Degrees of freedom

The number of independent pieces of information that go into the estimate of a parameter is called the degrees of freedom (DOF). In this guide, DOF are given for 3D images.

Basics

In general, the degrees of freedom of an estimate is equal to the number of independent scores that go into the estimate minus the number of parameters estimated as intermediate steps in the estimation of the parameter itself. In image registration, a transformation matrix establishes geometrical correspondence between coordinate systems of different images. It is used to transform one image into the space of the other.

Transformations are generally used in biomedical imaging

Rigid-body transformations

Rigid-body transformations include translations and rotations. They preserve all lengths and angles. These are 6 DOF transformations, and the transformation matrix is as follows:

<math> \begin{matrix}

 R_x & R_y & R_z \\
 T_x & T_y & T_z 
\end{matrix}

</math>