Data alignment

To calculate the helicity of a certain object, it is important to make sure that the helical axis is aligned to the z-axis and is centered in the volume. This can be done by finding the center and orientation of your object and entering that information in align_helical_axis. That function will rotate and translate your data such that the given orientation becomes parallel with the z-axis and is centered in the volume. You can find the orientation of the helical axis and the center either manually using external 3D visualization software, or for relatively simple objects these can also be found automatically using center_of_mass and/or helical_axis_pca. The former assumes that the helical axis goes through the center of mass of you object and will therefore select the center of mass as the center of the object. The latter assumes that the object is longer in one direction compared to the other directions, and will use this direction as the helical axis. Don’t use these functions if these assumptions are not correct for your object!

align_helical_axis(data: numpy.ndarray, orientation: Sequence[float], center: Sequence[float]) → numpy.ndarray

Transform a 3D object to align its helical axis to the z-axis.

Parameters

• data – A 3D array containing the shape of a (helical) object. The shape of the array should correspond to the (y, x, z) axes.

• orientation – A vector that points in the direction of the helical axis. The vector should be a numpy array, tuple or list with three components (x, y, z).

• center – The location of the center of the object represented as a nnumpy array, tuple or list with components (x, y, z). This is typically the center of mass of the object.

Returns

The transformed data. The helical axis of this object is parallel with the z-axis and is positioned in the center of the array in each dimension.

center_of_mass(data: numpy.ndarray) → numpy.ndarray

Calculate the center of mass of a 3D object.

Parameters

data – A 3D array containing the shape of an object. The shape of the array should correspond to the (y, x, z) axes.

Returns

An array of 3 elements (x, y, z) of the center of mass of the object.

helical_axis_pca(data: numpy.ndarray, threshold: float) → numpy.ndarray

Estimate the orientation of the helical axis of a 3D object using PCA.

The helical axis is assumed to be along the longest direction of the object. This is often true for rods, wires or similar shapes, but is not guaranteed to be the case. The longest direction can be detected using principal component analysis (PCA) by binarizing it using a certain threshold value. A list will then be made with the (x, y, z) coordinates of all the voxels that are considered part of the object, i.e. all the voxels with an intensity that is larger than the threshold value. PCA is executed on this list of coordinates such that the component with the largest score will be oriented in the direction along which the points are spread the most. This is the direction along which the object is the longest.

Parameters

• data – A 3D array containing the shape of an object. The shape of the array should correspond to the (y, x, z) axes.

• threshold – The threshold that will be used to binarize the data. Only voxels with a value larger than this threshold will be used.

Returns

An array of 3 elements (x, y, z) of the orientation of the estimated helical axis.