tools.md

icoCNN.tools

This subpackage includes some functions that could be useful when dealing with icosahedral signals, but whose implementation is not optimal and shouldn't be used inside your training or inference loops.

• clean_vertices
• smooth_vertices
• random_icosahedral_rotation_matrix
• rotate_signal

clean_vertices

Turn into 0 the vertices of an icosahedral signal. The class icoCNN.CleanVertices provides a more efficient implementation than this function if it will be used several times with maps of the same resolution.

Parameters

• x : torch tensor with shape [..., 5, 2^r, 2^(r+1)], input icosahedral signal

Returns

torch tensor with shape [..., 5, 2^r, 2^(r+1)]

smooth_vertices

Replace the vertices of an icosahedral signal with the mean of their neighbours. The class icoCNN.SmoothVertices provides a more efficient implementation than this function if it will be used several times with maps of the same resolution.

Parameters

• x : torch tensor with shape [..., 5, 2^r, 2^(r+1)], input icosahedral signal

Returns

torch tensor with shape [..., 5, 2^r, 2^(r+1)]

random_icosahedral_rotation_matrix

Random rotation matrix taken from the 60 icosahedral symmetries.

Parameters

• idx : int (optional), Index of the desired rotation matrix, following the same order as in this table. None (default) takes a random matrix

Returns

3x3 ndarray, Rotation matrix, you can apply it to an icosahedral signal with icoCNN.tools.rotate_signal(x, rotation_matrix) or to an icosahedral grid with np.matmul(ico_grid, rotation_matrix.transpose())

rotate_signal

Rotate an icosahedral with a given rotation matrix.

Parameters

• x : torch tensor with shape [..., 5, 2^r, 2^(r+1)], Input icosahedral signal
• rotation_matrix : 3x3 ndarray It can be obtained with icoCNN.tools.random_icosahedral_rotation_matrix()
• original_grid : 4D ndarray with shape [5, 2^r, 2^(r+1), 3] (optional), 3D Cartesian coordinates of every point of the icosahedral grid where x is defined. If it is not provided, it is computed inferring its resolution from the shape of x.

Returns

torch tensor with shape [..., 5, 2^r, 2^(r+1)], Rotated icosahedral signal