Topological mapping offers a compact and robust representation for navigation, but progress in the field is hindered by the lack of standardized evaluation metrics, datasets, and protocols. Existing systems are assessed using different environments and criteria, preventing fair and reproducible comparisons. Moreover, a key challenge - perceptual aliasing - remains under-quantified, despite its strong influence on system performance. We address these gaps by (1) formalizing topological consistency as the fundamental property of topological maps and showing that localization accuracy provides an efficient and interpretable surrogate metric, and (2) proposing the first quantitative measure of dataset ambiguity to enable fair comparisons across environments. To support this protocol, we curate a diverse benchmark dataset with calibrated ambiguity levels, implement and release deep-learned baseline systems, and evaluate them alongside classical methods. Our experiments and analysis yield new insights into the limitations of current approaches under perceptual aliasing. All datasets, baselines, and evaluation tools are fully open-sourced to foster consistent and reproducible research in topological mapping.

Accurate cardiac mesh reconstruction from volumetric data is essential for personalized cardiac modeling and clinical analysis. However, existing deformation-based approaches are prone to topological inconsistencies, particularly membrane penetration, which undermines the anatomical plausibility of the reconstructed mesh. To address this issue, we introduce Topology-Preserving Mesh Loss (TPM Loss), a novel loss function that explicitly enforces topological constraints during mesh deformation. By identifying topology-violating points, TPM Loss ensures spatially consistent reconstructions. Extensive experiments on CT and MRI datasets show that TPM Loss reduces topology violations by up to 93.1% while maintaining high segmentation accuracy (DSC: 89.1%- 92.9%) and improving mesh fidelity (Chamfer Distance reduction up to 0.26 mm). These results demonstrate that TPM Loss effectively prevents membrane penetration and significantly improves cardiac mesh quality, enabling more accurate and anatomically consistent cardiac reconstructions. The implementation is publicly available at GitHub Repository.

Enhancing the precision of segmenting coronary atherosclerotic plaques from CT Angiography (CTA) images is pivotal for advanced Coronary Atherosclerosis Analysis (CAA), which distinctively relies on the analysis of vessel cross-section images reconstructed via Curved Planar Reformation. This task presents significant challenges due to the indistinct boundaries and structures of plaques and blood vessels, leading to the inadequate performance of current deep learning models, compounded by the inherent difficulty in annotating such complex data. To address these issues, we propose a novel dual-consistency semi-supervised framework that integrates Intra-frame Topological Consistency (ITC) and Cross-frame Topological Consistency (CTC) to leverage labeled and unlabeled data. ITC employs a dual-task network for simultaneous segmentation mask and Skeleton-aware Distance Transform (SDT) prediction, achieving similar prediction of topology structure through consistency constraint without additional annotations. Meanwhile, CTC utilizes an unsupervised estimator for analyzing pixel flow between skeletons and boundaries of adjacent frames, ensuring spatial continuity. Experiments on two CTA datasets show that our method surpasses existing semi-supervised methods and approaches the performance of supervised methods on CAA. In addition, our method also performs better than other methods on the ACDC dataset, demonstrating its generalization.

--Network alignment task, which aims to identify corresponding nodes in different networks, is of great significance for many subsequent applications. Without the need for labeled anchor links, unsupervised alignment methods have been attracting more and more attention. However, the topological consistency assumptions defined by existing methods are generally low-order and less accurate because only the edge-indiscriminative topological pattern is considered, which is especially risky in an unsupervised setting. T o reposition the focus of the alignment process from low-order to higher-order topological consistency, in this paper, we propose a fully unsupervised network alignment framework named HTC. The proposed higher-order topological consistency is formulated based on edge orbits, which is merged into the information aggregation process of a graph convolutional network so that the alignment consistencies are transformed into the similarity of node embeddings. Furthermore, the encoder is trained to be multi-orbit-aware and then be refined to identify more trusted anchor links. Node correspondence is comprehensively evaluated by integrating all different orders of consistency. In addition to sound theoretical analysis, the superiority of the proposed method is also empirically demonstrated through extensive experimental evaluation. On three pairs of real-world datasets and two pairs of synthetic datasets, our HTC consistently outperforms a wide variety of unsupervised and supervised methods with the least or comparable time consumption. It also exhibits robustness to structural noise as a result of our multi-orbit-aware training mechanism. Network alignment task, which aims to identify entity correspondence across different networks, is usually the very first step of many downstream analyzing tasks. For instance, recognizing the same user on different social networks can facilitate friend suggestion, item recommendation, personalized advertisement [1]-[5]. Similar scenarios also exist widely in other fields, such as protein network analysis [6], knowledge discovery [7], etc. Identifying corresponding nodes across different networks is an extremely hard task, even for humans. Manually labelling correspondence can be prohibitively challenging, expensive (in human efforts, time, and money costs), and tedious [8]. Due to such obstacles, in some cases, it may be impractical to get access to sufficient labels for training well-performed supervised or even semi-supervised models [4], [9]. By contrast, unsupervised models can be trained without the need for labeled data, which is more flexible and practical in real-world application scenarios. Thus, unsupervised alignment methods have been drawing a surge of interest recently [10]-[12].

