Topological Correctness Research Articles

TopoPIS: Topology-constrained pipe instance segmentation via adaptive curvature convolution

Precise and fast pipe instance segmentation is a critical component in industrial automatic assembly, facilitating accurate object detection and pose estimation, optimizing and supervising the assembly process. However, this problem is challenging due to topological errors on fine-scale structures caused by the pipes being complex and slender. To address these challenges, we propose a topology-constrained pipe instance segmentation network (TopoPIS) for complex stacking scene to achieve accurate segmentation with topological correctness. To better extract the features of complex and variable morphological pipes, adaptive curvature convolution is introduced to dynamically adapt to the slender pipe structure and capture critical features. To handle topological errors like broken connections, we propose a novel topological constraint loss function based on persistent homology, which greatly improves the topological continuity of the segmentation. Experimental results on real-world and unseen datasets demonstrate that our TopoPIS outperforms other methods regrading segmentation accuracy and topological continuity.

Topology sensing of FANET under missing data

The topological structure of a flying ad hoc network (FANET) is crucial to understand, explain, and predict the behavior of unmanned aerial vehicle (UAV) swarms. Most studies focusing on topology sensing use perfect observations and complete datasets. However, the received signal dataset, being non-cooperative, commonly encounters instances of missing data, causing the performance of the existing algorithms to degrade. We investigate the issue of topology sensing of FANET based on external observations and propose a topology sensing method for FANET with missing data while introducing link-prediction methods to correct the topology inference results. First, we employ multi-dimensional Hawkes processes to model the communication event sequence in the network. Subsequently, to solve the problem in which the binary decision threshold is difficult to determine and cannot be adapted to the application scenario, we propose an extended multi-dimensional Hawkes model suitable for FANET and use the maximum likelihood estimation method for topology inference. Finally, to solve the problem of the low accuracy of inference results owing to missing data, we perform community detection on the observation network and combine the community detection and inference results to construct a mixed connection probability matrix, based on which we perform topology correction. The results of the analysis show that the topology sensing method proposed in this study is robust against missing data, indicating that it is an effective solution for solving this problem.

Geometric and topological corrections to Schwarzschild black hole

In this paper, we compute departures in the black hole thermodynamics induced by either geometric or topological corrections to general relativity. Specifically, we analyze the spherically symmetric spacetime solutions of two modified gravity scenarios with Lagrangians L∼R1+ϵ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {L}\\sim R^{1+\\epsilon }$$\\end{document} and L∼R+ϵG2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {L}\\sim R+\\epsilon \\, \\mathcal {G}^2$$\\end{document}, where G\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {G}$$\\end{document} is the Euler density in four dimensions, while 0<ϵ≪1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ 0<\\epsilon \\ll 1$$\\end{document} measures the perturbation around the Hilbert–Einstein action. Accordingly, we find the expressions of the Bekenstein–Hawking entropy by the Penrose formula, and the black hole temperature and horizon of the obtained solutions. We then investigate the heat capacities in terms of the free parameters of the theories under study. In doing so, we show that healing the problem of negative heat capacities can be possible under particular choices of the free constants, albeit with limitations on the masses allowed for the black hole solutions.

A Bridge-based Algorithm for Simultaneous Primal and Dual Defects Compression on Topologically Quantum-error-corrected Circuits

Topological quantum error correction (TQEC) using the surface code is among the most promising techniques for fault-tolerant quantum circuits. The required resource of a TQEC circuit can be modeled as a space-time volume of a three-dimensional diagram by describing the defect movement along the time axis. For large-scale complex problems, it is crucial to minimize the space-time volume for a quantum algorithm with a reasonable physical qubit number and computation time. Previous work proposed an automated tool for bridge compression on a large-scale TQEC circuit. However, the existing automated bridge compression is only for dual defects and not for primal defects. This paper presents an algorithm to simultaneously perform bridge compression on primal and dual defects. In addition, the automatic compression algorithm performs initialization/measurement simplification and flipping to improve the compression. Compared with the state-of-the-art work, experimental results show that our proposed algorithm can averagely reduce space-time volumes by 53%.

AlphaKnot 2.0: a web server for the visualization of proteins' knotting and a database of knotted AlphaFold-predicted models.

