Popular Deformable Convolutions

Diffeomorphic image registration is central to medical image analysis, enabling anatomically consistent alignment across subjects. Most learning-based diffeomorphic methods model autonomous ODEs(ordinary differential equations) by parameterizing a stationary velocity field and recovering deformations via scaling-and-squaring. While non-autonomous ODEs with time-dependent velocities increase expressiveness, existing approaches rely on numerical integration to implicitly enforce flow structure that entangles model expressiveness with discretization accuracy. We propose a framework to directly learn the continuous-time solution of a non-autonomous ODE formulated as a two-parameterflow map. By enforcing cocycle consistency, a fundamental structural property of time-varying flows, we learn the flow maps without time discretization and velocity integration during training. The framework recovers diffeomorphic mappings at inference using a small number of compositions. Our proposed framework seamlessly incorporates standard registration backbones and improves alignment accuracy consistently across nine datasets while preserving diffeomorphic structure. Notably, the proposed method achieves an average Dice improvement of 2.1% on brain MRI benchmarks, a 12% TRE reduction on lung CT, and a 2.6% Dice gain on cardiac MRI and ultrasound datasets.

Deformable convolution networks have recently become popular for many computer vision tasks, especially for semantic segmentation, because of their exceptional capabilities in dynamic spatial modeling. However, due to the dense deformable offsets and the lack of longer-range dependencies, they can not fully adopt proper and precise deformations for feature representations. To tackle the issues, in this paper, we propose Enhanced Deformable ConvNets (EDCN) for semantic segmentation. Specifically, a novel Enhanced Deformable Convolution (EDC) is exploited in the decoder, which integrates the Center-invariant Offset Module (COM) and Edge-aware Mask Module (EMM). The COM employs larger kernels and eliminates deformations at the kernel center, obtaining offsets that are more in line with the target from richer spatial information. Concurrently, the EMM obtains the significance of image content via Sobel edge detection, then selectively applies deformations based on the content significance, minimizing unnecessary deformations associated with relatively less important information, thereby avoiding impact from less informative regions. Experiments show that EDC outperforms state-of-the-art deformable convolution variants, including Deformable ConvNets V1-V4 and Entire Deformable ConvNets, across mainstream segmentation datasets with various decoder settings. Moreover, ablation studies confirm the effectiveness of each component. In addition, visualizations illustrate that EDC enhances spatial adaptation and target focus. We further analyze the extendibility of EDC to larger kernels on the image classification benchmark. Code will be publicly released.

Pancreatic tumor segmentation in 3D CT volumes is challenged by extreme scale variability across both the pancreas and tumor, and highly irregular tumor morphology. While recent advances have pushed segmentation performance, existing methods do not explicitly address these challenges and come at the cost of excessive computational complexity, limiting their practicality in resource-constrained clinical environments. We propose TRIUNE-Net, a lightweight unified architecture that harmonizes scale, shape, and efficiency through three synergistic innovations. A multi-scale context aggregation module with stage-adaptive dilated convolutions enables the model to reason across the broad range of anatomical scales present in both organs. A serial linear-deformable attention mechanism combines large effective receptive fields with shapeadaptive deformable convolutions to capture irregular, non-convex tumor morphologies. Finally, an information-preserving downsampling module replaces conventional max pooling entirely, retaining all spatial information while adding negligible parameters, preventing small tumors from being discarded before they can be recognized. On both the MSD Pancreas and NVD Pancreas datasets, TRIUNE-Net achieves state-of-theart results with only 5.86 M parameters and no external pre-training, outperforming all baselines across all key tumor metrics. Specifically, it surpasses the next-best model by 0.45% in tumor Dice, 6.0 points in F1 score, 6.6 points in sensitivity, and 3.4 points in precision, simultaneously reflecting its ability to suppress both missed tumors and false alarms in clinically realistic conditions. Our code is available at: https://github.com/abdora-ai/TRIUNE-Net

