Characterizing the precise three-dimensional morphology and anatomical context of neurons is crucial for neuronal cell type classification and circuitry mapping. Recent advances in tissue clearing techniques and microscopy make it possible to obtain image stacks of intact, interweaving neuron clusters in brain tissues. As most current 3D neuronal morphology reconstruction methods are only applicable to single neurons, it remains challenging to reconstruct these clusters digitally. To advance the state of the art beyond these challenges, we propose a fast and robust method named G-Cut that is able to automatically segment individual neurons from an interweaving neuron cluster. Across various densely interconnected neuron clusters, G-Cut achieves significantly higher accuracies than other state-of-the-art algorithms. G-Cut is intended as a robust component in a high throughput informatics pipeline for large-scale brain mapping projects.
Figure 1
A workflow for automated reconstruction of individual neurons from a neuron cluster. a. An image stack with a densely labeled neuron cluster is obtained with appropriate tissue preparation and imaging techniques (e.g. confocal microscopy, multiphoton microscopy on clarified tissue, etc.). b. An existing tracing method (e.g. NeuronStudio software) is applied to obtain an unsegmented reconstruction of the neural cluster as shown in c. G-Cut is applied to the unsegmented reconstruction. Resulting individual neurons are shown with distinct colors as shown in d. e and f show enlarged view of two reconstructed single neurons corresponding to the orange boxes in d. g shows segmentation result of G-Cut on four reconstructed neuron clusters. Initial unsegmented neuron clusters were reconstructed from experimental image stacks with APP2 algorithm in Vaa3D software. The result shows that G-Cut can be applied on clusters with numerous neurons.
Figure 2
G-Cut performs automatic segmentation based on biological features and graph theory. a The original graph representation of a neuron cluster consists of branches and somas. Each branch starts at one topological node, and ends at another topological node (soma node shown as blue, branch node shown as green, leaf node shown as yellow, path node shown as magenta, and edge between nodes shown as solid line). b The Growth Orientation Feature (GOF) quantifies the orientation of a branch with respect to a soma. Blue node: soma. Green node: branch node. Yellow node: leaf node. Red node: path node. c Left-hand panel shows an example histogram of the GOF for more than 70,000 experimentally reconstructed neuron morphologies from the NeuroMorpho.Org database. Right-hand panel shows cumulative distribution function of the GOF derived from its histogram. d We identify bridging branches between somas and establish their topological relations by constructing a directed acyclic graph (DAG) rooted at a given soma using the Dijkstra algorithm. The branches which are reachable from only one soma are excluded with a Breadth-first search algorithm in preprocessing to reduce problem size. The direction of each branch and its path from the soma are established in this step (direction of each branch shown as blue arrow). After that, the linear programming algorithm is used to find a globally optimal segmentation for the neuron cluster.
Figure 3
GOF distributions obtained from public datasets available on the NeuroMorpho.Org website. Neurons are catalogued by species or by brain regions. a. GOF distribution of each species contains more than one thousand neurons (excluding C. elegans which only has 424 neurons in total). b. GOF distribution of each brain region contains more than one thousand neurons. Kullback-Leibler divergence was performed on different species and different brain regions, respectively.
Figure 4
Segmentation accuracy of G-Cut on a simulated neuron cluster. (a) A simulated neuron cluster (left panel) and segmentation result (right panel). Each segmented neuron is given a unique color for easier visualization. (b) Comparison between each original neuron (left) and segmented neuron (right). The neurons are rotated for more effective visual presentation. Rendering is done with neuTube software.
Figure 5
Evaluating the segmentation accuracy of G-Cut on simulated neuron clusters. a Segmentation accuracy of G-Cut compared to NeuroGPS-tree and TREES toolbox on different scales of simulated neuron clusters (sample size: 100 neuron clusters for each scale). Mann-Whitney U tests with Holm-Bonferroni correction show that G-Cut has consistently higher accuracy (p < 0.01) across all scales of clusters. b The probability distribution of degree of entanglement in randomly generated neuron clusters with a fixed cluster scale of six. c Segmentation accuracy of G-Cut compared to NeuroGPS-Tree and TREES toolbox on simulated neuron clusters with different degrees of entanglement (sample size: 100 neuron clusters for each degree of entanglement). The MES result of G-Cut is consistently higher than both NeuroGPS-TREE and TREES toolbox at all degrees of entanglement (p < 0.01, Mann-Whitney U test with Holm-Bonferroni correction). Source data are provided as a Source Data file.
Figure 6
Performance of G-Cut, NeuroGPS-tree and TREES on densely connected neurons. a The raw image stack. Data size: 1024 x 1024 x 500 voxels. b A neuron cluster was automatically reconstructed from the image stack by NeuronStudio software. The neuron cluster contained 108 spurious links in total. Some representative spurious links were marked in yellow circles. c Sixteen neurons were manually reconstructed from the raw image stack with neuTube software and used as ground truth. d – f The neuron cluster in b was segmented into individual neurons by G-Cut, NeuroGPS-tree and the TREES toolbox, respectively. Identical post-processing was used on segmentation results from all three algorithms (see Supplementary Figure 7 and Supplementary Note 2). g Miss-Extra-Scores of the sixteen neurons reconstructed by G-Cut, NeuroGPS-Tree and the TREES toolbox. The MES was obtained by comparing an automatic reconstruction result with the manual reconstruction result of each neuron. The red line represents median MES. Source data are provided as a Source Data file.
Figure 7
Validation of G-Cut, NeuroGPS-tree and the TREES toolbox on a large number of neurons. a The raw Golgi-cox staining image stack. Data size: 8192 x 2048 x 46 voxels. b Forty-five neurons were manually reconstructed using neuTube software and used as ground truth. c Neuron clusters were reconstructed from the image stack by automatic tracing methods in NeuronStudio software. The neuron clusters contained 169 spurious links in total. d- f The neuron clusters in c were segmented by G-Cut, NeuroGPS-tree and the TREES tool box into 45 individual neurons respectively. Identical post-processing was applied to results from all three algorithms to fix tracing errors and prune redundant branches (see Supplementary Figure 7 and Supplementary Note 2). g Miss-Extra-Scores of the forty-five neurons segmented by G-Cut, NeuroGPS-Tree, and TREES toolbox. Source data are provided as a Source Data file.