The availability of 3D protein models is rapidly increasing with the development of structure prediction algorithms. With the expanding availability of data, new ways of analysis, especially topological analysis, of those predictions are becoming necessary. Here, we present the updated version of the AlphaKnot service that provides a straightforward way of analyzing structure topology. It was designed specifically to determine knot types of the predicted structure models, however, it can be used for all structures, including the ones solved experimentally. AlphaKnot 2.0 provides the user's ability to obtain the knowledge necessary to assess the topological correctness of the model. Both probabilistic and deterministic knot detection methods are available, together with various visualizations (including a trajectory of simplification steps to highlight the topological complexities). Moreover, the web server provides a list of proteins similar to the queried model within AlphaKnot's database and returns their knot types for direct comparison. We pre-calculated the topology of high-quality models from the AlphaFold Database (4th version) and there are now more than 680.000 knotted models available in the AlphaKnot database. AlphaKnot 2.0 is available at https://alphaknot.cent.uw.edu.pl/.

Construction of trail networks based on growing self-organizing maps and public GPS data

Manual creation of trail maps for hikers is time-consuming and can be inaccurate. This paper presents a new method to construct trail networks based on a growing self-organizing map (GSOM) using publicly available Global Positioning System (GPS) data. Unlike other network topology construction techniques, this approach is not dependent on sequential GPS traces. Fine-tuning multiple hyperparameters enables to customize this process based on unique features of datasets and networks. The generated maps, which are trained on public GPS data, are compared to a ground truth from Open Street Map (OSM). The performance evaluation is based on the accuracy, completeness, and topological correctness of the trail maps. The proposed approach outperforms, particularly on sparse networks without significant GPS noise.

Boundary-Repairing Dual-Path Network for Retinal Layer Segmentation in OCT Image with Pigment Epithelial Detachment.

Automatic retinal layer segmentation in optical coherence tomography (OCT) images is crucial for the diagnosis of ocular diseases. Currently, automatic retinal layer segmentation works well with normal OCT images. However, pigment epithelial detachment (PED) dramatically alters the retinal structure, causing blurred boundaries and partial disappearance of the Bruch's Membrane (BM), thus posing challenges to the segmentation. To tackle these problems, we propose a novel dual-path U-shaped network for simultaneous layer segmentation and boundary regression. This network first designs a feature interaction fusion (FIF) module to strengthen the boundary shape constraints in the layer path. To address the challenge posed by partial BM disappearance and boundary-blurring, we propose a layer boundary repair (LBR) module. This module aims to use contrastive loss to enhance the confidence of blurred boundary regions and refine the segmentation of layer boundaries through the re-prediction head. In addition, we introduce a novel bilateral threshold distance map (BTDM) designed for the boundary path. The BTDM serves to emphasize information within boundary regions. This map, combined with the updated probability map, culminates in topology-guaranteed segmentation results achieved through a topology correction (TC) module. We investigated the proposed network on two severely deformed datasets (i.e., OCTA-500 and Aier-PED) and one slightly deformed dataset (i.e., DUKE). The proposed method achieves an average Dice score of 94.26% on the OCTA-500 dataset, which was 1.5% higher than BAU-Net and outperformed other methods. In the DUKE and Aier-PED datasets, the proposed method achieved average Dice scores of 91.65% and 95.75%, respectively.

Rectification and converter control of the FPSLGs for energy storage applications

AbstractThis article presents two power converters with controllers attached to the Free‐Piston Stirling Linear Generator (FPSLG) and energy storage system (ESS). The rectifier uses hysteresis‐SVPWM current regulation and CB‐SPWM, while the buck‐boost converter utilizes the dual‐loop PI control method. The storage battery receives energy from a linear‐generator with a rectifier and converter. The FPSE and linear motors in the FPSLG convert thermal to electrical energy. A two‐level electrical energy conversion technique using a three‐phase AC signal to DC and DC‐DC converter has been devised to reduce output electrical energy oscillation as well as stabilize the generating system's DC power. Initially, the FPSE's nonlinear model and the three‐phase permanent magnet linear‐motor's linear mathematical model were created and followed by the ESS and control mechanism simulation. The simulation shows that the ESS system and control approach can give stable power to the storage battery using linear‐generator power. The PR controller replaces the PI controller in the position loop to improve frequency and displacement tracing. The control system design was simulated in MATLAB and the topology's feasibility and correctness were confirmed. Comparative analysis shows that, rectifier uses the H‐SVPWM's unity power factor of AC and stability controllability of the DC‐side voltage is better than the CB‐SPWM approach.

