# FFF.1.2 Acquisition Geometry

This chapter illustrates the relationships between the geometrical models of the patient, the table, the positioner, the detector and the pixel data.

The following figure shows the different steps in the X-Ray acquisition that influences the geometrical relationship between the patient and the pixel data.

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Figure FFF.1.2-1Acquisition Steps Influencing the Geometrical Relationship Between the Patient and the Pixel Data

## FFF.1.2.1 Patient Description

Refer to Annex A for the definition of the patient orientation.

A point of the patient is represented as: P = (P left , P posterior , P head ).

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Figure FFF.1.2-2Point P Defined in the Patient Orientation

## FFF.1.2.2 Patient Position

### FFF.1.2.2.1 Table Description

The table coordinates are defined in the section C.8.7.4.1.4 of PS 3.3.

The table coordinate system is represented as: (O t , X t , Y t , Z t ) where the origin O t is located on the tabletop and is arbitrarily defined for each system.

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Figure FFF.1.2-3Table Coordinate System

### FFF.1.2.2.2 Options for Patient Position on the X-Ray Table

The position of the patient in the X-Ray table is described in the section C.7.3.1.1.2 of PS 3.3.

The table below shows the direction cosines for each of the three patient directions (Left, Posterior, Head) related to the Table coordinate system (X t , Y t , Z t ), for each patient position on the X-Ray table:

 Patient Position Patient left direction Patient posterior direction Patient head direction Recumbent - Head First - Supine (1, 0, 0) (0, 1, 0) (0, 0, 1) Recumbent - Head First - Prone (-1, 0, 0) (0, -1, 0) (0, 0, 1) Recumbent - Head First - Decubitus Right (0, -1, 0) (1, 0, 0) (0, 0, 1) Recumbent - Head First - Decubitus Left (0, 1, 0) (-1, 0, 0) (0, 0, 1) Recumbent - Feet First - Supine (-1, 0, 0) (0, 1, 0) (0, 0, -1) Recumbent - Feet First - Prone (1, 0, 0) (0, -1, 0) (0, 0, -1) Recumbent - Feet First- Decubitus Right (0, -1, 0) (-1, 0, 0) (0, 0, -1) Recumbent - Feet First -Decubitus Left (0, 1, 0) (1, 0, 0) (0, 0, -1)

## FFF.1.2.3 Table Movement

### FFF.1.2.3.1 Isocenter Coordinate System

The Isocenter coordinate system is defined in section C.8.19.6.13.1.1 of PS 3.3.

### FFF.1.2.3.2 Table Movement in the Isocenter Coordinate System

The table coordinate system is defined in section C.8.19.6.13.1.3 of PS 3.3 where the table translation is represented as (T X ,T Y ,T Z ). The table rotation is represented as (At 1 , At 2 , At 3 ).

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Figure FFF.1.2-4At1: Table Horizontal Rotation Angle

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Figure FFF.1.2-5At2: Table Head Tilt Angle

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Figure FFF.1.2-6At3: Table Cradle Tilt Angle

A point (P Xt , P Yt , P Zt ) in the table coordinate system (see Figure FFF.1.2-7) can be expressed as a point (P X , P Y , P Z ) in the Isocenter coordinate system by applying the following transformation:

(P X , P Y , P Z ) T = (R 3 . R 2 . R 1 ) T . (P Xt , P Yt , P Zt ) T + (T X , T Y , T Z ) T

And inversely, a point (P X , P Y , P Z ) in the Isocenter coordinate system can be expressed as a point (P Xt , P Yt , P Zt ) in the table coordinate system by applying the following transformation:

(P Xt , P Yt , P Zt ) T = (R 3 . R 2 . R 1 ) . ( (P X , P Y , P Z ) T - (T X , T Y , T Z ) T )

Where R 1 , R 2 and R 3 are defined as follows:

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Figure FFF.1.2-7Point P in the Table and Isocenter Coordinate Systems

## FFF.1.2.4 Positioner Movement

### FFF.1.2.4.1 Positioner Movement in the Isocenter Coordinate System

The positioner coordinate system is defined in section C.8.19.6.13.1.2 of PS 3.3 where the positioner angles are represented as (Ap 1 , Ap 2 , Ap 3 ).

A point (P Xp , P Yp , P Zp ) in the positioner coordinate system can be expressed as a point (P X , P Y , P Z ) in the Isocenter coordinate system by applying the following transformation:

(P X , P Y , P Z ) T = (R 2 . R 1 ) T . ( R 3 T . (P Xp , P Yp , P Zp ) T )

And inversely, a point (P X , P Y , P Z ) in the Isocenter coordinate system can be expressed as a point (P Xp , P Yp , P Zp ) in the positioner coordinate system by applying the following transformation:

(P Xp , P Yp , P Zp ) T = R 3 . ( (R 2 . R 1 ) . (P X , P Y , P Z ) T )

Where R 1 , R 2 and R 3 are defined as follows:

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### FFF.1.2.4.2 X-Ray Incidence and Image Coordinate System

The following concepts illustrate the model of X-Ray cone-beam projection:

The X-Ray incidence represents the vector going from the X-Ray source to the Isocenter.

The receptor plane represents the plane perpendicular to the X-Ray Incidence, at distance SID from the X-Ray source. Applies for both image intensifier and digital detector. In case of digital detector it is equivalent to the detector plane.

