The registrations in this module are applied to the Registered RCS coordinates in the following order. First, transform the coordinates using the matrix described in the Pre Deformation Matrix Registration Sequence (0064,000F). Next apply the deformation offsets to the resulting coordinates. Finally, transform those coordinates using the matrix described in the Post Deformation Matrix Registration Sequence (0064,0010). The resulting coordinate addresses the sample point within the Source RCS.

Thus a source coordinate may be calculated using the following equation:

(This assumes that the center position of each deformation voxel will be transformed)

[pic]

Where:

[pic] The spatial coordinate in the Source RCS.

[pic] The start coordinate, in the Registered RCS, of the deformation grid as specified in the Image Position (Patient) attribute (0020,0032).

[pic] The values from the row (X) direction cosine of the Image Orientation (Patient) (0020,0037) attribute.

[pic] The values from the column (Y) direction cosine of the Image Orientation (Patient) (0020,0037) attribute.

[pic] The cross product between the row (X) direction cosine and the column (Y) direction cosine of the Image Orientation (Patient) (0020,0037) attribute.

[pic]

[pic] The index into the deformation grid in the X, Y, and Z dimension.

[pic] The resolution of the deformation grid in the X, Y, and Z dimension as specified in the Grid Resolution attribute (0064,0008).

[pic] The deformation specified at index (i,j,k) in the deformation grid. If the Deformation Registration Grid Sequence (0064,0005) has no items, the ( values are zero.

*
M
*
*
_{
Pre
}
*
The transformation matrix specified in the Pre Deformation Matrix Registration Sequence (0064,000F).

*
M
*
*
_{
Post
}
*
The transformation matrix specified in the Post Deformation Matrix Registration Sequence (0064,0010).

The vector represents the deformation at the center of the voxel. Deformations between voxel centers shall be determined through interpolation of the surrounding vectors in an implementation dependent manner.

The Vector Grid Data attribute (0064,0009) contains the vector data. Each voxel in the Vector Grid Data attribute (0064,0009) is represented by an [pic] vector. The vector describes the direction and magnitude of the deformation at the center of the deformation voxel.

The order of vectors sent for each vector plane shall be left to right, top to bottom, i.e., the upper left vector (labeled 1,1) is sent first followed by the remainder of row 1, followed by the first vector of row 2 (labeled 2,1) then the remainder of row 2 and so on.

A vector triple with values of (NaN,NaN,NaN) shall indicate that the transformation at that point of the deformation grid is undefined.

The size of this attribute value is determined by the dimensions specified in the Grid Dimensions attribute (0064,0007). For dimensions of X
_{
D
}
\Y
_{
D
}
\Z
_{
D
}
, the size of the attribute value can be calculated with the equation:

Number of Bytes = X
_{
D
}
* Y
_{
D
}
* Z
_{
D
}
* 3 * 4