Topology-Preserving Image Segmentation

Multi-structure segmentation of the uterus is important for computer-assisted screening, diagnosis, and treatment planning of uterine diseases, where ultrasound and MRI provide complementary clinical information. However, developing a unified model across these modalities is challenging due to their substantially different image appearances, anatomical contexts, spatial resolutions, and label spaces. Moreover, existing datasets often define different segmentation targets, making joint learning challenging and potentially leading to negative transfer across heterogeneous tasks. To this end, we propose a Topology-informed Prompt-conditioned Universal Segmentation (TPUS) framework for segmenting multiple uterine structures across ultrasound and MRI. TPUS introduces a graph-based multi-dataset backbone comprising modality-specific stems and a modality-shared graph-based encoder-decoder to support modality-sensitive input adaptation, structural feature reasoning, and joint representation learning across heterogeneous uterine segmentation tasks. In addition, TPUS uses task-aware class prompts to condition the segmentation process for different datasets and label spaces, a dynamic convolutional adaptation module to generate task-specific output responses, and a topology-informed loss to encourage anatomically consistent predictions. Experiments on a uterine ultrasound dataset and a T2-weighted uterine myoma MRI dataset demonstrate that TPUS achieves Dice scores of 0.898 and 0.693 on the two held-out test sets, respectively, outperforming several generic and universal segmentation baselines. Source code can be accessed at https://github.com/YonghengSun1997/TPUS.

Persistent homology (PH) is a frequently used tool for extracting and preserving topological information from image data, particularly in image segmentation, where preservation of topological structures is important. However, despite its general applicability across dimensionality, domains, and target structures, the runtime cost of PH-based methods often makes their practical use infeasible. In this work, we argue that this runtime cost is largely driven by processing information that is unimportant for downstream application (e.g. as optimization objective). We propose sparse cubical filtrations as an alternative foundation for PH computation, reducing subsequent computational costs by factors of up to 100 on real datasets. We show close agreement with the optimization signal of the dense counterpart and empirically evaluate our solution's effectiveness as an optimization objective in realistic training regimes where other PH-based objectives can practically not operate (i.e., 3D data with large patch sizes). We show how our solution improves topological accuracy by up to 80% across six diverse datasets while maintaining pixel- and region-based accuracy.

Vessel segmentation is commonly optimized as voxel-wise classification, but small local errors can strongly disrupt vascular connectivity while having little effect on overlap scores. This is particularly problematic for downstream analyses that rely on centerlines, branches, connected components, or graph structure. We propose a mesh-guided post-processing framework for repairing broken vessel segmentations produced by nnU-Net. For each predicted binary mask, a deformable template mesh is fitted to the mask surface in physical space and used as a case-specific geometric scaffold. The fitted mesh is not voxelized as the final segmentation; instead, it guides conservative reconnection of disconnected components by proposing or validating thin bridge candidates under foreground-growth constraints. We evaluated this approach in three vascular anatomies using AortaSeg24 and SEGA for the aorta, TopCoW for the Circle of Willis, and PARSE for the pulmonary arteries. Performance is measured using Dice, connected-component Dice (ccDice), and the Betti-0 number. Across these datasets, repair substantially improved connectivity while preserving overlap: Dice remained nearly unchanged, whereas ccDice increased from 0.596 to 0.992 for aorta, from 0.722 to 0.835 for TopCoW, and from 0.028 to 0.862 for PARSE. The FOMAML meta-initialization further accelerated the fitting per-case, supporting practical mesh-based repair of the vascular topology. These results suggest that explicit mesh representations can provide a useful geometric prior for correcting topological failures in otherwise accurate voxel segmentations.