The image coordinate system is represented by (o, u, v), where “o” is the projection of the Isocenter on the receptor plane.

The source to isocenter distance is called ISO. The source image receptor distance is called SID.

The projection of a point (P Xp , P Yp , P Zp ) in the positioner coordinate system is represented as a point (P u , P v ) in the image coordinate system.

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Figure FFF.1.2-8Projection of a Point of the Positioner Coordinate System

A point (P Xp , P Yp , P Zp ) in the positioner coordinate system (O p , X p , Y p , Z p ) can be expressed as a point (P u , P v ) in the image coordinate system by applying the following transformation:

P u = (SID / (ISO – P Yp ) ) . P Xp

P v = (SID / (ISO – P Yp ) ) . P Zp

The ratio SID / (ISO - P Yp ) is also called magnification ratio of this particular point.

## FFF.1.2.5 Field of View Transformations

### FFF.1.2.5.1 Detector

The following concepts illustrate the model of the X-Ray detector:

Physical detector array (or physical detector matrix) is the matrix composed of physical detector elements .

Note: Not all the detector elements are activated during an X-Ray exposure. The active detector elements are in the detector active area, which can be equal to or smaller than the physical detector area.

Physical detector element coordinates represented as (i det, j det ) are columns and rows of the physical detector element in the physical detector array.

Detector TLHC element is the detector element in the Top Left Hand Corner of the physical detector array and corresponds to (i det, j det ) = (0,0).

The attribute Detector Element Physical Size (0018,7020) represents the physical dimensions in mm of a detector element in the row and column directions.

The attribute Detector Element Spacing (0018,7022) contains the two values Δ jdet and Δ idet , which represent the physical distance in mm between the centers of each physical detector element:

• Δ idet = detector element spacing between two adjacent columns;

• Δ jdet = detector element spacing between two adjacent rows.

The attribute Detector Element Physical Size (0018,7020) may be different from the Detector Element Spacing (0018,7022) due to the presence of spacing material between detector elements.

The attribute Position of Isocenter Projection (0018,9430) contains the point (ISO_P idet, ISO_P jdet ), which represents the projection of the Isocenter on the detector plane, measured as the offset from the center of the detector TLHC element. It is measured in physical detector elements.

The attribute Imager Pixel Spacing (0018,1164) contains the two values Δ j and Δ i , which represent the physical distance measured at the receptor plane between the centers of each pixel of the FOV image:

• Δ i = imager pixel spacing between two adjacent columns;

• Δ j = imager pixel spacing between two adjacent rows.

The zoom factor represents the ratio between Imager Pixel Spacing (0018,1164) and Detector Element Spacing (0018,7022). It may be different from the detector binning (e.g., when a digital zoom has been applied to the pixel data).

• Zoom factor (columns) = Δ i / Δ idet ;

• Zoom factor (rows) = Δ j / Δ jdet .

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Figure FFF.1.2-9Physical Detector and Field of View Areas

### FFF.1.2.5.2 Field of View

The following concepts illustrate the model of the field of view:

The field of view (FOV) corresponds to a region of the physical detector array that has been irradiated.

The field of view image is the matrix of pixels of a rectangle circumscribing the field of view. Each pixel of the field of view image may be generated by multiple physical detector elements.

The attribute FOV Origin (0018,7030) contains the two values (FOV idet, FOV jdet ), which represent the offset of the center of the detector element at the TLHC of the field of view image, before rotation or flipping, from the center of the detector TLHC element. It is measured in physical detector elements. FOV Origin = (0,0) means that the detector TLHC element is at the TLHC of a rectangle circumscribing the field of view.

The attribute FOV Dimension (0018,9461) contains the two values FOV row dimension and FOV column dimension, which represent the dimension of the FOV in mm:

• FOV row dimension = dimension in mm of the field of view in the row direction;

• FOV column dimension = dimension in mm of the field of view in the column direction.

FOV pixel coordinates represented as (i , j) are columns and rows of the pixels in the field of view image.

FOV TLHC pixel is the pixel in the Top Left Hand Corner of the field of view image and corresponds to (i , j) = (0,0).

As an example, the point (ISO_P i, ISO_P j ) representing the projection of the Isocenter on the field of view image, and measured in FOV pixels as the offset from the center of the FOV TLHC pixel, can be calculated as follows:

ISO_P i = (ISO_P idet - FOV idet ) . Δ idet / Δ i - (1 - Δ idet / Δ i ) / 2

ISO_P j = (ISO_P jdet - FOV jdet ) . Δ jdet / Δ j - (1 - Δ jdet / Δ j ) / 2

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Figure FFF.1.2-10Field of View Image

### FFF.1.2.5.3 Field of View Rotation and Flip

The attribute FOV Rotation (0018,7032) represents the clockwise rotation in degrees of field of view relative to the physical detector.

The attribute FOV Horizontal Flip (0018,7034) defines whether or not a horizontal flip has been applied to the field of view after rotation relative to the physical detector.

The attribute Pixel Data (7FE0,0010) contains the FOV image after rotation and/or flipping.

Pixel data coordinates is the couple (c,r) where c is the column number and r is the row number.

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Figure FFF.1.2-11Examples of Field of View Rotation and Horizontal Flip