Summary and principle of PointTree.

(A) The reconstruction procedure of PointTree involves the generation, clustering, and connection of foreground points (the first row). Within this procedure, three optimization problems are designed to allocate the foreground points into their respective neurites (the second row). (B) Schematic diagram of information flow score calculation. In a neurite branch with a fixed root node (green circle), the information flow score is calculated based on the assumption that a neurite has few directional changes. The assumption determines the neurite directly connecting to the root node (red), resulting in two branch angles used to calculate the information flow score. (C) Statistical analysis of the consistency between the minimum information flow and the real situation. For 208 neurite branches, the information flow scores are calculated as ground truth according to their manually determined skeletons and root nodes. These scores are then displayed in ascending order. The root nodes of neurite branches are changed to generate both maximum and minimum information flow scores. (D) One neurite branch is decomposed into two by minimizing the total information flow scores. (E) Performance of different methods on separating closely paralleled neurites. In PointTree, a single neurite is represented by a series of ellipsoids whose centerlines are not simultaneously located within different neurites. They are connected using ellipsoid shape which results in perfect reconstruction (Left). However, skeleton-based methods fail to separate two closely paralleled neurites due to interference from other signals (Red circle in middle) or connections being interfered with by another neighboring skeleton point (Red circle in right).

Performance of PointTree on crossover and closely paralleled neurites.

(A) The reconstruction process of crossover and closely paralleled neurites. (B) Quantitative evaluation of PointTree and several skeleton-based methods on identifying closely distributed neurites. The box plots present the statistical information in which the horizontal line in the box, the lower and upper borders of the box represent the median value, the first quartile (Q1) and the third quartile (Q3) respectively. The vertical black lines indicate 1.5 × IQR. (C) Three reconstruction examples derived from PointTree and several skeleton-based methods.

Comparison of reconstruction methods on image blocks containing densely distributed neurites.

(A) Comparison of reconstruction performance among six methods, including PointTree, NGPST, neuTube, APP2, PHDF, and MOST. Individual neurite branches are delineated in different colors. (B) Quantitative evaluation of reconstruction performance using precision, recall, and F1-score. The box plots display these three evaluation indexes (n=8). In the box, the horizontal line represents the median value. The box shows the interquartile range (IQR) from the first quartile (Q1) to the third quartile (Q3). The vertical lines indicate 1.5× IQR.

Minimal information flow tree effectively restrains the accumulation of reconstruction errors.

(A) Reconstruction comparisons in the fusion process with MIFT and without MIFT are shown. Both image blocks and neurites reconstructions are displayed using maximum projection along the z-direction. Two fusion procedures are performed, and the final fusion reconstructions are presented in the third column. (B) The variation in reconstruction accuracy during the fusion process with MIFT and without MIFT is illustrated. Blue points represent the initial reconstruction accuracy from six image blocks, while green points and red points denote the merged reconstruction accuracy with MIFT and without MIFT, respectively. The squares represent the mean values of the evaluation indexes. (C) The skeletons of three neurite branches from the final merged reconstructions with MIFT are shown. Additionally, corresponding ground-truth reconstructions and reconstruction evaluations are also presented.

Long-range axonal reconstruction using PointTree.

(A) The image block contains eight neurons in the ventral posteromedial thalamic region. The projection of these neurons includes a large number of densely distributed axons, which are enlarged in A1 and A2. (B) The reconstruction of the eight neurons is achieved by annotators with semi-automatic software GTree, serving as ground-truth reconstruction to evaluate automatic algorithms. The reconstructions B1 and B2 correspond to the image blocks A1 and A2. (C) Automatic reconstruction with PointTree results in reconstructions of the densely distributed axons, which are enlarged in C1 and C2. (D) A comparison between automatic reconstruction and ground-truth reconstruction of axonal projection for one neuron is shown. Green indicates consistent reconstruction, blue indicates missed branches, and red denotes branches from other neurons. (E) Quantitative analysis of long-range projections for these neurons is presented. Statistical information is displayed in boxes, while black points represent the accuracy of the reconstructions for these neurons.