Automated deep learning segmentation of high-resolution 7 Tesla postmortem MRI for quantitative analysis of structure-pathology correlations in neurodegenerative diseases.

Postmortem MRI allows brain anatomy to be examined at high resolution and to link pathology measures with morphometric measurements. However, automated segmentation methods for brain mapping in postmortem MRI are not well developed, primarily due to limited availability of labeled datasets, and heterogeneity in scanner hardware and acquisition protocols. In this work, we present a high-resolution dataset of 135 postmortem human brain tissue specimens imaged at 0.3 mm3 isotropic using a T2w sequence on a 7T whole-body MRI scanner. We developed a deep learning pipeline to segment the cortical mantle by benchmarking the performance of nine deep neural architectures, followed by post-hoc topological correction. We evaluate the reliability of this pipeline via overlap metrics with manual segmentation in 6 specimens, and intra-class correlation between cortical thickness measures extracted from the automatic segmentation and expert-generated reference measures in 36 specimens. We also segment four subcortical structures (caudate, putamen, globus pallidus, and thalamus), white matter hyperintensities, and the normal appearing white matter, providing a limited evaluation of accuracy. We show generalizing capabilities across whole-brain hemispheres in different specimens, and also on unseen images acquired at 0.28 mm3 and 0.16 mm3 isotropic T2*w fast low angle shot (FLASH) sequence at 7T. We report associations between localized cortical thickness and volumetric measurements across key regions, and semi-quantitative neuropathological ratings in a subset of 82 individuals with Alzheimer's disease (AD) continuum diagnoses. Our code, Jupyter notebooks, and the containerized executables are publicly available at the project webpage (https://pulkit-khandelwal.github.io/exvivo-brain-upenn/).

RoadCorrector: A Structure-Aware Road Extraction Method for Road Connectivity and Topology Correction

RoadCorrector: A Structure-Aware Road Extraction Method for Road Connectivity and Topology Correction

A H-Bridge-Multiplexing-Based Novel Power Electronic Transformer

Cascaded H-bridge power electronic transformers (CHB-PET) play a pivotal role in distribution grids and their efficient operation. The input series and output parallel (ISOP) configurations result in a huge number of power switching devices, high-frequency transformers (HFT), and capacitors in high-voltage, high-capacity CHB-PET, leading to the need for high hardware costs and huge-sized CHB-PET, which further poses a significant challenge to the engineering feasibility and marketability of the CHB-PET. To address these issues, a CHB-PET topology is proposed in this paper. The novel topology exploits the concept of multi-frequency modulation to achieve power decoupling and power unit multiplexing through reasonable LC resonant frequency selection, which optimizes the ISOP structure and ultimately reduces the hardware cost and size of the CHB-PET. In this study, the effectiveness of reducing the number of power switching devices and HFT is firstly analyzed, and after describing its working principle, the control strategy of each power conversion link of PET is discussed before the correctness and effectiveness of the CHB-PET topology and control strategy proposed in this paper are verified via simulation.

GENERATING LIGHTWEIGHT BUILDING MODELS WITH PRESERVED STRUCTURAL FEATURES FROM NOISY 3D MESHES

Abstract. Obtaining building instance models directly through photogrammetry and other means results in high polygon counts and structural detail levels. Therefore, it is an important challenge to preserve the features of instant building models and generate lightweight building models from them. In this paper, we propose an improved lightweight reconstruction method for 3D building models based on planar primitives extraction, topology correction, and optimal planes selection. Improvements due to our method arise from three aspects: (1) After plane segmentation based on a simple region growing method, a second plane segmentation is performed on the building model based on the similarity of normal vectors. (2) According to the building structural characteristics, the initial plane segmentation is checked to generate new plane regions within the necessary connection regions. (3) The intersection of candidate planes is improved by enlarging the region of candidate faces, and the topological connection is improved. Furthermore, the topological relations of all planar primitives that have been optimized are recorded in an undirected graph. Finally, a watertight and manifold lightweight model is extracted from the faces of a candidate set by energy minimization. Experiments on different data sets show that the improved method is more reasonable in plane segmentation, and has superior performance in algorithm robustness and necessary structure recovery of buildings. Even when dealing with imperfect data, a watertight model is still obtained.