Vessel segmentation in X-ray coronary angiography (XCA) is a fundamental step for quantitative coronary analysis and subsequent assessment of coronary artery disease. However, accurate vessel segmentation remains challenging because of imaging noise, complex bifurcations, and the overlap of vessels and background structures, which can lead to disrupted vascular connectivity and missed small branches. In this work, we propose BSC-Net, a ResNet-U-Net-based framework tailored to improve small-vessel representation and repair vascular structural continuity. BSC-Net enhances small-vessel representation through targeted sampling and improves vascular structural continuity by integrating long-range contextual modeling and Edge-Informed Loss (EIL). BSC-Net was validated on two public XCA datasets, demonstrating state-of-the-art (SOTA) performance in coronary vessel segmentation with Dice and IoU scores of 77.8%/90.6% and 64.5%/83.0%, respectively. Furthermore, based on the obtained vessel segmentation, we performed automated quantitative coronary analysis and derived clinically relevant morphological and hemodynamic parameters, including stenosis ratio, time-to-peak, and relative propagation velocity. These results demonstrate that BSC-Net produces accurate vessel segmentation results with preserved vascular continuity for quantitative coronary assessment, enabling reliable downstream analysis and clinical evaluation of coronary artery disease.

Accurate segmentation of vascular structures in digital subtraction angiography (DSA) images remains challenging due to the thin, elongated, and branching nature of blood vessels. Pixel-wise deep learning approaches such as U-Net achieve strong general-purpose segmentation performance but often produce fragmented or discontinuous predictions in fine vascular regions, since they do not explicitly enforce structural connectivity. Region growing algorithms preserve spatial context and topological continuity, but are highly sensitive to seed point initialization and can be computationally expensive. We propose UI-VISA (U-Net Initialized Vascular Image Segmentation Architecture), a hybrid pipeline that combines the complementary strengths of both approaches. UI-VISA uses U-Net's foreground predictions as informed seed points for a CNN-guided region growing algorithm, which then iteratively refines the segmentation by enforcing local connectivity and recovering fine vessel details that U-Net alone tends to miss or over-predict. We evaluate UI-VISA against standalone U-Net and a prior region-growing-based method (VISA) using 5-fold cross-validation on 26 DSA images. UI-VISA achieves the highest mean Dice and clDice scores across folds, and a paired Wilcoxon signed-rank test shows the improvement in clDice is statistically significant ($p=0.023$), consistent with the method's design goal of preserving vascular connectivity, while the improvement in Dice does not reach significance ($p=0.104$).

Accurate 3D neuron segmentation in fluorescence microscopy is critical for neuroscience. However, the sparse and elongated morphology of neurons poses significant challenges to existing segmentation methods. These methods struggle to preserve both local details and global topology, leading to fragmented results. To address this, we propose NeuroRefiner, a multi-agent system that formalizes the human expert workflow involving iterative global observation and local editing. Specifically, NeuroRefiner comprises three collaborative agents dedicated to diagnosing topological errors, generating correction instructions, and validating refinement quality. To facilitate agent instruction-guided segmentation refinement, we propose TopoRefineNet, a dedicated 3D U-Net-based tool that leverages cross-modality feature fusion to generate refined masks. Through multi-round agent reasoning and voxel-level editing, NeuroRefiner produces topologically more accurate segmentations with enhanced interpretability. Experiments on the BigNeuron, CWMBS, and ZBFWB datasets demonstrate that NeuroRefiner outperforms state-of-the-art methods, notably achieving a 3.02% improvement in F1 score on the challenging ZBFWB dataset.

Accurate crack assessment in electroluminescence (EL) images is important for photovoltaic (PV) reliability analysis, yet existing segmentation methods often fail to capture the thin, elongated, and structurally constrained nature of crack defects. This paper proposes a Solar Topology Crack Network (STC-Net) that incorporates edge priors, spectral priors, and a boundary-topology refinement module to improve crack continuity and boundary preservation. The framework further extends segmentation to power-loss estimation by deriving a crack-associated inactive-area proxy from the predicted masks. Experiments on the PVEL-S dataset show that STC-Net achieves 95.98 MIoU, 98.01 MDice, and 98.00 MAcc during training, and 72.52 MIoU and 80.16 MDice on unseen test samples. These results demonstrate that STC-Net provides accurate crack localization while offering a practical link between EL-based defect segmentation and PV degradation assessment.

