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Semantic segmentation of microscopic neuroanatomical data by combining topological priors with encoder–decoder deep networks

A preprint version of the article is available at bioRxiv.


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.

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Fig. 1: Three prevalent modalities of light-microscopic data acquisition where we have applied our algorithm.
Fig. 2: Existing CNN architectures suitable for neurite segmentation.
Fig. 3: Architecture of the MaskRCNN network and semantic segmentation workflow.
Fig. 4: Illustrations of results from the process detection pipeline for single-colour STPT images, three-colour fluorescent WSIs from the MBA and the bright-field WSIs.
Fig. 5: Semantic segmentation results.

Data availability

The STPT data were collected as a part of the Brain Initiative Cell Census Network and shared online. The raw images of the STPT dataset are available from The sample MBA data can be viewed at The trained models and the annotated data are available at

Code availability

The process detection and semantic segmentation code for reproduction of the results in this paper and limited data with their links and documentation are available on Github at


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We gratefully acknowledge IHC Brightfield Imaged data from P. Strick at U Pitt, and thank J. Nagashima and M. Hanada also at U Pitt for annotating these images. We acknowledge the effort from annotators at the Center for Computational Brain Research at IIT Madras for the bulk of the data annotation and proofreading for this project. This work was supported by the NIH (EB022899, MH114824, MH114821, NS107466, AT010414), the Crick-Clay Professorship (Cold Spring Harbor Laboratory), the Mathers Charitable Foundation, and H. N. Mahabala Chair (IIT Madras). Work at Ohio State University was in addition partly supported by the NSF under grants CCF-1740761, RI-1815697 and DMS-1547357.

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Authors and Affiliations



The idea of using topological priors in the pipeline was conceptualized by Y.W. and P.P.M. Algorithmic design and development was performed by S.B. and L.M. Proofreading assistance and neuroanatomical expertise for neuroanatomical ground truth data was provided by J.J. and K.M. Data preparation, including quality control and acquisition, was performed by B.-X.H., J.J. and K.M. under the supervision of J.H. and P.P.M. The ALBU baseline was tested by D.W. Evaluation of the algorithm was conducted by S.B., D.W., L.M. and X.L. Data preparation, including design of an online proofreading interface and hosting, was done by M.-K.L., M.S. and K.R. S.B., L.M., J.J. and P.P.M. prepared and edited the paper.

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Correspondence to Partha P. Mitra.

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Extended data

Extended Data Fig. 1 Working of Discrete Morse Algorithm.

The Discrete Morse algorithm is given an input image (a). A Gaussian filter is applied to the image (b) - a density function is defined at the pixels. Then the algorithm extracts the ridges of the function across the domain (c) - these ridges form the 1-stable manifold. Finally, each path in the 1-stable manifold is assigned an grayscale value based on intensity along the path, and a grayscale mask is outputted in (d).

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Supplementary Information

Supplementary Figs. 1–5, evaluations, discussion and Tables 1–7.

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Banerjee, S., Magee, L., Wang, D. et al. Semantic segmentation of microscopic neuroanatomical data by combining topological priors with encoder–decoder deep networks. Nat Mach Intell 2, 585–594 (2020).

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