# C.7.6.21 Image - Equipment Coordinate Relationship Module

This section describes the Image - Equipment Coordinate Relationship module. Table C.7.6.21-1 contains the attributes that specify how the equipment (e.g. gantry) and patient oriented coordinate system (in conjunction with the Image Position (Patient) (0020,0032) and Image Orientation (Patient) (0020,0037) attributes) are related.

Table C.7.6.21-1IMAGE - EQUIPMENT COORDINATE RELATIONSHIP MODULE ATTRIBUTES

 Attribute Name Tag Type Attribute Description Image to Equipment Mapping Matrix (0028,9520) 1 A 4x4 homogeneous transformation matrix that maps patient coordinate space of the reconstructed image to the equipment defined original coordinate space. Matrix elements shall be listed in row-major order. See C.7.6.21.1. Equipment Coordinate System Identification (0028,9537) 1 Identification of the type of equipment coordinate system in which the projection images were acquired. See C.7.6.21.2. Defined Terms: ISOCENTER

## C.7.6.21.1 Image to Equipment Mapping Matrix

The Image to Equipment Mapping Matrix (0028,9520) is used to describe the relationship between the Patient oriented coordinate system and a modality specific equipment coordinate system. This mapping can only be used with systems that have a well-defined equipment coordinate system (such as XA, etc.).

The Image to Equipment Mapping Matrix A M B describes how to transform a point ( B x, B y, B z) with respect to the Patient coordinate system into ( A x, A y, A z) with respect to the equipment coordinate system according to the equation below.

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The Image to Equipment Mapping Matrix is a rigid transformation that involves only translations and rotations. Mathematically, the matrix shall be orthonormal and can describe six degrees of freedom: three translations, and three rotations.

Note: Both the Patient Coordinate System and the Equipment Coordinate System are expressed in millimeters.

C.7.6.21.2 Equipment Coordinate System Identification

The Equipment Coordinate System Identification (0028,9537) identifies the Reference Coordinate System to which the Image to Equipment Mapping Matrix (0028,9520) is related.

The Defined Term ISOCENTER refers to a coordinate reference system where the origin corresponds with the center of rotation of the projections.

Note: For X-Ray 3D Angiographic Images created from SOP Instances of the Enhanced XA SOP Class (1.2.840.10008.5.1.4.1.1.12.1.1) the isocenter coordinate system is used to describe the positioning of the table and positioner (see C.8.19.6.13), and will use only the Defined Term ISOCENTER.