The operator identifies the position of an object of interest projected on the stored pixel data of an image A, and estimates the magnification of the conic projection by a calibration process.

The operator wants to know the position of the projection of such object of interest on a second image B acquired under different geometry, assuming that the patient does not move between image A and image B (i.e., the images share the same frame of reference).

The XA SOP Class encodes the information in a patient-related coordinate system.

The Enhanced XA SOP Class additionally encodes the geometry of the acquisition system with respect to a fixed reference system defined by the manufacturer, so-called Isocenter reference system. Therefore, it allows encoding the absolute position of an object of interest and to track the projection of such object across the different images acquired under different geometry.

This section provides detailed recommendations of the key attributes to address this particular scenario.

In this example, the operator identifies the position (i, j) of an object of interest projected on the stored pixel data of an image A, and estimates the magnification of the conic projection by a calibration process.

The operator wants to know the position of the projection of such object of interest on a second image B acquired under different geometry.

The attributes that define the geometry of both images A and B are described in the following figure:

The following steps describe the process to calculate the position (i, j)_B of the projection of the object of interest in the Pixel Data of the image B, assuming that (i, j)_A is known and is the offset of the projection of the object of interest from the TLHC of the Pixel Data of the image A, measured in pixels of the Pixel Data matrix as a column offset "i" followed by a row offset "j". TLHC is defined as (0,0).

Step 1: Calculate the point (i, j)_A in FOV coordinates of the image A.

Step 2: Calculate the point (i, j)_A in physical detector coordinates of the image A.

Step 3: Calculate the point (P_u, P_v)_A in positioner coordinates of the image A.

Step 4: Calculate the point (P_Xp, P_Yp, P_Zp)_A in positioner coordinates of the image A.

Step 5: Calculate the point (P_X, P_Y, P_Z)_A in Isocenter coordinates of the image A.

Step 6: Calculate the point (P_Xt, P_Yt, P_Zt)_A in Table coordinates of the image A.

Step 7: Calculate the point (P_Xt, P_Yt, P_Zt)_B in Table coordinates in mm of the image B.

Step 8: Calculate the point (P_X, P_Y, P_Z)_B in Isocenter coordinates in mm of the image B.

Step 9: Calculate the point (P_Xp, P_Yp, P_Zp)_B in positioner coordinates of the image B.

Step 10: Calculate the point (P_u, P_v)_B in positioner coordinates of the image B.

Step 11: Calculate the point (i, j)_B in physical detector coordinates of the image B.

Step 12: Calculate the point (i, j)_B in FOV coordinates of the image B.

Step 13: Calculate the point (i, j)_B in Pixel Data of the image B.

In this example let's assume:

(i, j)_A = (310,122) pixels

Magnification ratio = 1.3

Step 1 : Image A: Point (i, j)_A in FOV coordinates

In this step, the FOV coordinates are calculated by taking into account the FOV rotation and Horizontal Flip applied to the FOV matrix when the Pixel Data were created:

1.1: Horizontal Flip : YES

new i = (columns -1) - i = 850 - 1 - 310 = 539

new j = j = 122

1.2: Image Rotation : 90 (clockwise)

new i = j = 122

new j = (columns -1) - i = 850 - 1 - 539 = 310

(i, j)_A = (122, 310) in stored pixel data.

Step 2: Image A: Point (i, j)_A in physical detector coordinates

In this step, the physical detector coordinates are calculated by taking into account the FOV origin and the ratio between Imager Pixel Spacing and Detector Element Spacing:

D_i = Imager Pixel Spacing (column) = 0.2 mm

D_j = Imager Pixel Spacing (row) = 0.2 mm

D_idet = Detector Element Spacing between two adjacent columns = 0.2 mm

D_jdet = Detector Element Spacing between two adjacent rows = 0.2 mm

Zoom Factor (column) = D_i / D_idet = 1.0

Zoom Factor (row) = D_j / D_jdet = 1.0

FOV Origin (column) = FOV_idet = 600.0

FOV Origin (row) = FOV_jdet = 600.0

new i = FOV_idet + (i + (1 - D_idet / D_i) / 2) * D_j / D_jdet = 600 + 122 * 1.0 = 722

new j = FOV_jdet + (j + (1 - D_jdet / D_j) / 2) * D_i / D_idet = 600 + 310 * 1.0 = 910

(i, j)_A = (722, 910) in detector elements.

