arXiv subjects

Guangyu Meng

Publications and source records attributed to Guangyu Meng.

9 recordsLinked to original sources

arXiv2026

CuPH: Parallel Cubical Persistent Homology via Level-Synchronous Component Tracking

Persistent homology (PH) is a mathematically principled multi-scale topological descriptor of shape and connectivity in data. It is widely applied in image classification, segmentation, and shape analysis across medical and aerial imaging, providing structural information that pixel-wise deep learning may overlook. Standard cubical PH decomposes an image into cubical cells (vertices, edges, and squares) and reduces them sequentially in filtration order. This sequential reduction has $Θ(n)$ parallel depth for an $n$-pixel image, limiting within-image GPU parallelism and constraining its use in topology-aware deep learning. We introduce CuPH, a GPU-based parallel algorithm for computing cubical PH on 2D images that operates directly on pixels rather than cubical cells. CuPH buckets pixels by filtration values, activates them with a level-synchronous sweep, and tracks connected components with a lock-free union-find method. We prove that CuPH produces persistence diagrams identical to standard cubical PH on integer inputs, with a stability bound for floating-point inputs. CuPH reduces parallel depth from $Θ(n)$ to $O(L\log n)$ for an image with $L$ intensity levels. We implement the level sweep as a single CUDA kernel, eliminating cross-level kernel-launch overhead. Empirically, CuPH is $18.6$--$99.6\times$ faster than the existing GPU baseline (CMP). As a drop-in PH backend, CuPH accelerates topology-aware classification ($4.2$--$16.7\times$) and segmentation ($8.3$--$44\times$) while preserving accuracy. It also enables computing full-image PH losses on high-resolution images, improving segmentation Dice by $2.2$--$4.6$ points over patch-local PH baselines and accelerating training by $25$--$31\times$.

cs.CV↗

arXiv2026

MS-COOT: Comparing Morse-Smale Complexes with Co-Optimal Transport

Understanding and comparing structures in scalar fields is a central challenge in scientific visualization, with applications ranging from feature analysis to temporal and structural comparison. The Morse-Smale (MS) complex provides a natural representation by decomposing a scalar field into regions induced by gradient flow. However, existing approaches typically rely on graph-based representations, matching critical points without explicitly establishing correspondences between regions. In this work, we represent the MS complex as a hypergraph, where critical points form nodes and regions define hyperedges. We introduce MS-COOT, a co-optimal transport distance that jointly computes correspondences between critical points and regions. This formulation enables explicit region-to-region matching within a distance-based framework, allowing identification of region-level events such as splitting and merging. We instantiate this framework with domain-specific components, including a hypernetwork function encoding relationships between critical points and regions, persistence-based probability measures, and a sample cost term that incorporates critical point attributes. We evaluate MS-COOT on datasets spanning 2D simulations, 3D surface meshes, and volumetric data. Our results show that MS-COOT provides distinct characterization of certain region-level structural changes compared to graph-based distances, achieves competitive accuracy in shape classification, and improves classification of simulation parameter settings in a 3D ensemble.

cs.GR↗

arXiv2026

VTRL-Med: Progressive Visual Refinement with Topology-Guided Regularization for Medical Image Clustering

Deep clustering offers a promising approach for analyzing large unlabeled medical image datasets, yet prevailing methods still face two limitations: they may neglect class-agnostic structural priors that capture object boundaries and regions, and they do not explicitly encode topological patterns (e.g., connectivity and holes). These sources of information play distinct and complementary roles: visual-structural features provide the primary discriminative representation for clustering, while topological features provide additional global geometric cues for residual visual ambiguities. We introduce VTRL-Med, a progressive visual-structural learning framework with topology-guided regularization for medical image clustering. VTRL-Med first adapts the Segment Anything Model (SAM) to extract image features that retain structural cues inherited from mask-supervised pretraining. It then generates reliable pseudo-labels through a two-step filtering process that combines prototype-based selection with k-nearest neighbor consistency validation. Finally, it progressively refines the visual branch while an auxiliary topology branch, constructed from persistent homology (PH) descriptors, provides additional geometric regularization during training. Across 13 medical image benchmarks, VTRL-Med achieves state-of-the-art clustering performance, improving average accuracy by 4.48% over existing methods. On three representative datasets, topology-guided regularization further improves accuracy by 1.3--4.3% over visual refinement alone.