Data-driven inverse design enables efficient generation of nanophotonic structures with prescribed optical responses, but spectrum-to-geometry mapping remains challenging due to non-uniqueness and fine geometric features. This work presents a two-stage deformable-convolutional framework for reconstructing metal--insulator--metal resonator geometries from 80-dimensional absorption spectra. The spectrum is projected to a $150\times4\times4$ latent representation and decoded into a $64\times64$ resonator mask. Training combines supervised reconstruction with least-squares adversarial refinement initialized from the best supervised checkpoint. A three-run ablation compares deformable convolution with plain convolution, involution, Dynamic Conv, and ODConv under the same architecture. The proposed model achieves $20.79\pm0.31$dB PSNR and $0.8501\pm0.0082$ SSIM, improving over plain convolution by 2.16dB and 0.0831, respectively. It further achieves Dice $0.9623\pm0.0027$, IoU $0.9342\pm0.0038$, and boundary F-score $0.9550\pm0.0027$. Spectral consistency evaluated using a frozen forward surrogate yields RMSE $0.0805\pm0.0013$ and $R^2=0.7923\pm0.0065$. Learned offsets show stronger adaptive sampling at coarse and intermediate decoder stages. Overall, deformable sampling with supervised initialization and adversarial refinement improves spectrum-conditioned geometry reconstruction.

Deformable image registration (DIR) is a core problem in medical image analysis; but, unlike labeling decision problems such as classification and segmentation, registration is a problem class that involves stringent physical constraints. Although deep learning methods have made faster registration possible, the resulting models are often difficult to interpret compared to hand-crafted methods with explicit objectives and interpretable physical meaning. In this work, we show that an analytical method can still yield competitive and superior results to deep learning in a common deformable registration task. We study pTVreg as a parametric total variation based registration in that context. Observing its different implementations to perform at various degrees, we introduce here an accessible implementation of this method, together with a Bayesian optimization framework that automatically sets self-parameters for any DIR task from a set of sample examples. Experiments on Lung250M-4B show that our proposed implementation achieves state-of-the-art results in this benchmark, substantially superior to existing deep learning solutions and other pTVreg variants as baselines. The source code will be made publicly available at https://github.com/oazeybekoglu/ptvreg-python .

Steel surface defect segmentation is critical for industrial quality inspection, yet existing methods struggle with elongated, anisotropic defects such as cracks and scratches due to the isotropic receptive fields of standard convolutions and rigid sampling grids that cannot adapt to irregular defect boundaries. To address these limitations, we propose Strip-based Predictor for Deformable Convolutional Networks (SPDCN) with two key innovations. The \textbf{Fuzzy-enhanced Multi-scale Context Module (FMCM)} employs group-wise multi-branch convolutions with an intuitionistic fuzzy channel attention mechanism to adaptively capture multi-scale contextual information across varying defect sizes. The \textbf{Adaptive Direction-Aware Deformable Convolution (ADADC)} replaces the conventional offset predictor with decoupled horizontal and vertical strip convolutions, enabling the deformable sampling grid to anisotropically align with the principal orientation of elongated defects. Extensive experiments on public steel surface defect benchmarks demonstrate that SPDCN consistently outperforms state-of-the-art methods, achieving 89.60% mIoU on NEU-Seg with only 3.54M parameters. The source code is publicly available at https://github.com/DWlzm .