Joint simplification of various types spatial objects while preserving topological relationships

Cartographic generalization includes the process of graphically reducing information from reality or larger scaled maps to display only the information that is necessary at a specific scale. After generalization, maps can show the main things and essential characteristics. The scale, use and theme of maps, geographical features of cartographic regions and graphic dimensions of symbols are the main factors affecting cartographic generalization. Geometric simplification is one of the core components of cartographic generalization. The topological relations of spatial features also play an important role in spatial data organization, queries, updates, and quality control. Various map transformations can change the relationships between features, especially since it is common practice to simplify each type of spatial feature independently (first administrative boundaries, then road network, settlements, hydrographic network, etc.). In order to detect the spatial conflicts a refined description of topological relationships is needed. Considering coverings and mesh structures allows us to reduce the more general problem of topological conflict correction to the problem of resolving topological conflicts within a single mesh cell. In this paper, a new simplification algorithm is proposed. Its peculiarity is the joint simplification of a set of spatial objects of different types while preserving their topological relations. The proposed algorithm has a single parameter — the minimum map detail size (usually it is equal to one millimeter in the target map scale). The first step of the algorithm is the construction of a special mesh data structure. On its basis for each spatial object a sequence of cells is formed, to which points of this object belong. If a cell contains points of only one object, its geometric simplification is performed within the bounding cell using the sleeve-fitting algorithm. If a cell contains points of several objects, geometric simplification is performed using a special topology-preserving procedure.

Topology Guaranteed B-Spline Surface/Surface Intersection

The surface/surface intersection technique serves as one of the most fundamental functions in modern Computer Aided Design (CAD) systems. Despite the long research history and successful applications of surface intersection algorithms in various CAD industrial software, challenges still exist in balancing computational efficiency, accuracy, as well as topology correctness. Specifically, most practical intersection algorithms fail to guarantee the correct topology of the intersection curve(s) when two surfaces are in near-critical positions, which brings instability to CAD systems. Even in one of the most successfully used commercial geometry engines ACIS, such complicated intersection topology can still be a tough nut to crack. In this paper, we present a practical topology guaranteed algorithm for computing the intersection loci of two B-spline surfaces. Our algorithm well treats all types of common and complicated intersection topology with practical efficiency, including those intersections with multiple branches or cross singularities, contacts in several isolated singular points or highorder contacts along a curve, as well as intersections along boundary curves. We present representative examples of these hard topology situations that challenge not only the open-source geometry engine OCCT but also the commercial engine ACIS. We compare our algorithm in both efficiency and topology correctness on plenty of common and complicated models with the open-source intersection package in SISL, OCCT, and the commercial engine ACIS.

Bulk-to-boundary anyon fusion from microscopic models

Topological quantum error correction based on the manipulation of the anyonic defects constitutes one of the most promising frameworks towards realizing fault-tolerant quantum devices. Hence, it is crucial to understand how these defects interact with external defects such as boundaries or domain walls. Motivated by this line of thought, in this work, we study the fusion events between anyons in the bulk and at the boundary in fixed-point models of 2 + 1-dimensional non-chiral topological order defined by arbitrary fusion categories. Our construction uses generalized tube algebra techniques to construct a bi-representation of bulk and boundary defects. We explicitly derive a formula to calculate the fusion multiplicities of a bulk-to-boundary fusion event for twisted quantum double models and calculate some exemplary fusion events for Abelian models and the (twisted) quantum double model of S3, the simplest non-Abelian group-theoretical model. Moreover, we use the folding trick to study the anyonic behavior at non-trivial domain walls between twisted S3 and twisted Z2 as well as Z3 models. A recurring theme in our construction is an isomorphism relating twisted cohomology groups to untwisted ones. The results of this work can directly be applied to study logical operators in two-dimensional topological error correcting codes with boundaries described by a twisted gauge theory of a finite group.

Topology-sensitive weighting model for myocardial segmentation

Accurate myocardial segmentation is crucial for the diagnosis of various heart diseases. However, segmentation results often suffer from topology structural errors, such as broken connections and holes, especially in cases of poor image quality. These errors are unacceptable in clinical diagnosis. We proposed a Topology-Sensitive Weight (TSW) model to keep both pixel-wise accuracy and topological correctness. Specifically, the Position Weighting Update (PWU) strategy with the Boundary-Sensitive Topology (BST) module can guide the model to focus on positions where topological features are sensitive to pixel values. The Myocardial Integrity Topology (MIT) module can serve as a guide for maintaining myocardial integrity. We evaluate the TSW model on the CAMUS dataset and a private echocardiography myocardial segmentation dataset. The qualitative and quantitative experimental results show that the TSW model significantly enhances topological accuracy while maintaining pixel-wise precision.

