Hidden Markov modeling for maximum probability neuron reconstruction

Recent advances in brain clearing and imaging have made it possible to image entire mammalian brains at sub-micron resolution. These images offer the potential to assemble brain-wide atlases of neuron morphology, but manual neuron reconstruction remains a bottleneck. Several automatic reconstruction algorithms exist, but most focus on single neuron images. In this paper, we present a probabilistic reconstruction method, ViterBrain, which combines a hidden Markov state process that encodes neuron geometry with a random field appearance model of neuron flourescence. Our method utilizes dynamic programming to compute the global maximizers of what we call the ``most probable'' neuron path. Our most probable estimation method models the task of reconstructing neuronal processes in the presence of other neurons, and thus is applicable in images with several neurons. Our method operates on image segmentations in order to leverage cutting edge computer vision technology. We applied our algorithm to imperfect image segmentations where false negatives severed neuronal processes, and showed that it can follow axons in the presence of noise or nearby neurons. Additionally, it creates a framework where users can intervene to, for example, fit start and endpoints. The code used in this work is available in our open-source Python package brainlit.

[1]  Hang Zhou,et al.  GTree: an Open-source Tool for Dense Reconstruction of Brain-wide Neuronal Population , 2020, Neuroinformatics.

[2]  H. Mannila,et al.  Computing Discrete Fréchet Distance ∗ , 1994 .

[3]  Hanchuan Peng,et al.  TeraVR Empowers Precise Reconstruction of Complete 3-D Neuronal Morphology in the Whole Brain , 2019 .

[4]  Changle Zhou,et al.  Precise segmentation of densely interweaving neuron clusters using G-Cut , 2019, Nature Communications.

[5]  Alex Bateman,et al.  An introduction to hidden Markov models. , 2007, Current protocols in bioinformatics.

[6]  D. W. Scott,et al.  Multivariate Density Estimation, Theory, Practice and Visualization , 1992 .

[7]  Pascal Fua,et al.  Reconstructing Loopy Curvilinear Structures Using Integer Programming , 2013, 2013 IEEE Conference on Computer Vision and Pattern Recognition.

[8]  Hang Zhou,et al.  Brain-Wide Shape Reconstruction of a Traced Neuron Using the Convex Image Segmentation Method , 2019, Neuroinformatics.

[9]  Giulio Iannello,et al.  Automated Neuron Tracing Methods: An Updated Account , 2016, Neuroinformatics.

[10]  Zhi Zhou,et al.  Ensemble Neuron Tracer for 3D Neuron Reconstruction , 2017, Neuroinformatics.

[11]  Shuiwang Ji,et al.  Deep Learning Segmentation of Optical Microscopy Images Improves 3-D Neuron Reconstruction , 2017, IEEE Transactions on Medical Imaging.

[12]  Eugene W. Myers,et al.  Anisotropic path searching for automatic neuron reconstruction , 2011, Medical Image Anal..

[13]  Drew Friedmann,et al.  Mapping mesoscale axonal projections in the mouse brain using a 3D convolutional network , 2019, Proceedings of the National Academy of Sciences.

[14]  Heng Wang,et al.  Voxel-wise Cross-Volume Representation Learning for 3D Neuron Reconstruction , 2021, MLMI@MICCAI.

[15]  Hanchuan Peng,et al.  V3D enables real-time 3D visualization and quantitative analysis of large-scale biological image data sets , 2010, Nature Biotechnology.

[16]  Fred A. Hamprecht,et al.  ilastik: interactive machine learning for (bio)image analysis , 2019, Nature Methods.

[17]  Charles R. Gerfen,et al.  Reconstruction of 1,000 Projection Neurons Reveals New Cell Types and Organization of Long-Range Connectivity in the Mouse Brain , 2019, Cell.

[18]  Hanchuan Peng,et al.  APP2: automatic tracing of 3D neuron morphology based on hierarchical pruning of a gray-weighted image distance-tree , 2013, Bioinform..

[19]  Hanchuan Peng,et al.  Automatic tracing of ultra-volumes of neuronal images , 2016, Nature Methods.

[20]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[21]  Jack Bresenham,et al.  Algorithm for computer control of a digital plotter , 1965, IBM Syst. J..

[22]  Linlin Shen,et al.  3D Neuron Reconstruction in Tangled Neuronal Image With Deep Networks , 2020, IEEE Transactions on Medical Imaging.

[23]  Hanchuan Peng,et al.  Automatic reconstruction of 3D neuron structures using a graph-augmented deformable model , 2010, Bioinform..

[24]  Zhi Zhou,et al.  DeepNeuron: an open deep learning toolbox for neuron tracing , 2018, Brain Informatics.

[25]  Tianming Liu,et al.  SmartTracing: self-learning-based Neuron reconstruction , 2015, Brain Informatics.

[26]  Jr. G. Forney,et al.  Viterbi Algorithm , 1973, Encyclopedia of Machine Learning.

[27]  Chia-Ling Tsai,et al.  A Broadly Applicable 3-D Neuron Tracing Method Based on Open-Curve Snake , 2011, Neuroinformatics.

[28]  Hang Zhou,et al.  NeuroGPS-Tree: automatic reconstruction of large-scale neuronal populations with dense neurites , 2015, Nature Methods.

[29]  Thomas Brox,et al.  U-Net: Convolutional Networks for Biomedical Image Segmentation , 2015, MICCAI.

[30]  Donald L. Snyder,et al.  Random Point Processes in Time and Space , 1991 .

[31]  Shih-Fu Chang,et al.  Automatic Reconstruction of Neural Morphologies with Multi-Scale Tracking , 2012, Front. Neural Circuits.

[32]  Xueping Wang,et al.  Improved V-Net Based Image Segmentation for 3D Neuron Reconstruction , 2018, 2018 IEEE International Conference on Bioinformatics and Biomedicine (BIBM).

[33]  T. Lindvall ON A ROUTING PROBLEM , 2004, Probability in the Engineering and Informational Sciences.

[34]  Demetri Terzopoulos,et al.  Snakes: Active contour models , 2004, International Journal of Computer Vision.

[35]  Claudia Clopath,et al.  Deep Reinforcement Learning for Subpixel Neural Tracking , 2018, MIDL.

[36]  Xiaoyang Liu,et al.  FMST: an Automatic Neuron Tracing Method Based on Fast Marching and Minimum Spanning Tree , 2018, Neuroinformatics.

[37]  Joel Nothman,et al.  SciPy 1.0-Fundamental Algorithms for Scientific Computing in Python , 2019, ArXiv.

[38]  Michael I. Miller,et al.  Dynamic Programming Generation of Curves on Brain Surfaces , 1998, IEEE Trans. Pattern Anal. Mach. Intell..

[39]  Erik H. W. Meijering,et al.  Automated Neuron Reconstruction from 3D Fluorescence Microscopy Images Using Sequential Monte Carlo Estimation , 2018, Neuroinformatics.

[40]  Erik H. W. Meijering,et al.  Automated neuron tracing using probability hypothesis density filtering , 2017, Bioinform..

[41]  Michael I. Miller,et al.  Fitting Splines to Axonal Arbors Quantifies Relationship Between Branch Order and Geometry , 2021, Frontiers in Neuroinformatics.

[42]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[43]  Laurent D. Cohen,et al.  On active contour models and balloons , 1991, CVGIP Image Underst..