We propose FA-LAM, a Focus-Aware Large Avatar Model for one-shot animatable Gaussian head creation, while simultaneously enabling static 3D and dynamic 4D full-head recovery. The core of our method lies in a thorough analysis of the attention mechanisms and the entangled reconstruction and animation training pipeline adopted by prior state-of-the-art approaches. Our analysis identifies two main factors that compromise the quality of 3D full-head generation: (1) incorrect and noisy attention activations, and (2) conflicts between the tasks of reconstruction and animation. To address the first issue, we introduce a symmetric and semantic attention regularization strategy that leverages the inherent semantics and structural symmetry of human heads. To disentangle the objectives of reconstruction and animation, we develop a novel dual-phase training pipeline that separates the model's capabilities for large-view hallucination and animation into distinct modules. Moreover, we enhance our model to support multi-view and streaming 4D reconstruction in an efficient and memory-friendly manner through a core autoregressive modification with tailored visibility-aware token fusion. Collectively, these innovations enable FA-LAM to reconstruct animatable Gaussian full heads with superior quality, particularly in fine facial regions and large viewing angles.

Face super-resolution is the task of increasing the resolution of an image containing a face thereby adding finer detail. It is a ubiquitous task in many computer vision applications and quite often the user isn't even aware that it is being performed. However, doing it with high fidelity is challenging as it is an ill-posed problem. In this paper we present a reference-based solution for face super-resolution that uses higher resolution reference images to aid in the task. We show an alignment module based on the spatial transformer that is considerably more stable than the popular deformable convolutions. We also show an aggregation function that can take good quality information from the reference images when available or suppress the function when such information is unavailable. Finally, we show that our relatively smaller model can achieve state of the art results on multiple datasets. The source code is available at https://github.com/varun-jois/FSRST.

We propose Bi-PT, a pipeline for reconstructing 3D four-chamber human heart meshes from clinical sparsely sampled cardiac magnetic resonance imaging (CMR) data. This work addresses the error-prone generation of 3D cardiac shape from a sparse point cloud (SPC) extracted from 2D long-axis and short-axis views used in routine clinical CMR protocols. Bi-PT enables accurate inference of the four-chamber heart mesh from the SPC by learning robust point features via bidirectional point cross-attention between an atlas and the SPC, together with per-point semantic labels that improve correspondence estimation. We formulate the deformation field as a Neural Ordinary Differential Equation (NODE) parameterized by a per-point affine transformation and translation to deform the atlas toward the target heart shape. By learning such a NODE, we can guarantee the deformation field to be a locally affine diffeomorphic deformation. We also integrate a semantic label loss into the Chamfer distance to encourage label-consistent correspondences and add a smoothness regularization to stabilize and improve the learning of the deformation field. Extensive experiments demonstrate that Bi-PT achieves accurate and robust performance compared to baselines.

Existing deep learning methods perform well in medical image classification but struggle with multi-scale morphology and limited annotations due to fixed sampling and data-hungry training. Existing approaches address these challenges in isolation: DCN-based models provide adaptive sampling but lack explicit multi-scale attention fusion and label-efficient regularisation; multi-scale architectures typically rely on static fusion; and semi-supervised methods target label scarcity without jointly modelling adaptive cross-scale representations. We propose MSA-DCNN, a scale-consistent deformable attention learning framework that introduces adaptive multi-scale sampling, within-scale saliency refinement, learned cross-scale fusion, and auxiliary self-distillation within a unified optimisation scheme, with potential to generalise to structurally heterogeneous anatomy. We evaluate on three public benchmarks and an external hold-out set for leukaemia. MSA-DCNN demonstrates competitive and often better performance against ViT baselines, CNN baselines, and a MICCAI semi-supervised baseline under distribution shift and label scarcity in accuracy, F1, and AUC (binary), while using fewer parameters. Ablations confirm complementary component contributions, supporting MSA-DCNN as a practical foundation for data-efficient medical image classification.

Accurate patient-specific tetrahedral cardiac meshes are essential for in-silico trials, yet common segmentation-then-modelling pipelines can blur thin-wall anatomy and offer limited cross-case correspondence. We propose HeartVolMesh, which lifts each template vertex to an anisotropic Gaussian kernel and uses a 3D CNN-GNN to predict per-vertex displacements and Cholesky-parameterized covariances from volumetric images. Training is guided by a covariance-aware negative log-likelihood loss with lightweight mesh regularization. For volumetric meshing, we warp a fixed tetrahedral template to the reconstructed surface via staged alignment, non-rigid registration, and deformation propagation, preserving connectivity and correspondence by construction, with resolution controlled by template density. Experiments show consistent gains over deformation-based baselines in surface mesh accuracy and volumetric mesh fidelity.

