Reconstructing anatomically faithful vascular structures from clinically accessible imaging modalities is of substantial clinical significance. However, existing cross-modal translation methods mainly emphasize pixel-level fidelity or visual realism and treat structure preservation as a property of the final output rather than an invariant of the generative process. This limitation often leads to structural discontinuities and artifacts, compromising anatomical coherence and clinical reliability. In this work, we propose a Structure-Preserving Mean Flow (SPMF) framework that formulates vascular image translation as a topology-invariant transport process. Based on a structural invariance principle, we derive an orthogonality constraint on the flow velocity field that formally separates appearance transport from topological distortion. We implement this constraint as a time-weighted surrogate objective within a Brownian bridge diffusion model to preserve topology at every diffusion step. Moreover, we propose a Prototype-Guided Structural Refinement (PGSR) module to align degraded inference-time structures with reliable training-time structures. Experiments on paired NIRII-to-2PF and fundus datasets demonstrate consistent improvements over state-of-the-art methods, achieving peak PSNR values of 24.96 dB and 24.83 dB, respectively.
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.
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.
Alexander Kolpakov, Igor Rivincs.LG cs.AI cs.SE cs.SI
Dimensionality reduction methods such as UMAP and t-SNE are central tools for visualising high-dimensional data, but their local-neighborhood objectives can preserve sampling noise while distorting global topology. We show that standard local metrics reward this noise memorisation: top-performing embeddings invent cycles and disconnected islands absent from the data. We introduce a topology-faithfulness benchmark based on noisy manifolds with known homology, tune DiRe against it, and find Pareto-optimal configurations that match or beat GPU-accelerated UMAP on classification while recovering exact first Betti numbers on stress tests. On 723K arXiv paper embeddings, DiRe preserves 3-4 times more topological structure than UMAP at comparable wall-clock.