Fractional flow reserve derived from CT angiography (FFR-CT) simulates flow through a patient-specific vessel model, so its accuracy depends on the connectedness of the segmented tree, not only on volumetric overlap: a segmentation can reach high Dice yet sever a bifurcation, dropping the downstream subtree and reversing the treatment decision. Topology-aware losses such as clDice and Skeleton Recall act on the global centreline and can miss localised breaks. We study the Bifurcation Connectedness Score (BCS), which scores connectedness at each ground-truth bifurcation, and soft-BCS, its differentiable training surrogate. BCS captures a property of segmentation quality the standard metrics miss: it responds strongly to breaks in connectedness while staying largely unchanged under connectedness-preserving narrowing. Higher BCS accompanies closer agreement between the FFR-CT decisions a solver makes on predicted versus ground-truth geometry, most clearly in severe disease (OR 2.16, CI [1.23, 4.18]). Both decisions come from the same solver, so this reflects geometric, not clinical, fidelity. In training, soft-BCS and Skeleton Recall recover the same branches but build different trees. Recovering branches and keeping them connected are separable properties, so we recommend reporting a measure of each.

Segmenting slender curvilinear structures such as retinal vessels, cracks, and roads demands topological correctness, as even a single-pixel discontinuity can fragment a continuous network and invalidate downstream analysis. Under standard binary-mask supervision, models optimized for pixel-level overlap frequently produce topologically broken predictions. We trace this to a fundamental mismatch: pixel-wise losses distribute gradients uniformly, yet connectivity hinges on a sparse set of bottleneck pixels. These pixels are vastly outnumbered by thick structures and background, rendering their aggregate gradient contribution negligible. We term this phenomenon topological gradient starvation (TGS). To address it, we propose Widest-Path Reachability Fields (WPRF), a differentiable Max-Min reachability objective that redirects gradient flow to connectivity bottlenecks. The module is plug-and-play, backbone-agnostic, and incurs no inference overhead. WPRF implements a differentiable Max-Min objective via dynamic programming on a domain-restricted graph, coupled with a bottleneck-aware observation term that balances gradient contributions across varying structures. Compared to prior topology-aware losses that rely on post-hoc skeletonization or homology computation, WPRF directly optimizes end-to-end reachability via differentiable Max-Min algebra, enabling gradient flow to concentrate on connectivity bottlenecks without auxiliary structures. We introduce OMVIS, a new oral microvessel segmentation dataset. Experiments across nine architectures and six datasets validate the bottleneck-focused gradient routing mechanism. WPRF improves 87% of experiments with fixed hyperparameters and achieves clDice gains of 7.2 percentage points on structurally fragile datasets.

Accurate pulmonary vessel segmentation remains challenging due to the sparse, tortuous, and multi-scale nature of vascular structures, where small branches are easily lost and topology integrity is difficult to preserve under voxel-wise supervision. Existing deep segmentation models primarily optimize binary masks, lacking explicit geometric constraints, thus struggling to recover continuous tubular morphology and fine vascular connectivity. In this study, we introduce MorVess, a morphology-aware segmentation framework that integrates differentiable geometric priors with large-scale foundation model adaptation to achieve fine-grained vascular parsing. MorVess jointly predicts vessel masks, distance maps, and thickness maps, providing explicit supervision for vascular boundaries, centerline consistency, and smooth diameter transitions. A lightweight 2.5D adapter bridges 3D spatial context and 2D SAM representations, while a global-local fusion block aggregates multi-level semantics and geometric cues for high-fidelity topology reconstruction. Across two challenging pulmonary CT benchmarks, MorVess delivers superior Dice, clDice, and HD95 scores, substantially improving small-vessel recovery and global connectivity. These results demonstrate that embedding geometric intelligence into pretrained vision models offers a principled and scalable pathway toward precise vessel analysis and clinically reliable structural quantification. Our source code is available at https://github.com/MaoFuyou/MorVess.

Curvilinear object segmentation, including vessels and cracks, is challenging due to extreme spatial sparsity and topological fragility, where small local errors can cause severe structural disconnections. Meanwhile, modern segmentation pipelines increasingly rely on strong but hard-to-modify foundation encoders whose heavy downsampling limits fine structural recovery. Motivated by this, we focus on the post-encoder stage and study two recurring and actionable failure modes: a reconstruction bottleneck in high-resolution feature restoration and a decision bottleneck in binarization. We present PEPA, a lightweight Post-Encoder Plug-in Adapter for 2D curvilinear segmentation pipelines with accessible decoder/head features and target, query, or class descriptors. PEPA couples (i) Target-Conditioned Snake Upsampling (TCSU), which uses target-conditioned continuous snake-like sampling to better recover thin and tortuous structures during upsampling, and (ii) Target-Adaptive Differentiable Thresholding (TADT), which predicts target-specific thresholds and optimizes a soft-threshold surrogate with explicit safeguards against trivial bias shifting. Under this post-encoder interface, PEPA can be attached to both prompt-based decoders and conventional dense predictors. Experiments on five medical and industrial benchmarks show that adding PEPA to frozen-encoder baselines yields consistent improvements, with gains in topological connectivity (clDice) typically exceeding those in region overlap (IoU), indicating improved structural continuity. With only $\sim$0.26M additional parameters, PEPA offers a practical post-encoder enhancement for structure-centric segmentation.