We introduce GenSP, a data-driven framework that learns consistent spherical parameterizations across a collection of genus-0 shapes. Instead of optimizing the parameterization of each shape independently, our method learns a neural generative model that predicts a continuous mapping from the unit sphere to shapes in a dataset. Under this formulation, spherical parameterizations are obtained through the inverse mappings of the learned generator, which encourages similar shapes to share consistent parameterizations. To make this formulation practical, we address several key challenges in learning such a generative model. First, we introduce a continuous neural deformation model that predicts surface points from sphere coordinates and latent shape codes, avoiding discretization artifacts common in mesh-based formulations. Second, we augment the training space with intermediate shapes that bridge the sphere and input shapes, allowing the model to learn meaningful deformations across a heterogeneous shape collection. Third, we compute reliable initial correspondences by propagating mappings along a spanning tree of training shapes in the latent space. Experiments on the ShapeNet dataset demonstrate that our approach significantly reduces geometric distortion and improves cross-shape consistency compared with state-of-the-art spherical parameterization methods.

We present FFAvatar, a Transformer-based 3D Gaussian framework for fast construction of high-quality and animatable 4D head avatars from one or more reference portrait images. Unlike existing feed-forward approaches that require a fixed number of input views, FFAvatar supports incremental reconstruction, progressively refining the avatar representation as additional reference images become available. At the core of our method is an alternating attention mechanism that disentangles identity appearance from expression and viewpoint variations, enabling the reconstruction of a canonical 3D appearance that remains consistent across poses and facial expressions. To balance visual fidelity and computational efficiency, we introduce a sparse-to-dense learning paradigm. Coarse appearance features are first learned using sparse primitives anchored to the FLAME vertex level and are subsequently densified in the UV domain to capture fine-grained geometric and texture details. We further propose a plug-and-play motion refinement module that enables subject-specific dynamic personalization by modeling residual motion beyond parametric deformation. Extensive experiments demonstrate that FFAvatar efficiently produces high-fidelity and controllable 4D head avatars, achieving superior flexibility, driving efficiency, and identity-consistent rendering across diverse expressions and viewpoints.

Medical image registration benefits significantly from deep learning, yet existing approaches often lack physical explainability and fine-grained deformation control. Motivated by Demons algorithms, we propose a novel DrivenMorph framework that bridges attention mechanisms with variational image registration by incorporating difference modeling as a physically inspired inductive bias. The resulting driving force, computed from local differences in the latent feature space, provides explicit semantic guidance throughout the registration process. It directly drives the registration process through a neural Demons layer that simulates force-displacement interactions to generate smooth and anatomically consistent deformation. Unlike previous methods, our approach not only integrates traditional registration principles with popular deep networks, providing an explainable and efficient solution for learning-based medical image registration, but also separates difference modeling from deformation, improving modularity and explainability. Extensive experiments on multiple 3D brain MRI datasets demonstrate superior performance over state of-the-art learning-based and optimization-based methods. Furthermore, visualizations and statistical analyses confirm that the learned driving force aligns closely with actual deformation patterns, supporting its explanatory value.

Remanufacturing large white goods is essential for a circular economy, yet visual quality assessment remains a manual bottleneck for training and pricing. Conventional detection methods require extensive annotation and struggle with small defects in high-resolution multi-view data. We present a multi-view framework based on Deformable-DETR for automated quality scoring that aggregates information across redundant views to extract fine-grained features. To enhance robustness with limited labels, we employ self-supervised pretraining followed by supervised fine-tuning on expert-annotated scores. Additionally, a linear projection over frozen feature maps identifies regions of interest to explain model decisions. Evaluated on an industrial multi-view dataset, our approach delivers precise quality assessments while reducing reliance on manual annotation and per-part customization, enabling scalable and transparent inspection for remanufacturing lines.

