DICOM PS3.3 2020b - Information Object Definitions |
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Table C.20.2-1 defines the general Attributes of the Spatial Registration Module.

**Table C.20.2-1. Spatial Registration Module Attributes**

Include Table 10-12 “Content Identification Macro Attributes” |
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A Sequence of registration Items. Each Item defines a spatial registration of the images referenced in that Item to the Registered RCS established by this SOP Instance. All referenced images are in the same spatial Frame of Reference or atlas. |
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Identifies the Frame of Reference of the referenced data, that may or may not be an image set (e.g., atlas or physical space). See Section C.7.4.1.1.1 for further explanation. Required if Referenced Image Sequence (0008,1140) is absent. May be present otherwise. |
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Identifies the set of images of the referenced data, registered in this Item. One or more Items shall be included in this Sequence. Required if Frame of Reference UID (0020,0052) is absent. May be present otherwise. |
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>>Include Table 10-3 “Image SOP Instance Reference Macro Attributes” |
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Describes the information input into the registration process. |
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>>>Include Table 8.8-1 “Code Sequence Macro Attributes” |
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Specifies one transformation, that registers the Source RCS/images to the Registered RCS. It is expressible as multiple matrices, each in a separate Item of the Sequence. One or more Items shall be included in this Sequence. The Item order is significant and corresponds to matrix multiplication order. See Section C.20.2.1.1. |
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A 4x4 affine transformation matrix that registers a homogeneous coordinate system A to B. Matrix elements shall be listed in row-major order. See Section C.20.2.1.1. |
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Type of Frame of Reference Transformation Matrix (3006,00C6). |
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The fiducials used to determine the Frame of Reference Transformation Matrix. |
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>>Include Table 10-11 “SOP Instance Reference Macro Attributes” |
Reference to the Spatial Fiducial SOP Instance identifying the Used Fiducial(s) |
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The UID that identifies the fiducial used as registration input. |
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The segments used to determine the Frame of Reference Transformation Matrix. |
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>>Include Table 10-11 “SOP Instance Reference Macro Attributes” |
Reference to the Segmentation or Surface Segmentation SOP Instance identifying the Used Segments. |
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Uniquely identifies the segment described in Segment Sequence (0062,0002) by reference to Segment Number (0062,0004). Referenced Segment Number (0062,000B) shall not be multi-valued. |

The Frame of Reference Transformation Matrix (3006,00C6) ^{A}M_{B} describes how to transform a point (^{B}x,^{B}y,^{B}z) with respect to RCS_{B} into (^{A}x,^{A}y,^{A}z) with respect to RCS_{A} according to Equation C.20.2-1.

The Matrix Registration is expressible as multiple matrices, each in a separate Item of Matrix Sequence (0070,030A). Equation C.20.2-2 specifies the order of the matrix multiplication where
**M _{1}
**
,

Registration often involves two or more RCS, each with a corresponding Frame of Reference Transformation Matrix. For example, another Frame of Reference Transformation Matrix ^{A}M_{C} can describe how to transform a point (
^{C}x,^{C}y,^{C}z) with respect to RCS
_{C}
into (
^{A}x,^{A}y,^{A}z) with respect to RCS_{A}. It is straightforward to find the Frame of Reference Transformation Matrix
^{B}
M
_{C}
that describes how to transform the point (
^{C}x,^{C}y,^{C}z) with respect to RCS_{C} into the point (
^{B}x,^{B}y,^{B}z) with respect to RCS_{B}. The solution is to invert ^{A}M_{B} and multiply by ^{A}M_{C}, as shown in Equation C.20.2-3.

If two or more transformation matrices describe the relation between Patient coordinates and a device-centric Well-known Frame of Reference, any calculations assuming transitivity via the Well-known Frame of Reference must be performed with great care to assure that both registrations reflect the same positioning of the patient with respect to the common Well-known Frame of Reference.

There are three types of Registration Matrices:

RIGID: This is a registration involving only translations and rotations. Mathematically, the matrix is constrained to be orthonormal and describes six degrees of freedom: three translations, and three rotations.

RIGID_SCALE: This is a registration involving only translations, rotations and scaling. Mathematically, the matrix is constrained to be orthogonal and describes nine degrees of freedom: three translations, three rotations and three scales. This type of transformation is sometimes used in atlas mapping.

AFFINE: This is a registration involving translations, rotations, scaling and shearing. Mathematically, there are no constraints on the elements of the Frame of Reference Transformation Matrix other than that the last row shall be (0,0,0,1) to preserve the homogeneous coordinates, so it conveys twelve degrees of freedom. This type of transformation is sometimes used in atlas mapping.

See Annex P “Transforms and Mappings (Informative)” in PS3.17 for more detail.

DICOM PS3.3 2020b - Information Object Definitions |
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