cs.CV↗

arXiv2026

TopoAgent: An Agentic Framework for Automated Topology Learning in Medical Imaging

Topological data analysis (TDA), particularly persistent homology (PH), captures geometric structural properties in medical images (e.g., connected components, loops, shape characteristics), which conventional pixel-level deep learning approaches often neglect. While many topological descriptors are known for converting persistence diagrams (PDs) or raw images into topological feature vectors, existing methods mostly default to a single fixed descriptor (e.g., persistence images), leaving the diversity of topological representations largely unexplored. To the best of our knowledge, there is no known large language model (LLM)-based agentic framework that can automatically determine the most suitable topological descriptors for a given image dataset and produce the corresponding topological feature vectors for downstream tasks. To fill this gap, we propose \textbf{TopoAgent}, an LLM-based agentic framework that automates topology learning for medical image analysis.TopoAgent operates through a Perception--Reasoning--Action--Reflection loop supported by 21 domain-specific tools and dual memory that accumulates experience across runs. Its skill set is distilled from systematic evaluation of 15 topological descriptors across 26 datasets with six classifiers. TopoAgent analyzes input images and their topological characteristics, reasons about which topological descriptors best suit the input, and determines the optimal descriptor and its configuration, all without task-specific training.

cs.CV↗

arXiv2026

TopoCL: Topological Contrastive Learning for Medical Imaging

Contrastive learning (CL) has become a powerful approach for learning representations from unlabeled images. However, existing CL methods focus predominantly on visual appearance features while neglecting topological characteristics (e.g., connectivity patterns, boundary configurations, cavity formations) that provide valuable cues for medical image analysis. To address this limitation, we propose a new topological CL framework (TopoCL) that explicitly exploits topological structures during contrastive learning for medical imaging. Specifically, we first introduce topology-aware augmentations that control topological perturbations using a relative bottleneck distance between persistence diagrams, preserving medically relevant topological properties while enabling controlled structural variations. We then design a Hierarchical Topology Encoder that captures topological features through self-attention and cross-attention mechanisms. Finally, we develop an adaptive mixture-of-experts (MoE) module to dynamically integrate visual and topological representations. TopoCL can be seamlessly integrated with existing CL methods. We evaluate TopoCL on five representative CL methods (SimCLR, MoCo-v3, BYOL, DINO, and Barlow Twins) and five diverse medical image classification datasets. The experimental results show that TopoCL achieves consistent improvements: an average gain of +3.26% in linear probe classification accuracy with strong statistical significance, verifying its effectiveness.

cs.CV↗

arXiv2025

A Psychology-based Unified Dynamic Framework for Curriculum Learning

Directly learning from examples of varying difficulty levels is often challenging for both humans and machine learning models. A more effective strategy involves exposing learners to examples in a progressive order from easy to difficult. Curriculum Learning (CL) has been proposed to implement this strategy in machine learning model training. However, two key challenges persist in CL framework design: defining the difficulty of training data and determining the appropriate amount of data to input at each training step. Drawing inspiration from psychometrics, this paper presents a Psychology-based Unified Dynamic Framework for Curriculum Learning (PUDF). We quantify the difficulty of training data by applying Item Response Theory (IRT) to responses from Artificial Crowds (AC). This theory-driven IRT-AC approach leads to global (i.e., model-independent) and interpretable difficulty values. Leveraging IRT, we propose a training strategy, Dynamic Data Selection via Model Ability Estimation (DDS-MAE), to schedule the appropriate amount of data during model training. Since our difficulty labeling and model ability estimation are based on a consistent theory, namely IRT, their values are comparable within the same scope, potentially leading to aligned training data selection and faster convergence compared to the other CL methods. Experimental results demonstrate that fine-tuning pre-trained large language models with PUDF leads to higher accuracy and faster convergence on a suite of benchmark datasets compared to standard fine-tuning and state-of-the-art CL methods. Ablation studies and downstream analyses further validate the impact of PUDF for CL.