Building patient-specific cardiac models sits at the heart of precision cardiology, yet getting those models into clinical use keeps running into the same wall: mesh generation is slow, messy, and frustrating. The standard workflow -- segmenting the image, running Marching Cubes, and then manually cleaning up the result -- is time-consuming, inconsistent across operators, and demands specialist knowledge most clinical teams do not have. We take a fundamentally different approach. Instead of treating segmentation and mesh generation as two separate problems, we train a single end-to-end network that goes directly from a raw 3D medical image to a smooth, simulation-ready cardiac surface mesh. The core is a 3D Swin Transformer encoder-decoder that extracts volumetric features from CT or MRI volumes, paired with a Graph Attention Network (GAT) head that iteratively deforms a template mesh to fit the patient's cardiac boundary. We tested on the MM-WHS 2017 benchmark using both CT and MRI. Segmentation scores were competitive (Dice of 0.84 on CT, 0.83 on MRI), but the primary focus is mesh quality: mean Chamfer distance of 1.8 mm, with 95th-percentile surface distance below 5 mm. Every mesh is produced in a single forward pass -- no Marching Cubes, no smoothing filters, no manual cleanup. We argue that for cardiac digital twin pipelines, geometric fidelity and topological correctness matter more than pixel-level Dice scores. By removing the post-processing bottleneck, this approach makes patient-specific cardiac simulation substantially more accessible for clinical use.

Modeling dynamic facial expressions using 3D Gaussian representations remains challenging due to their unstructured nature. Conventional Gaussian avatar pipelines require extensive multiview and sequential expression data, limiting scalability and accessibility. In this work, we introduce Self-Adaptive Gaussian Expression (SAGE), a framework for self-learning expression-induced Gaussian deformations that enables high-fidelity, animatable avatars from minimal input data. Our method jointly optimizes 2D Gaussian surfels and a Signed Distance Field (SDF) to enforce compact, surface-aligned Gaussian distributions, while a self-supervised expression learning phase replaces long training sequences with geometric and appearance consistency constraints. This design allows flexible deployment across multiple reconstruction regimes: in the multiview setting, only a single frame (timestep) is required instead of thousands; in the monocular setting, only head rotations are needed without expression sequences; and in the one-shot setting, no pretraining or priors are necessary. Experiments demonstrate that our approach achieves reconstruction and animation quality comparable to state-of-the-art methods, while reducing data requirements by several orders of magnitude. Our results highlight the potential of self-supervised Gaussian deformation learning as a step toward accessible, data-efficient avatar creation.

Deformable 3D Gaussian Splatting (D-3DGS) re-constructs dynamic scenes from monocular video by deforming a canonical set of 3D Gaussians through a positional-encoded MLP of frame time t. Although fitted to a continuous variable, the MLP couples no two values of t in its architecture and effectively predicts discrete per-frame offsets, leaving temporal smoothness to emerge only as a byproduct of optimisation. We redesign the deformation field as a stack of Closed-form Continuous-time (CfC) cells, a Liquid Neural Network (LNN), that is the closed-form solution of the Liquid Time-constant ODE while preserving every other part of the D-3DGS pipeline. Each cell exposes a sigmoidal time gate that interpolates between two candidate hidden states, baking a learned smooth response to t into the loss landscape without invoking any numerical solver. On the eight D-NeRF and seven NeRF-DS scenes the liquid field matches or exceeds the MLP baseline in aggregate, with its largest gains concentrated on the scenes with the most high-frequency articulated motion. The result is a near-zero-friction architectural design that turns the discrete MLP deformation field into an explicit continuous-time function of t.

