Geodesic Library

The tvb-gdist module is a Cython interface to a C++ library (https://code.google.com/archive/p/geodesic/) for computing geodesic distance which is the length of shortest line between two vertices on a triangulated mesh in three dimensions, such that the line lies on the surface.

The algorithm is due Mitchell, Mount and Papadimitriou, 1987; the implementation is due to Danil Kirsanov and the Cython interface to Gaurav Malhotra and Stuart Knock (TVB Team).

Original library (published under MIT license): https://code.google.com/archive/p/geodesic/

We added a Python wrapped and made small fixes to the original library, to make it compatible with Cython.

To install this, either run pip install tvb-gdist or download sources from GitHub and run python setup.py install in current folder.

You can also use pip to directly install from GitHub: pip install git+https://github.com/the-virtual-brain/tvb-gdist.

Basic test could be:

python
import gdist

Python 3, Cython, and a C++ compiler are required unless the Pypi whl files are compatible with your system.

APIs

The module exposes 2 APIs.

gdist.compute_gdist(numpy.ndarray[numpy.float64_t, ndim=2] vertices, numpy.ndarray[numpy.int32_t, ndim=2] triangles, numpy.ndarray[numpy.int32_t, ndim=1] source_indices = None, numpy.ndarray[numpy.int32_t, ndim=1] target_indices = None, double max_distance = GEODESIC_INF, bool is_one_indexed = False)

This is the wrapper function for computing geodesic distance between a set of sources and targets on a mesh surface.

Args:

vertices (numpy.ndarray[numpy.float64_t, ndim=2]): Defines x,y,z

coordinates of the mesh's vertices.

triangles (numpy.ndarray[numpy.float64_t, ndim=2]): Defines faces of

the mesh as index triplets into vertices.

source_indices (numpy.ndarray[numpy.int32_t, ndim=1]): Index of the

source on the mesh.

target_indices (numpy.ndarray[numpy.int32_t, ndim=1]): Index of the

targets on the mesh.

max_distance (double): Propagation algorithm stops after reaching the

certain distance from the source.

is_one_indexed (bool): defines if the index of the triangles data is

one-indexed.

Returns:

numpy.ndarray((len(target_indices), ), dtype=numpy.float64): Specifying

the shortest distance to the target vertices from the nearest source vertex on the mesh. If no target_indices are provided, all vertices of the mesh are considered as targets, however, in this case, specifying max_distance will limit the targets to those vertices within max_distance of a source. If no source_indices are provided, it defaults to 0.

NOTE: This is the function to use when specifying localised stimuli and parameter variations. For efficiently using the whole mesh as sources, such as is required to represent local connectivity within the cortex, see the local_gdist_matrix() function.

Basic usage then looks like::

>>> import numpy
>>> temp = numpy.loadtxt("data/flat_triangular_mesh.txt", skiprows=1)
>>> vertices = temp[0:121].astype(numpy.float64)
>>> triangles = temp[121:321].astype(numpy.int32)
>>> src = numpy.array([1], dtype=numpy.int32)
>>> trg = numpy.array([2], dtype=numpy.int32)
>>> import gdist
>>> gdist.compute_gdist(vertices, triangles, source_indices=src, target_indices=trg)
 array([0.2])

gdist.local_gdist_matrix(numpy.ndarray[numpy.float64_t, ndim=2] vertices, numpy.ndarray[numpy.int32_t, ndim=2] triangles, double max_distance = GEODESIC_INF, bool is_one_indexed = False)

This is the wrapper function for computing geodesic distance from every vertex on the surface to all those within a distance max_distance of them.

Args:

vertices (numpy.ndarray[numpy.float64_t, ndim=2]): Defines x,y,z

coordinates of the mesh's vertices.

triangles (numpy.ndarray[numpy.float64_t, ndim=2]): Defines faces of

the mesh as index triplets into vertices.

max_distance (double): Propagation algorithm stops after reaching the

certain distance from the source.

is_one_indexed (bool): defines if the index of the triangles data is

one-indexed.

Returns:

scipy.sparse.csc_matrix((N, N), dtype=numpy.float64): where N is the number of vertices, specifying the shortest distance from all vertices to all the vertices within max_distance.

Basic usage then looks like::

>>> import numpy
>>> temp = numpy.loadtxt("data/flat_triangular_mesh.txt", skiprows=1)
>>> import gdist
>>> vertices = temp[0:121].astype(numpy.float64)
>>> triangles = temp[121:321].astype(numpy.int32)
>>> gdist.local_gdist_matrix(vertices, triangles, max_distance=1.0)
 <121x121 sparse matrix of type '<type 'numpy.float64'>'
     with 6232 stored elements in Compressed Sparse Column format>

Runtime and guesstimated memory usage as a function of max_distance for the reg_13 cortical surface mesh, ie containing 2**13 vertices per hemisphere. :: [[10, 20, 30, 40, 50, 60, 70, 80, 90, 100], # mm [19, 28, 49, 81, 125, 181, 248, 331, 422, 522], # s [ 3, 13, 30, 56, 89, 129, 177, 232, 292, 358]] # MB]

where memory is a min-guestimate given by: mem_req = nnz * 8 / 1024 / 1024.

gdist.distance_matrix_of_selected_points(numpy.ndarray[numpy.float64_t, ndim=2] vertices, numpy.ndarray[numpy.int32_t, ndim=2] triangles, numpy.ndarray[numpy.int32_t, ndim=1] points, double max_distance = GEODESIC_INF, bool is_one_indexed = False)

Function for calculating pairwise geodesic distance for a set of points within a distance max_distance of them.

Args:

vertices (numpy.ndarray[numpy.float64_t, ndim=2]): Defines x,y,z

coordinates of the mesh's vertices.

triangles (numpy.ndarray[numpy.float64_t, ndim=2]): Defines faces of

the mesh as index triplets into vertices.

points (numpy.ndarray[numpy.int32_t, ndim=1]): Indices of the points

among which the pairwise distances are to be calculated.

max_distance (double): Propagation algorithm stops after reaching the

certain distance from the source.

is_one_indexed (bool): defines if the index of the triangles data is

one-indexed.

Returns:

scipy.sparse.csc_matrix((N, N), dtype=numpy.float64): where N

is the number of vertices, specifying the pairwise distances among the given points.

Basic usage then looks like::

>>> import numpy
>>> temp = numpy.loadtxt("data/flat_triangular_mesh.txt", skiprows=1)
>>> vertices = temp[0:121].astype(numpy.float64)
>>> triangles = temp[121:321].astype(numpy.int32)
>>> points = numpy.array([2, 5, 10], dtype=numpy.int32)
>>> import gdist
>>> gdist.distance_matrix_of_selected_points(
        vertices, triangles, points
    )
 <121x121 sparse matrix of type '<class 'numpy.float64'>'
    with 6 stored elements in Compressed Sparse Column format>

Notes

• The obtained matrix will be almost symmetrical due to floating point imprecision.
• In order for the algorithm to work the mesh must not be numbered incorrectly or disconnected or of somehow degenerate.

Acknowledgments

This project has received funding from the European Union’s Horizon 2020 Framework Programme for Research and Innovation under the Specific Grant Agreement No. 826421 - VirtualBrainCloud.