Cortical depth & radial distance¶

This guide covers the streamline measurements. For the why, see Depth vs. radial distance.

Get a streamline¶

from standard_transform import v1dd_ds
sl = v1dd_ds.streamline()          # nm input (default)
sl = v1dd_ds.streamline("vx")      # voxel input

Streamlines are tied to a transform (they use its y-axis orientation), so like transforms they take a resolution ("nm", "vx", or an [x, y, z] list) telling them what units the points you pass in are in.

All methods below take a transform_points flag (default True): inputs are assumed to be in the original pre-transform coordinates and are transformed first. Pass transform_points=False if your inputs are already in oriented microns.

Depth along the streamline¶

Straight y is only an approximation of depth where cortex curves. To measure depth as path length down the curving axis from the pia:

d = sl.depth_along(xyz, depth_from=0)     # depth of each point along the streamline

To measure the depth between two points along the streamline:

d = sl.depth_between(xyz0, xyz1)

Radial (in-plane) distance¶

To measure how far apart two points are within the laminar plane, using the streamline as the d = 0 reference:

d = sl.radial_distance(xyz0, xyz1)                       # xyz1 may be n x 3
d, angle = sl.radial_distance(xyz0, xyz1, return_angle=True)

xyz0 is a single anchor point; xyz1 can be many points. With return_angle=True you also get the in-plane angle (radians from the x-axis).

The streamline at a location¶

To get the x, z position of the streamline passing through an anchor xyz at one or more depths y (in oriented microns):

x, z = sl.streamline_at(xyz, y)
pts  = sl.streamline_at(xyz, y, return_as_point=True)   # n x 3 instead

Cylindrical-like coordinates¶

radial_points maps points into a coordinate system where one axis is radial distance from an anchor and the other is depth-along-the-streamline, preserving each point's radial distance and angle:

xyz_rad = sl.radial_points(xyz0, pts)

This is the operation used to "straighten" a neuron's coordinates along the cortical axis. (Transforming MeshParty objects directly is deprecated in favor of Ossify — see Morphology objects.)

Unit invariance¶

The nm, voxel, and arbitrary-resolution variants all produce the same results for equivalent inputs:

root_nm = np.array([817335.0, 611523.0, 336240.0])
a = v1dd_ds.streamline("nm").radial_points(root_nm, pts_nm)
b = v1dd_ds.streamline("vx").radial_points(root_nm / [9, 9, 45], pts_vx)
# a == b