Motivated by the challenging segmentation task of pancreatic tubular networks, this paper tackles two commonly encountered problems in biomedical imaging: Topological consistency of the segmentation, and expensive or difficult annotation. Our contributions are the following: a) We propose a topological score which measures both topological and geometric consistency between the predicted and ground truth segmentations, applied to model selection and validation. b) We provide a full deep-learning methodology for this difficult noisy task on time-series image data. In our method, we first use a semisupervised U-net architecture, applicable to generic segmentation tasks, which jointly trains an autoencoder and a segmentation network. We then use tracking of loops over time to further improve the predicted topology. This semi-supervised approach allows us to utilize unannotated data to learn feature representations that generalize to test data with high variability, in spite of our annotated training data having very limited variation. Our contributions are validated on a challenging segmentation task, locating tubular structures in the fetal pancreas from noisy live imaging confocal microscopy. We show that our semi-supervised model outperforms not only fully supervised and pre-trained models but also an approach which takes topological consistency into account during training. Further, our approach achieves a mean loop score of 0.808 for detecting loops in the fetal pancreas, compared to a U-net trained with clDice with mean loop score 0.762.

Generative Adversarial Networks (GANs) have been widely adopted in various fields. However, existing GANs generally are not able to preserve the manifold of data space, mainly due to the simple representation of discriminator for the real/generated data. To address such open challenges, this paper proposes Manifold-preserved GANs (MaF-GANs), which generalize Wasserstein GANs into high-dimensional form. Specifically, to improve the representation of data, the discriminator in MaF-GANs is designed to map data into a high-dimensional manifold. Furthermore, to stabilize the training of MaF-GANs, an operation with precise and universal solution for any K-Lipschitz continuity, called Topological Consistency is proposed. The effectiveness of the proposed method is justified by both theoretical analysis and empirical results. When adopting DCGAN as the backbone on CelebA (256*256), the proposed method achieved 12.43 FID, which outperforms the state-of-the-art model like Realness GAN (23.51 FID) by a large margin. Code will be made publicly available.

Traditional online maps, widely used on Internet such as Google map and Baidu map, are rendered from vector data. Timely updating online maps from vector data, of which the generating is time-consuming, is a difficult mission. It is a shortcut to generate online maps in time from remote sensing images, which can be acquired timely without vector data. However, this mission used to be challenging or even impossible. Inspired by image-to-image translation (img2img) techniques based on generative adversarial network (GAN), we propose a semi-supervised structure-augmented online map GAN (S$^{2}$OMGAN) model to generate online maps directly from remote sensing images. In this model, we designed a semi-supervised learning strategy to pre-train S$^{2}$OMGAN on rich unpaired samples and finetune it on limited paired samples in reality. We also designed image gradient L1 loss and image gradient structure loss to generate an online map with global topological relationship and detailed edge curves of objects, which are important in cartography. Moreover, we propose edge structural similarity index (ESSI) as a metric to evaluate the quality of topological consistency between generated online maps and ground truths. Experimental results present that S$^{2}$OMGAN outperforms state-of-the-art (SOTA) works according to mean squared error, structural similarity index and ESSI. Also, S$^{2}$OMGAN wins more approval than SOTA in the human perceptual test on visual realism of cartography. Our work shows that S$^{2}$OMGAN is potentially a new paradigm to produce online maps. Our implementation of the S$^{2}$OMGAN is available at \url{https://github.com/imcsq/S2OMGAN}.

Phylogenetic tree inference using deep DNA sequencing is reshaping our understanding of rapidly evolving systems, such as the within-host battle between viruses and the immune system. Densely sampled phylogenetic trees can contain special features, including "sampled ancestors" in which we sequence a genotype along with its direct descendants, and "polytomies" in which multiple descendants arise simultaneously. These features are apparent after identifying zero-length branches in the tree. However, current maximum-likelihood based approaches are not capable of revealing such zero-length branches. In this paper, we find these zero-length branches by introducing adaptive-LASSO-type regularization estimators to phylogenetics, deriving their properties, and showing regularization to be a practically useful approach for phylogenetics.