Recent developments in 3D shape representation opened new possibilities for generating detailed 3D shapes. Despite these advances, there are few studies dealing with the generation of 4D dynamic shapes that have the form of 3D objects deforming over time. To bridge this gap, we focus on generating 4D dynamic shapes with an emphasis on both generation quality and efficiency in this paper. HyperDiffusion, a previous work on 4D generation, proposed a method of directly generating the weight parameters of 4D occupancy fields but suffered from low temporal consistency and slow rendering speed due to motion representation that is not separated from the shape representation of 4D occupancy fields. Therefore, we propose a new neural deformation representation and combine it with conditional neural signed distance fields to design a 4D representation architecture in which the motion latent space is disentangled from the shape latent space. The proposed deformation representation, which works by predicting skinning weights and rigid transformations for multiple parts, also has advantages over the deformation modules of existing 4D representations in understanding the structure of shapes. In addition, we design a training process of a diffusion model that utilizes the shape and motion features that are extracted by our 4D representation as data points. The results of unconditional generation, conditional generation, and motion retargeting experiments demonstrate that our method not only shows better performance than previous works in 4D dynamic shape generation but also has various potential applications.

Deformable medical image registration aligns anatomical structures across images but remains computationally dense at 3D resolution. Spiking neural networks (SNNs) offer sparse event-driven computation, yet have not been systematically studied for deformable medical image registration. We introduce SpikeReg, a spiking U-Net for 3D brain MRI registration. SpikeReg is initialized from an analog ANN registration teacher, converted by layer-wise weight transfer and activation-percentile threshold calibration, and fine-tuned with a surrogate-gradient objective combining local cross-correlation, diffusion regularization, and spike-rate sparsity. On the OASIS Learn2Reg validation split ($19$ image pairs), SpikeReg reaches Dice $0.7474 \pm 0.032$, with no significant paired Dice difference from the ANN teacher ($0.7480 \pm 0.037$, $p = 0.67$), at a $12.8\%$ mean spike rate and a $55.5\times$ projected arithmetic-energy reduction under an event-sparse SynOps/MAC proxy relative to the dense-ANN baseline. We additionally report two negative findings: displacement distillation from the ANN teacher hurts performance, and ANN teachers trained with a label-Dice loss fail to transfer through rate-code conversion. Together these results show that dense geometric prediction can be performed under sparse event-driven computation, opening a path toward neuromorphic medical image registration.

Anatomical mesh segmentation requires models that operate directly on irregular surface geometry while remaining robust to arbitrary patient pose and mesh resolution variation. Existing task-specific mesh and point-cloud methods are not equivariant, and can degrade sharply under test-time perturbation, for example dropping by 25-26 IoU points on intraoral scan segmentation at $40^\circ$ tilt. We present EAMS, an Equivariant Anatomical Mesh Segmentor built on Equivariant Mesh Neural Networks (EMNN), and evaluate it across four clinically distinct tasks spanning edge-, vertex-, and face-level supervision. We combine intrinsic mesh descriptors with anatomy-aware priors, including PCA-derived frames for dental arches and liver surfaces, and augment message passing to provide lightweight global context. Across intracranial aneurysm and intraoral segmentation, EAMS variants are competitive with specialized baselines on unperturbed inputs while remaining stable under geometric perturbations, and on liver surfaces they expose a favorable trade-off between canonical-pose accuracy and rotation robustness. These results show that a lightweight ($<2$M parameters) equivariant framework can deliver robust anatomical mesh segmentation across diverse supervision types without task-specific architectures.

