🍩 Database of Original & Non-Theoretical Uses of Topology

(found 3 matches in 0.000912s)

  1. 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.

  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. 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.