# DICOM Standard Browser

Built with by Innolitics, a team of medical imaging software developers.

Data synced with official DICOM standard on 18 April 2024. The DICOM Standard is under continuous maintenance, and the current official version is available at http://www.dicomstandard.org/current/. DICOM Parts 3, 4, and 6, © NEMA. Please note that the most recent PDF version of the standard is the official reference, and should checked when making technical decisions.

## Matrix Sequence Attribute

Tag (0070,030A) Required (1) MatrixSequence 1 Sequence (SQ)

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.

## Section C.20.2.1.1

##### C.20.2.1.1 Frame of Reference Transformation Matrix

The Frame of Reference Transformation Matrix (3006,00C6) AMB describes how to transform a point (Bx,By,Bz) with respect to RCSB into (Ax,Ay,Az) with respect to RCSA according to Equation C.20.2-1.

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 M1 , M2 and M3 are the first, second and third Items in the Sequence.

Equation C.20.2-2.

where

Registration often involves two or more RCS, each with a corresponding Frame of Reference Transformation Matrix. For example, another Frame of Reference Transformation Matrix AMC can describe how to transform a point ( Cx,Cy,Cz) with respect to RCS C into ( Ax,Ay,Az) with respect to RCSA. It is straightforward to find the Frame of Reference Transformation Matrix B M C that describes how to transform the point ( Cx,Cy,Cz) with respect to RCSC into the point ( Bx,By,Bz) with respect to RCSB. The solution is to invert AMB and multiply by AMC, as shown in Equation C.20.2-3.

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.