Adaptive Slicing of Implicit Porous Structure with Topology Guarantee

Adaptive slicing is an important step in 3D printing, where the thicknesses of slices are adaptively adjusted to achieve a trade-off between printing time reduction and surface quality improvement. However, in conventional slicing algorithms, the topological information inside the model is usually not considered, and then, they are not suitable for slicing porous structures with complicated inner topological structures. In this study, based on the persistent homology theory, a novel method is developed to adaptively slice implicit porous structures, which guarantees the topological correctness of the generated adaptive slice model. Given an implicit porous structure, we generate the finest slice model, and calculate the topological information of the finest slices, i.e., persistent diagram (PD) and Betti number. Next, the finest slice model is partitioned into parts based on the Betti number of the finest slices. In each part, the Betti numbers of the finest slices are the same. Moreover, in each part, we first determine the slices for printing by solving the ℓ0−norm optimization problem to optimize the printing time, and then, the thicknesses of the slices for printing are calculated by optimizing the surface quality. In this way, not only can the printing time and surface quality be optimized, but also the topological correctness of the adaptive slice model can be guaranteed. Experimental results show the effectiveness of the developed algorithm.

FAmesh: Generating Frequency Adaptive Meshes from Single Images under 2D Hole Constraints

Reconstructing 3D models from a single image has numerous applications in fields such as VR/AR, medical imaging, and gaming. However, most mesh-based methods are limited by the use of 0-genus initial templates, which makes it difficult to reconstruct 3D meshes with complex topologies. Additionally, existing methods often prioritize reconstructing the overall shape and neglect to study local meshes with varying curvatures, resulting in a lack of correct and detailed local features in the generated meshes. This paper proposes a 3D reconstruction framework that transitions from global to local and incorporates MLP and GCN. The framework introduces a mesh pruning strategy under a 2D hole constraint to restore the correct mesh topology. Moreover, the framework fine-tunes local details by separately learning corresponding mapping functions on high-frequency and low-frequency local extended patches. The experiment with the proposed network on the ShapeNet dataset shows that the network has a CD value of 1.763 and an F-score of 85.40. The results from extensive experiments demonstrate that our proposed method outperforms existing methods in topology correction and local detail reconstruction.

Topological and disorder corrections to the transverse Wiedemann-Franz law and Mott relation in kagome magnets and Dirac materials

Topological and disorder corrections to the transverse Wiedemann-Franz law and Mott relation in kagome magnets and Dirac materials

IBEAT V2.0: a multisite-applicable, deep learning-based pipeline for infant cerebral cortical surface reconstruction.

The human cerebral cortex undergoes dramatic and critical development during early postnatal stages. Benefiting from advances in neuroimaging, many infant brain magnetic resonance imaging (MRI) datasets have been collected from multiple imaging sites with different scanners and imaging protocols for the investigation of normal and abnormal early brain development. However, it is extremely challenging to precisely process and quantify infant brain development with these multisite imaging data because infant brain MRI scans exhibit (a) extremely low and dynamic tissue contrast caused by ongoing myelination and maturation and (b) inter-site data heterogeneity resulting from the use of diverse imaging protocols/scanners. Consequently, existing computational tools and pipelines typically perform poorly on infant MRI data. To address these challenges, we propose a robust, multisite-applicable, infant-tailored computational pipeline that leverages powerful deep learning techniques. The main functionality of the proposed pipeline includes preprocessing, brain skull stripping, tissue segmentation, topology correction, cortical surface reconstruction and measurement. Our pipeline can handle both T1w and T2w structural infant brain MR images well in a wide age range (from birth to 6 years of age) and is effective for different imaging protocols/scanners, despite being trained only on the data from the Baby Connectome Project. Extensive comparisons with existing methods on multisite, multimodal and multi-age datasets demonstrate superior effectiveness, accuracy and robustness of our pipeline. We have maintained a website, iBEAT Cloud, for users to process their images with our pipeline ( http://www.ibeat.cloud ), which has successfully processed over 16,000 infant MRI scans from more than 100 institutions with various imaging protocols/scanners.