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# Spatial Transformations

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# Spatial Transformations

Spatial Transformations

PMOD supports two types of spatial transformations:

1.Rigid transformations R rotate and translate the contents of an image volume, for instance to calculate slices at oblique orientations. Rigid transformations are defined by 6 parameters, the rotation angles and translation distances in the three spatial directions.

2.Elastic transformations E allow adjusting the shape of the objects in an image volume to objects with a different shape in another image volume (the template). They have an affine part and an elastic part. The affine part has 12 parameters to account for an overall rotation, translation, scaling and shearing in the three spatial directions. The elastic part consists of a deformation field which performs the local adjustments.

Combination of Transformations

The PMOD fusion tools support the analytical combination of spatial transformations, avoiding hereby multiple interpolations. For example, when image A is matched to image B by the rigid transformation R1, and B is matched to image C by the rigid transformation R2, A is inherently matched to C by the combination R1*R2 of the transforms.

In PMOD, an arbitrary number of rigid transformations can be combined, but only one elastic transformation at the end of the chain. So for example:

A CT image from a PET-CT study is matched to MR by R1.

An MR image is elastically matched to the MNI template by E1.

Then the CT image is matched to the MNI template by the combined transform R1*E1.

If (and only if) the PET image has the origin at the same anatomical position as the CT, PET can also be matched to the MNI template by R1*E1.

Inverse Transformations

All the automatic methods can not only return the matching transformation, but also the inverse transformation which applies if the role of the Reference and the Input is reversed. Additionally, PMOD can always calculate the inverse of the current transformation, even if it was created by combining transformations.

Transformation of VOIs

The spatial transformations cannot only be applied to reslice images to reference images, but also to project VOIs from the reference space to the target image space. An application of particular interest is the use of standard VOIs which are defined in the MNI space for the analysis of subject images. This can be achieved with the following steps:

1.The subject images are normalized to a MNI template with Calculate InverseTransformation checked.

2.The inverse normalization transform is saved.

3.The subject images are loaded in the PMOD viewing tool.

4.The MNI VOIs are loaded and the inverse normalization transform applied.

As a result the standard VOIs, adjusted for the particular subject anatomy, are available in the VOI tool as outline contours. The user can adjust them if needed, then save them and calculate image statistics on the unchanged subject data.