Thin-structure segmentation--power lines, cracks, lane markings at 1-3 pixel width--requires preserving connectivity that standard representations preclude: patching severs continuous structures and conventional superpixels merge thin targets into background before classification. Topology-aware losses penalize connectivity breaks at the objective level but cannot recover what the representation has already destroyed. We propose SEMIR, a framework that replaces the pixel lattice with a parameterized graph minor whose contraction map preserves thin-structure connectivity under the contraction criterion. The minor collapses millions of pixels into tens or hundreds of boundary-aligned supernodes, enabling full-resolution inference without patching at scales demonstrated up to 21 MP in this paper; a lightweight GNN classifies the reduced graph and an exact map lifts predictions to pixel resolution. One pipeline--identical architecture, features, loss, and GNN hyperparameters across all dataset--matches or exceeds domain-specific baselines on TTPLA (power lines), CrackSeg9k (pavement cracks), and SkyScapes Lane (aerial markings) on Dice, IoU, and Boundary F1 while reducing mask fragmentation by at least 4.6x relative to SLIC at matched inference.

Reliable crack assessment requires not only accurate pixel-level masks but also connected crack geometry and confidence estimates that remain stable under domain shift. However, existing segmentation models can achieve high overlap scores while fragmenting cracks, missing fine branches, and providing no calibrated uncertainty. To address this gap, this paper proposes CrackGeoFM, a multi-task framework that combines a frozen visual foundation backbone with crack-specific adaptation for mask prediction, skeleton reconstruction, and uncertainty estimation. The framework integrates a Frequency-Guided Crack Enhancement Module (FCEM) to enhance high-frequency crack cues, a Crack-Domain Feature Adaptation Module (CFAM) to adapt frozen backbone features to crack-domain patterns, and a Structure-Aware Multi-Task Decoder (SMTD) to jointly decode masks, skeletons, and uncertainty. Across 20 crack datasets, CrackGeoFM achieves state-of-the-art segmentation, improved topology preservation, calibrated uncertainty, and effective few-shot adaptation with only five labeled images. These results support reliable, generalizable, and engineering-oriented crack analysis for infrastructure assessment.

Accurate road segmentation from aerial imagery is fundamental to many geospatial applications. However, existing datasets often suffer from limited scene diversity, low semantic granularity, and poor structural continuity, restricting their generalization across environments. To address these challenges, we introduce WorldRoadSeg-360K, the largest and most diverse road segmentation dataset to date, comprising 366,947 high-resolution images collected from 38 countries and 223 cities across various terrains and continents. WorldRoadSeg-360K serves as a comprehensive benchmark and reveals key challenges in handling diverse and structurally complex scenes. Automated approaches often struggle to preserve road connectivity, while current interactive methods lack efficient, topology-sensitive tools for real-world road editing. To this end, we present RoadGIE, establishing a novel interactive paradigm for road extraction in remote sensing. Unlike prior point- or box-based prompting strategies, RoadGIE supports connectivity-aware prompts, including clicks and scribbles, which inherently align with the topology of road networks. To improve structural consistency and mitigate performance degradation during iterative interactions, RoadGIE integrates an expert-guided prompting strategy and adapts the skeleton-based recall loss for interactive scenarios. RoadGIE achieves state-of-the-art performance in both segmentation accuracy and topological consistency on WorldRoadSeg-360K and other benchmarks, while maintaining efficient operation with only 3.7M parameters. The code are publicly available at: https://github.com/chaineypung/RoadGIE

