M-AMST: an automatic 3D neuron tracing method based on mean shift and adapted minimum spanning tree

Abstract

Background: Understanding the working mechanism of the brain is one of the grandest challenges for modern science. Toward this end, the BigNeuron project was launched to gather a worldwide community to establish a big data resource and a set of the state-of-the-art of single neuron reconstruction algorithms. Many groups contributed their own algorithms for the project, including our mean shift and minimum spanning tree (M-MST). Although M-MST is intuitive and easy to implement, the MST just considers spatial information of single neuron and ignores the shape information, which might lead to less precise connections between some neuron segments. In this paper, we propose an improved algorithm, namely M-AMST, in which a rotating sphere model based on coordinate transformation is used to improve the weight calculation method in M-MST.

Results: Two experiments are designed to illustrate the effect of adapted minimum spanning tree algorithm and the adoptability of M-AMST in reconstructing variety of neuron image datasets respectively. In the experiment 1, taking the reconstruction of APP2 as reference, we produce the four difference scores (entire structure average (ESA), different structure average (DSA), percentage of different structure (PDS) and max distance of neurons' nodes (MDNN)) by comparing the neuron reconstruction of the APP2 and the other 5 competing algorithm. The result shows that M-AMST gets lower difference scores than M-MST in ESA, PDS and MDNN. Meanwhile, M-AMST is better than N-MST in ESA and MDNN. It indicates that utilizing the adapted minimum spanning tree algorithm which took the shape information of neuron into account can achieve better neuron reconstructions. In the experiment 2, 7 neuron image datasets are reconstructed and the four difference scores are calculated by comparing the gold standard reconstruction and the reconstructions produced by 6 competing algorithms. Comparing the four difference scores of M-AMST and the other 5 algorithm, we can conclude that M-AMST is able to achieve the best difference score in 3 datasets and get the second-best difference score in the other 2 datasets.

Conclusions: We develop a pathway extraction method using a rotating sphere model based on coordinate transformation to improve the weight calculation approach in MST. The experimental results show that M-AMST utilizes the adapted minimum spanning tree algorithm which takes the shape information of neuron into account can achieve better neuron reconstructions. Moreover, M-AMST is able to get good neuron reconstruction in variety of image datasets.

Keywords: Coordinate transformation; M-AMST; Mean shift; Neuron reconstruction; Sphere model.

Fig. 1

Overview of the M-AMST and the related reconstruction result in four steps. a an original neuron image. b the node set in green color extracted by mean shift algorithm and pruned by the node pruning method are overlaid on top of original neuron image. c the initial reconstruction result is overlaid on top of original neuron image, the white line between green nodes pointed by the yellow arrow is the pathway extracted by the rotating sphere model based on coordinate transformation, the green line is not a pathway generated by the model since there is a gap between the two nodes. d final reconstruction result in red color is overlaid on top of original neuron image

Fig. 2

Three covering situations of mark. Red and purple dots represent two different marks, their own radiuses are r₁ and r₂ respectively. D is their Euclidean distance. a Keep; b prune one mark and c prune one mark

Fig. 3

The schematic map of the rotating sphere model. Part A indicates the coordinate system (X, Y and Z) in Vaa3D platform, the two red dots (S and T) imply the starting and terminal node respectively. Part B means the new coordinate system (X’, Y’ and Z’). Part C illustrates the rotating procedure from the starting voxel (marked with red (a)) to the terminal voxel (marked with red (d)). Red (b) and red (c) are the schematic sphere center which are selected from the rotating procedures

Fig. 4

The comparison of neuron reconstructions using M-AMST and M-MST for two Drosophila neuron images. The reconstructions are overlaid on top of the original images for better visualization. The yellow box points out the different reconstruction results and the red box with the arrow make them more clearly

Fig. 5

The average of the four difference scores of the five algorithms compared with APP2 reconstructions

Fig. 6

The box plots of the four difference scores of the neuron reconstructions obtained by the four neuron tracing algorithms