🍩 Database of Original & Non-Theoretical Uses of Topology

(found 7 matches in 0.001476s)

  2. Equivariant Geometric Learning for Digital Rock Physics: Estimating Formation Factor and Effective Permeability Tensors From Morse Graph (2023)

    Chen Cai, Nikolaos Vlassis, Lucas Magee, Ran Ma, Zeyu Xiong, Bahador Bahmani, Teng-Fong Wong, Yusu Wang, WaiChing Sun
    Abstract We present a SE(3)-equivariant graph neural network (GNN) approach that directly predicts the formation factor and effective permeability from micro-CT images. ...

  3. Position: Topological Deep Learning Is the New Frontier for Relational Learning (2024)

    Theodore Papamarkou, Tolga Birdal, Michael M. Bronstein, Gunnar E. Carlsson, Justin Curry, Yue Gao, Mustafa Hajij, Roland Kwitt, Pietro Lio, Paolo Di Lorenzo, Vasileios Maroulas, Nina Miolane, Farzana Nasrin, Karthikeyan Natesan Ramamurthy, Bastian Rieck, Simone Scardapane, Michael T. Schaub, Petar Veličković, Bei Wang, Yusu Wang, Guowei Wei, Ghada Zamzmi
    Abstract Topological deep learning (TDL) is a rapidly evolving field that uses topological features to understand and design deep learning models. This paper posits that TDL is the new frontier for relational learning. TDL may complement graph representation learning and geometric deep learning by incorporating topological concepts, and can thus provide a natural choice for various machine learning settings. To this end, this paper discusses open problems in TDL, ranging from practical benefits to theoretical foundations. For each problem, it outlines potential solutions and future research opportunities. At the same time, this paper serves as an invitation to the scientific community to actively participate in TDL research to unlock the potential of this emerging field.

  4. Optimal Topological Cycles and Their Application in Cardiac Trabeculae Restoration (2017)

    Pengxiang Wu, Chao Chen, Yusu Wang, Shaoting Zhang, Changhe Yuan, Zhen Qian, Dimitris Metaxas, Leon Axel
    Abstract In cardiac image analysis, it is important yet challenging to reconstruct the trabeculae, namely, fine muscle columns whose ends are attached to the ventricular walls. To extract these fine structures, traditional image segmentation methods are insufficient. In this paper, we propose a novel method to jointly detect salient topological handles and compute the optimal representations of them. The detected handles are considered hypothetical trabeculae structures. They are further screened using a classifier and are then included in the final segmentation. We show in experiments the significance of our contribution compared with previous standard segmentation methods without topological priors, as well as with previous topological method in which non-optimal representations of topological handles are used.

  5. Semantic Segmentation of Microscopic Neuroanatomical Data by Combining Topological Priors With Encoder–decoder Deep Networks (2020)

    Samik Banerjee, Lucas Magee, Dingkang Wang, Xu Li, Bing-Xing Huo, Jaikishan Jayakumar, Katherine Matho, Meng-Kuan Lin, Keerthi Ram, Mohanasankar Sivaprakasam, Josh Huang, Yusu Wang, Partha P. Mitra
    Abstract Understanding of neuronal circuitry at cellular resolution within the brain has relied on neuron tracing methods that involve careful observation and interpretation by experienced neuroscientists. With recent developments in imaging and digitization, this approach is no longer feasible with the large-scale (terabyte to petabyte range) images. Machine-learning-based techniques, using deep networks, provide an efficient alternative to the problem. However, these methods rely on very large volumes of annotated images for training and have error rates that are too high for scientific data analysis, and thus requires a substantial volume of human-in-the-loop proofreading. Here we introduce a hybrid architecture combining prior structure in the form of topological data analysis methods, based on discrete Morse theory, with the best-in-class deep-net architectures for the neuronal connectivity analysis. We show significant performance gains using our hybrid architecture on detection of topological structure (for example, connectivity of neuronal processes and local intensity maxima on axons corresponding to synaptic swellings) with precision and recall close to 90% compared with human observers. We have adapted our architecture to a high-performance pipeline capable of semantic segmentation of light-microscopic whole-brain image data into a hierarchy of neuronal compartments. We expect that the hybrid architecture incorporating discrete Morse techniques into deep nets will generalize to other data domains.

  6. Topology-Aware Segmentation Using Discrete Morse Theory (2021)

    Xiaoling Hu, Yusu Wang, Li Fuxin, Dimitris Samaras, Chao Chen
    Abstract In the segmentation of fine-scale structures from natural and biomedical images, per-pixel accuracy is not the only metric of concern. Topological correctness, such as vessel connectivity and membrane closure, is crucial for downstream analysis tasks. In this paper, we propose a new approach to train deep image segmentation networks for better topological accuracy. In particular, leveraging the power of discrete Morse theory (DMT), we identify global structures, including 1D skeletons and 2D patches, which are important for topological accuracy. Trained with a novel loss based on these global structures, the network performance is significantly improved especially near topologically challenging locations (such as weak spots of connections and membranes). On diverse datasets, our method achieves superior performance on both the DICE score and topological metrics.

  7. Efficient Map Reconstruction and Augmentation via Topological Methods (2015)

    Suyi Wang, Yusu Wang, Yanjie Li
    Abstract In recent years, with the rapid growth in the amount of publicly available Volunteered Geographic Information (VGI) data, automatic map generation from GPS trajectories has attracted great attention. Maps generated from these data can for example complement commercial maps in less developed areas. Two main challenges in the automatic generation of maps from volunteered GPS data are the handling of noise and of non-homogeneous sampling of road segments (for example, roads in downtown area can receive significantly more GPS traces than roads in residential areas). In this paper, we present a novel framework for map reconstruction based on a topological idea: the Morse theory. In particular, the use of Morse theory and topological simplification allows us to handle the issues of both noise and non-homogeneous sampling in an elegant unified framework. Our algorithm is significantly simpler than previous approaches, both conceptually and implementation speaking. Little pre- and post-processing is required, and yet the algorithm can reconstruct robust road-networks from challenging data sets (such as GPS traces for Berlin or Beijing cities) that are comparable or better than the output of previous state-of-the-art approaches. The new algorithm is also orders of magnitude faster than previous approaches on large data sets (for example, the entire processing of the Berlin city data with about 27189 trajectories takes less than one minute).Furthermore, our framework can be easily extended to handle the map integration problem, where one wishes to integrate multiple maps into a single one. Here, roads in different maps can have different confidence levels, and higher confident roads will have larger influence in the final integrated road. We also present an effective algorithm for a slightly different map augmentation problem, where one wishes to augment a map, say G2, using partial but more trust-worthy map G1, in the sense that in the final map, information in G1 needs to be completely preserved.