We introduce MeshLAM, a feed-forward framework for one-shot animatable mesh head reconstruction that generates high-fidelity, animatable 3D head avatars from a single image. Unlike previous work that relies on time-consuming test-time optimization or extensive multi-view data, our method produces complete mesh representations with inherent animatability from a single image in a single forward pass. Our approach employs a dual shape and texture map architecture that simultaneously processes mesh vertices and texture map with extracted image features from a shared transformer backbone, allowing for coherent shape carving and appearance modeling. To prevent mesh collapse and ensure topological integrity during feed-forward deformation, we propose an iterative GRU-based decoding mechanism with progressive geometry deformation and texture refinement, coupled with a novel reprojection-based texture guidance mechanism that anchors appearance learning to the input image. Extensive experiments demonstrate that our method outperforms state-of-the-art approaches in reconstruction quality, animation capability, and computational efficiency. Project page at https://meshlam.github.io.

Accurate vehicle detection is a critical component of autonomous driving, traffic surveillance, and intelligent transportation systems. This paper presents an enhanced YOLOv8n-based model that integrates the Ghost Module, Convolutional Block Attention Module (CBAM), and Deformable Convolutional Networks v2 (DCNv2) to improve detection performance. The Ghost Module reduces feature redundancy through efficient feature generation, CBAM refines feature representation via channel and spatial attention, and DCNv2 enhances adaptability to geometric variations in vehicle structures. Evaluated on the KITTI dataset, the proposed model achieves 95.4% mAP@0.5, representing an 8.97% improvement over the baseline YOLOv8n, along with 96.2% precision, 93.7% recall, and a 94.93% F1-score. Comparative analysis against seven state-of-the-art detectors demonstrates consistent superiority across key performance metrics, while ablation studies validate the individual and combined contributions of the integrated modules. By addressing feature redundancy, attention refinement, and spatial adaptability, the proposed approach offers a robust and computationally efficient solution for vehicle detection in diverse and complex traffic environments.

Encoder-Decoder architectures are widely used in deep learning-based Deformable Image Registration (DIR), where the encoder extracts multi-scale features and the decoder predicts deformation fields by recovering spatial locations. However, current methods lack specialized extraction of features (that are useful for registration) and predict deformation jointly and homogeneously in all three directions. In this paper, we propose a novel expert-guided DIR network with Mixture of Experts (MoE) mechanism applied in both encoder and decoder, named SHMoAReg. Specifically, we incorporate Mixture of Attention heads (MoA) into encoder layers, while Spatial Heterogeneous Mixture of Experts (SHMoE) into the decoder layers. The MoA enhances the specialization of feature extraction by dynamically selecting the optimal combination of attention heads for each image token. Meanwhile, the SHMoE predicts deformation fields heterogeneously in three directions for each voxel using experts with varying kernel sizes. Extensive experiments conducted on two publicly available datasets show consistent improvements over various methods, with a notable increase from 60.58% to 65.58% in Dice score for the abdominal CT dataset. Furthermore, SHMoAReg enhances model interpretability by differentiating experts' utilities across/within different resolution layers. To the best of our knowledge, we are the first to introduce MoE mechanism into DIR tasks.

Imaging through inhomogeneous media often results in severe distortions, posing significant challenges to downstream image-processing tasks. The lack of clean paired images makes supervised learning impractical, motivating unsupervised restoration approaches. In this work, we propose the Circular Quasi-Conformal Deturbulence (CQCD) framework, an unsupervised approach that reconstructs distortion-free images from multiple frames using a circular architecture. The framework minimizes reconstruction errors by jointly estimating forward and backward transformations between distorted observations and the restored image. A key advancement of CQCD is the integration of computational quasi-conformal geometry, which encourages bijective non-rigid deformations and improves the well-posedness of both forward and inverse mappings for cycle consistency. The deformation field is further regularized to preserve structural coherence and reduce non-physical artifacts such as folding or tearing. Additionally, tight-frame blocks are employed to effectively encode distortion-sensitive features, enhancing the precision of the restoration process. To assess the effectiveness of the proposed framework, extensive evaluations are conducted on synthetic and real-world image datasets. Experimental findings indicate that CQCD not only surpasses existing state-of-the-art deturbulence techniques in restoration quality but also achieves highly accurate deformation field estimation.