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| __TOC__
| | #REDIRECT [[Main Page]] |
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| ==SimilarityRegistration==
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| ===Understanding rotation parameters (versors)===
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| In SimilarityRegistration, former AppSimilarityRegistrationV3, used when registering images with Shape, the config file
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| allows for setting inital rotations <code>initial_transform_axis_x, initial_transform_axis_y, initial_transform_axis_z</code>. These correspond to the versor components and are calculated as follows:
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| <pre>
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| initial_transform_axis_x = n_x * sin(alpha/2)
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| initial_transform_axis_y = n_y * sin(alpha/2)
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| initial_transform_axis_z = n_z * sin(alpha/2)
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| </pre>
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| where <code>n=[n_x,n_y,n_z]^T</code> is the unit vecotr representing the axis of rotation and <code>alpha</code> is the angle of rotation. Example 45 degree rotation around x-axis:
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| <pre>
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| initial_transform_axis_x = 1 * sin(45/2) = 0.382
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| initial_transform_axis_y = 0 * sin(45/2) = 0
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| initial_transform_axis_z = 0 * sin(45/2) = 0
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| </pre>
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| The rotations after registration <code>final_transform_axis_x, final_transform_axis_y, final_transform_axis_z</code> can be interpreted the same way.
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| ITK provides the functions GetAxis() and GetAngle to obtain <code>[n_x, n_y, n_z]</code> and <code>alpha</code> respectively, which are calculated as follows:
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| <pre>
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| v_1 = initial_transform_axis_x
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| v_2 = initial_transform_axis_y
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| v_3 = initial_transform_axis_z
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| magnitude = sqrt(v_1^2 + v_2^2 + v_3^2)
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| n_x = v_1/magnitude
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| n_y = v_2/magnitude
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| n_z = v_3/magnitude
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| alpha = 2 * atan(magnitude/1)
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| </pre>
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| ==Statistics and Analysis==
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| ===JAGS (analysis of Bayesian models using Markov Chain Monte Carlo)===
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| See [[JAGS Usage]].
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