How To's

SimilarityRegistration

Understanding rotation parameters (versors)

In SimilarityRegistration, former AppSimilarityRegistrationV3, used when registering images with Shape, the config file allows for setting inital rotations initial_transform_axis_x, initial_transform_axis_y, initial_transform_axis_z. These correspond to the versor components and are calculated as follows:

initial_transform_axis_x = n_x * sin(alpha/2)
initial_transform_axis_y = n_y * sin(alpha/2)
initial_transform_axis_z = n_z * sin(alpha/2)

where n=[n_x,n_y,n_z]^T is the unit vecotr representing the axis of rotation and alpha is the angle of rotation. Example 45 degree rotation around x-axis:

initial_transform_axis_x = 1 * sin(45/2) = 0.382
initial_transform_axis_y = 0 * sin(45/2) = 0
initial_transform_axis_z = 0 * sin(45/2) = 0

The rotations after registration final_transform_axis_x, final_transform_axis_y, final_transform_axis_z can be interpreted the same way. ITK provides the functions GetAxis() and GetAngle to obtain [n_x, n_y, n_z] and alpha respectively, which are calculated as follows:

v_1 = initial_transform_axis_x
v_2 = initial_transform_axis_y
v_3 = initial_transform_axis_z
magnitude = sqrt(v_1^2 + v_2^2 + v_3^2)
n_x = v_1/magnitude
n_y = v_2/magnitude
n_z = v_3/magnitude
alpha = 2 * atan(magnitude/1)

Statistics and Analysis

JAGS (analysis of Bayesian models using Markov Chain Monte Carlo)

See JAGS Usage.