Module: Spatial Graph Statistics ()

Description:

This module calculates some basic statistical information on the Spatial Graph data object it is attached to. The output of this module depends on the port Output. By default, it generates a Spreadsheet.

The content of the spreadsheet can be viewed by pressing the Show button in the Properties Area of the Spreadsheet object.

If the spreadsheet is connected to a Spatial Graph View modules Spatial Graph object.

In some cases, you might want to select more than one row at once. You can do this by selecting the first row and then shift-selecting the last row. Then all intermediate rows will be selected as well. Moreover, you may ctrl-click a row in order to toggle its selection state individually.

Clicking the column headers, toggles between ascending and descending order. To restore the initial order of a table, click the rightmost button inside the tab area.

In order to export all tables of the spreadsheet, the Spreadsheet Project View object has to be saved. Here the user could choose among several file formats, including xml, data...

The meaning of the columns in the Segment Statistics tab are:

• Segment ID: Unique line ID in Spatial Graph data structure.
• Curved Length: Curved segment length. It is the sum of the Euclidean distances between paired points framing the segment. Units are the same as the bounding box.
• Chord Length: Distance between start and end point of the segment. Units are the same as the bounding box.
• Tortuosity: Tortuosity of the segment which is equal to curved-length/chord-length. This ratio is always greater than or equal to 1. For the specific case of chord-length is null, tortuosity is not defined.
• Mean Radius: 's skeletonization tools (AutoSkeleton, CenterlineTree) store at each point an estimate of the local thickness of the filamentous object as point attribute thickness. Thereby, it is assumed that the filament has a circular cross section with a certain radius. This column presents the mean radius of all points of the segment in units of the bounding box.
• Volume: The sum of the partial volumes for all points of a segment assuming truncated cones between paired points. It can be noticed a truncated cone is a cylinder if the two side radius are equal.
• Orientation Theta: Polar angle for the segment's orientation in spherical coordinates (see http://en.wikipedia.org/wiki/Spherical_coordinates ). Theta represents the angle formed with the Z-axis and varies in the range [0, 90] degrees. The orientation is calculated using the first eigen vector of the tensor which represents the segment orientation.
• Orientation Phi: Azimuthal angle of the segment's orientation in spherical coordinates. Phi is the angle in the xy plane, measured from the x-axis towards the y-axis in the range [0, 360[ degrees. The orientation is calculated using the first eigen vector of the tensor which represents the segment orientation.
• Graph ID: ID of the connected component the segment belongs to.
• Label Groups...: One column for each label group of the SpatialGraph. Shows the corresponding label name or <unlabeled> if no label has been defined for a segment.
• Length: It is the sum of the Euclidean distances between paired points framing the segment. It is a curved length.
• Tensor: The orientation tensor is described by its matrix. Each component is in a column in the segment spreadsheet. These components are "Tensor XX", "Tensor YY","Tensor ZZ", "Tensor XY", "Tensor XZ" and "Tensor YZ".

For each segment label group of the SpatialGraph object, a table is generated providing segment statistics, the number of different node types and the overall number of nodes for every label. The tables are inserted as separate tabs in the spreadsheet where each tab has the name of the label group. One table for each Label Group of the Spatial Graph providing some basic group based

• Label Name: Name of the label or <unlabeled>.
• Number of Segments: Total number of segments with Label Name.
• Mean Length: Mean curv-length of all segments with Label Name.
• Mean Radius: Mean radius of all segments with Label Name.
• Total Length: Sum of the curv-lengths of all segments with Label Name.
• Total Volume: Sum of the volume of all segments with Label Name.
• Number of Nodes: Total number of segments with Label Name.
• Total Nodes: Total number of nodes for the segments with Label Name.
• Intermediate Nodes: Number of inner nodes for the segments with Label Name.
• Terminal Nodes: Number of ending nodes of segments with Label Name.
• Branching Nodes: Number of branching nodes of segments with Label Name.
• Isolated Nodes: Number of isolated nodes of segments with Label Name.

The following node types are identified based on the number of incident segments:

• Isolated: 0 incident segments
• Terminal: 1 incident segments
• Intermediate: 2 incident segments
• Branching: 3 or more incident segments

Connections:

Data [required]
The Spatial Graph input data object.

Ports:

Output

Selects which output data to compute:

• Spreadsheet: create a tabbed spreadsheet.
• SpatialGraph: create a SpatialGraph with statistics stored as attributes. Note that the attributes are persistant, meaning if the SpatialGraph topology is modified afterwards, the statistics won't be updated. In this case, you need to recompute them again.

Options

• Create a new tab per graph: Create a new tab for each sub-graph of the SpatialGraph object. Note this option is enabled only if the output Spreadsheet is checked and the number of sub-graphs is less than 50. The number of the sub-graphs is computed at the first compute of the statistics.