Mapping Neurons

Fragment Generation

class brainlit.map_neurons.DiffeomorphismAction

Interface for differentiable mappings e.g. transformations that register a brain image to an atlas.

D(self, position: np.array, deriv: np.array, order: int = 1)

Evaluate the mapping on a set of derivatives at specified positions.

Parameters:

  • position (np.array) -- Coordinates in the original space.

  • deriv (np.array) -- Derivatives at the respective positions

  • order (int, optional) -- Derivative order. Defaults to 1.

Returns:

Transformed derivatives.

Return type:

np.array

evaluate(self, position: np.array)

Evaluate the mapping at specified positions.

Parameters:

position (np.array) -- Coordinates in original space.

Returns:

Transformed coordinates.

Return type:

np.array

class brainlit.map_neurons.CloudReg_Transform(vpath: str, Apath: str, direction: str = 'atlas')

Object that can read mat files from CloudReg, and compute transformations on points and Jacobians. Implements DiffeomorphismAction which is an interface to transform points and tangent vectors.

D(self, position: np.array, deriv: np.array, order: int = 1)

Compute transformed derivatives of mapping at given positions. Only for the non-affine component.

Parameters:

  • position (np.array) -- nx3 positions at which to compute derivatives.

  • deriv (np.array) -- nx3 derivatives at the respective positions.

  • order (int, optional) -- Order of derivative (must be 1). Defaults to 1.

Raises:

ValueError -- Only derivative order 1 is allowed here.

Returns:

Transformed derivatives

Return type:

np.array

Jacobian(self, pos: np.array)

Compute Jacobian of transformation at a given point.

Parameters:

pos (np.array) -- Coordinate in space.

Returns:

Jacobian at that coordinate

Return type:

np.array

apply_affine(self, position: np.array)

Apply affine transformation in the transformation of positions in target space to atlas space.

Parameters:

position (np.array) -- nx3 array with positions in target space.

Returns:

positions after affine transformation was applied.

Return type:

np.array

evaluate(self, position: np.array)

Apply non-affine component of mapping to positions, in direction of self.direction (default from target to atlas).

Parameters:

position (np.array) -- Positions at which to compute mappings.

Returns:

Mappings of the input.

Return type:

np.array

brainlit.map_neurons.compute_derivs(us: np.array, tck: tuple = None, positions: np.array = None, deriv_method: str = 'difference')

Estimate derivatives of a sequence of points. Derivatives can be estimated in three ways: - For curves parameterized by scipy's spline API, spline estimation uses scipy's derivative computation - For a sequence of points, we use the finite-difference method from:

Sundqvist, H., & Veronis, G. (1970). A simple finite‐difference grid with non‐constant intervals. Tellus, 22(1), 26-31.

  • one-sided derivatives are derived from the piecewise linear interpolation.

Parameters:

  • us (np.array) -- Parameter values (in form returned by scipy.interpolate.splprep).

  • tck (tuple) -- Knots, bspline coefficients, and degree of spline (in form returned by scipy.interpolate.splprep).

  • positions (np.array) -- nx3 array of positions (for use by difference method).

  • deriv_method (str, optional) -- Method to use (from list above), spline for scipy.interpolate.splev, difference for the finite difference method, two-sided for one-sided derivatives from linear interpolation. Defaults to "difference".

Raises:

  • ValueError -- If the wrong combination of arguments/deriv_method is used.

  • ValueError -- If derivative method is unrecognized.

Returns:

Derivative estimates at specified positions, or tuple of np.array for two-sided option.

Return type:

np.array