Segmenting small and sparse structures in large-scale images is fundamentally constrained by voxel-level, lattice-bound computation and extreme class imbalance -- dense, full-resolution inference scales poorly and forces most pipelines to rely on fixed regionization or downsampling, coupling computational cost to image resolution and attenuating boundary evidence precisely where minority structures are most informative. We introduce SEMIR (Semantic Minor-Induced Representation Learning), a representation framework that decouples inference from the native grid by learning a task-adapted, topology-preserving latent graph representation with exact decoding. SEMIR transforms the underlying grid graph into a compact, boundary-aligned graph minor through parameterized edge contraction, node deletion, and edge deletion, while preserving an exact lifting map from minor predictions to lattice labels. Minor construction is formalized as a few-shot structure learning problem that replaces hand-tuned preprocessing with a boundary-alignment objective: minor parameters are learned by maximizing agreement between predicted boundary elements and target-specific semantic edges under a boundary Dice criterion, and the induced minor is annotated with scale- and rotation-robust geometric and intensity descriptors and supports efficient region-level inference via message passing on a graph neural network (GNN) with relational edge features. We benchmark SEMIR on three tumor segmentation datasets -- BraTS 2021, KiTS23, and LiTS -- where targets exhibit high structural variability and distributional uncertainty. SEMIR yields consistent improvements in minority-structure Dice at practical runtime. More broadly, SEMIR establishes a framework for learning task-adapted, topology-preserving latent representations with exact decoding for high-resolution structured visual data.

We propose a topology-constrained quantized nnUNet framework for efficient and anatomically accurate 3D tooth segmentation, addressing the challenges of spatial distortion introduced by quantization in deep learning models. The proposed method integrates a novel tooth-specific topological loss into quantization-aware training, preserving critical anatomical structures such as tooth count, adjacency relationships, and cavity integrity while maintaining computational efficiency. The system employs an 8-bit quantized nnUNet backbone, where weights and activations are dynamically calibrated to minimize precision loss during inference. Furthermore, the topological loss combines connected-component analysis, adjacency consistency, and hole detection penalties, ensuring anatomical fidelity without modifying the underlying network architecture. The joint optimization objective harmonizes cross-entropy loss, quantization regularization, and topological constraints, enabling end-to-end training with gradient approximations for persistent homology terms. Experiments demonstrate that our approach significantly reduces topological errors compared to conventional quantized models, achieving clinically plausible segmentations on dental CBCT scans. The method retains the hardware efficiency of integer-only inference, making it suitable for deployment in resource-constrained clinical environments. This work bridges the gap between computational efficiency and anatomical precision in medical image segmentation, offering a practical solution for real-world dental applications.

Topological features play an essential role in ensuring geometric plausibility and structural consistency in image analysis tasks such as segmentation and skeletonization. However, integrating topology-preserving learning based on simple points into deep learning tasks remains challenging, as existing simple point detection methods are confined to binary images and are non-differentiable, rendering them incompatible with gradient-based optimization in modern deep learning. Moreover, morphological and purely data-driven approaches often fail to guaranty topological consistency. To address these limitations, we propose a novel method that directly computes simple points on continuous-valued images, enabling differentiable topological inference. Building on this theory, we develop an efficient skeleton extraction algorithm that preserves topological structures in binary and continuous-valued images. Furthermore, we design a variational model that enforces topological constraints by preserving topologically non-removable (i.e., non-simple) points, which can be seamlessly integrated into any deep neural network segmentation with softmax or sigmoid outputs. Experimental results demonstrate that the proposed approach effectively improves topological integrity and structural accuracy across multiple benchmarks. The codes are available in https://github.com/levnsio/CSP.

A levelset free but a hybrid image segmentation approach based on a modified version of the piece wise constant shape gradient of an Mumford Shah shape functional and a repulsive function is considered. The segmentation is performed a non-local shape based through an evolution of discrete curves driven by a non local shape based energy to segment images containing disjoint regions and multiple boundaries. This formulation has a novel additional component as a multivariable function dependent on a few sampled points of the curves that handles the occurrence of self intersection during boundary curves evolution. The method is applied to a few gray scale and color images, including images with nested structures and astronomical objects. The results indicate effective segmentation in complex scenarios with absolute control on the topology of the segments and self-intersections of the boundaries