms of the balance between batch mixing and spatial domain identification, and it demonstrates the advantage of joint modeling when compared to STAGATE and GraphST. The source code implemented by R is available at https://github.com/zhanglabtools/STADIA and archived with version 1.01 on Zenodo https://zenodo.org/records/13637744.