The FARSIGHT Trace Editor: An Open Source Tool for 3-D Inspection and Efficient Pattern Analysis Aided Editing of Automated Neuronal Reconstructions

Appendix A: Feature Calculation

Intrinsic Features

• 1 Trace ID:

  • The ID is a unique number to look up each trace

• 2 Radius:

  • Average Radius of the Trace

• 3 Type:

  • The type of neural structure it is

• 4 Parent:

  • The ID of the previous Trace in the tree, -1 if it is a root

• 5 Root ID:

  • The ID of the first trace of each tree

• 6 Level:

  • Following the shortest path how many bifurcations in the tree to reach the root.

• 7 Number of Children:

  • How many children branch from the trace

  • 0 or 2, if it is not a soma

• 8 Leaf Node:

  • Determine if the Trace is a terminal tip

Computed Features

• 1 # of Bits:

  • How many traced points in the segment

  • n

• 2 Euclidian Length:

  • The length of a straight line fitted between two points

  • $$ D = \sqrt[2]{{{{\left( {{p_{{1,x}}} - {p_{{2,x}}}} \right)}^2} + {{\left( {{p_{{1,y}}} - {p_{{2,y}}}} \right)}^2} + {{\left( {{p_{{1,z}}} - {p_{{2,z}}}} \right)}^2}}} $$

• 3 Path Length:

  • Summation of the Euclidian distance between bits

  • $L = \sqrt[{\sum {_{{i = 0}}^{{n - {1^2}}}} }]{{{{\left( {{p_{{i,x}}} - {p_{{i + 1,x}}}} \right)}^2} + {{\left( {{p_{{i,y}}} - {p_{{i + 1,y}}}} \right)}^2} + {{\left( {{p_{{i,z}}} - {p_{{1,z}}}} \right)}^2}}}$

• 4 Fragmentation Smoothness:

  • Ratio of path length to Euclidian distance

  • $s = \frac{L}{D}$

• 5 Trace Density:

  • The average spacing between traced points

  • $\frac{L}{n}$

• 6 Volume:

  • Calculates as a sum of cylinders along the path

  • $V = \sum {_0^{{n - 1}}\pi {{\left( {{r_i}} \right)}^2}*Di,i + 1}$

• 7 Distance to Parent:

  • Euclidian distance between parent and child end points

• 8 Path to Root:

  • Summation of the path length and distance to parent

Features specific for merging

• 1 Gap Size:

  • Minimum Distance between the endpoints of two traces

  • $d = \sqrt[2]{{{{\left( {{x_1} - {x_2}} \right)}^2} + {{\left( {{y_1} - {y_2}} \right)}^2} + {{\left( {{z_1} - {z_2}} \right)}^2}}}$

• 2 Gap Angle:

  • Angle between two traces represented as normalized vectors

  • $\theta = {\cos^{{ - 1}}}\left( {\frac{{{v_1}*{v_2}}}{{|{v_1}||{v_2}|}}} \right)$

• 3 Maximum Gap Distance:

  • User parameter to set maximum gap size

  • ∆

• 4 Merging Cost:

  • Function for determining merging probability

  • $C = \theta \left[ { \frac{d}{\Delta } } \right]s$