cs.CL↗

arXiv2025

Cell Instance Segmentation: The Devil Is in the Boundaries

State-of-the-art (SOTA) methods for cell instance segmentation are based on deep learning (DL) semantic segmentation approaches, focusing on distinguishing foreground pixels from background pixels. In order to identify cell instances from foreground pixels (e.g., pixel clustering), most methods decompose instance information into pixel-wise objectives, such as distances to foreground-background boundaries (distance maps), heat gradients with the center point as heat source (heat diffusion maps), and distances from the center point to foreground-background boundaries with fixed angles (star-shaped polygons). However, pixel-wise objectives may lose significant geometric properties of the cell instances, such as shape, curvature, and convexity, which require a collection of pixels to represent. To address this challenge, we present a novel pixel clustering method, called Ceb (for Cell boundaries), to leverage cell boundary features and labels to divide foreground pixels into cell instances. Starting with probability maps generated from semantic segmentation, Ceb first extracts potential foreground-foreground boundaries with a revised Watershed algorithm. For each boundary candidate, a boundary feature representation (called boundary signature) is constructed by sampling pixels from the current foreground-foreground boundary as well as the neighboring background-foreground boundaries. Next, a boundary classifier is used to predict its binary boundary label based on the corresponding boundary signature. Finally, cell instances are obtained by dividing or merging neighboring regions based on the predicted boundary labels. Extensive experiments on six datasets demonstrate that Ceb outperforms existing pixel clustering methods on semantic segmentation probability maps. Moreover, Ceb achieves highly competitive performance compared to SOTA cell instance segmentation methods.

cs.CV↗

arXiv2025

A Stable and Theoretically Grounded Gromov-Wasserstein Distance for Reeb Graph Comparison using Persistence Images

Reeb graphs are a fundamental structure for analyzing the topological and geometric properties of scalar fields. Comparing Reeb graphs is crucial for advancing research in this domain, yet existing metrics are often computationally prohibitive or fail to capture essential topological features effectively. In this paper, we explore the application of the Gromov-Wasserstein distance, a versatile metric for comparing metric measure spaces, to Reeb graphs. We propose a framework integrating a symmetric variant of the Reeb radius for robust geometric comparison, and a novel probabilistic weighting scheme based on Persistence Images derived from extended persistence diagrams to effectively incorporate topological significance. A key contribution of this work is the rigorous theoretical proof of the stability of our proposed Reeb Gromov-Wasserstein distance with respect to perturbations in the underlying scalar fields. This ensures that small changes in the input data lead to small changes in the computed distance between Reeb graphs, a critical property for reliable analysis. We demonstrate the advantages of our approach, including its enhanced ability to capture topological features and its proven stability, through comparisons with other alternatives on several datasets, showcasing its practical utility and theoretical soundness.

cs.CG↗

arXiv2025

Efficient approximation of Earth Mover's Distance Based on Nearest Neighbor Search

Earth Mover's Distance (EMD) is an important similarity measure between two distributions, used in computer vision and many other application domains. However, its exact calculation is computationally and memory intensive, which hinders its scalability and applicability for large-scale problems. Various approximate EMD algorithms have been proposed to reduce computational costs, but they suffer lower accuracy and may require additional memory usage or manual parameter tuning. In this paper, we present a novel approach, NNS-EMD, to approximate EMD using Nearest Neighbor Search (NNS), in order to achieve high accuracy, low time complexity, and high memory efficiency. The NNS operation reduces the number of data points compared in each NNS iteration and offers opportunities for parallel processing. We further accelerate NNS-EMD via vectorization on GPU, which is especially beneficial for large datasets. We compare NNS-EMD with both the exact EMD and state-of-the-art approximate EMD algorithms on image classification and retrieval tasks. We also apply NNS-EMD to calculate transport mapping and realize color transfer between images. NNS-EMD can be 44x to 135x faster than the exact EMD implementation, and achieves superior accuracy, speedup, and memory efficiency over existing approximate EMD methods.

cs.CV↗