Step 3: Image A: Point ( P_u, P_v)_A in positioner coordinates

In this step, the (P_u, P_v)_A coordinates in mm are calculated from (i, j)_A by taking into account the projection of the Isocenter in physical detector coordinates, and the Detector Element Spacing:

ISO_P_idet = Position of Isocenter Projection (column) = 1024.5

ISO_P_jdet = Position of Isocenter Projection (row) = 1024.5

D_idet = Detector Element Spacing between two adjacent columns = 0.2 mm

D_jdet = Detector Element Spacing between two adjacent rows = 0.2 mm

Pu = (i - ISO_P_idet) * D_idet = (722 - 1024.5) * 0.2 = -60.5 mm

Pv = (ISO_P_jdet - j) * D_jdet = (1024.5 - 910) * 0.2 = 22.9 mm

( P_u, P_v)_A = (-60.5, 22.9) in mm.

Step 4: Image A: Point (PXp, PYp, PZp)A in positioner coordinates

In this step, the positioner coordinates (P_Xp, P_Yp, P_Zp)_A are calculated from (P_u, P_v)_A by taking into account the magnification ratio, the Distance Source to Detector and the Distance Source to Isocenter:

SID = Distance Source to Detector = 1300 mm

ISO = Distance Source to Isocenter = 780 mm

Magnification ratio = SID / (ISO - P _Yp ) = 1.3

P _Yp = ISO - SID / 1.3 = 780 - 1300/1.3 = -220 mm

P _Xp = Pu / Magnification ratio = -60.5 / 1.3 = -46.54 mm

P _Zp = Pv / Magnification ratio = 22.9 / 1.3 = 17.62 mm

(P_Xp, P_Yp, P_Zp)_A = (-46.54, -220, 17.62) in mm.

Step 5: Image A: Point (P_X, P_Y, P_Z)_A in Isocenter coordinates

In this step, the isocenter coordinates (P_X, P_Y, P_Z)_A are calculated from the positioner coordinates (P_Xp, P_Yp, P_Zp)_A by taking into account the positioner angles of the image A in the Isocenter coordinate system:

Ap₁ = Positioner Isocenter Primary Angle = 60.0 deg

Ap₂ = Positioner Isocenter Secondary Angle = 20.0 deg

Ap₃ = Positioner Isocenter Detector Rotation Angle = 0.0 deg

(P_X, P_Y, P_Z)^T= (R₂ ·R₁)^T·(R₃ ^T·(P_Xp, P_Yp, P_Zp)^T)

(P_X, P_Y, P_Z)_A = (150.55, -65.41, 91.80) in mm.

Step 6: Image A: Point (P_Xt, P_Yt, P_Zt)_A in Table coordinates

In this step, the table coordinates (P_Xt, P_Yt, P_Zt)_A are calculated from the isocenter coordinates (P_X, P_Y, P_Z)_A by taking into account the table position and angles of the image A in the Isocenter coordinate system:

Tx =Table X Position to Isocenter = 10.0 mm

Ty =Table Y Position to Isocenter = 30.0 mm

Tz =Table Z Position to Isocenter = 100.0 mm

At₁ = Table Horizontal Rotation Angle = -10.0 deg

At₂ = Table Head Tilt Angle = 0.0 deg

At₃ = Table Cradle Tilt Angle = 0.0 deg

(P_Xt, P_Yt, P_Zt)^T= (R₃ · R₂ · R₁) · ((P_X, P_Y, P_Z)^T- (T_X, T_Y, T_Z)^T)

(P_Xt, P_Yt, P_Zt)_A = (136.99, -95.41, -32.48) in mm.

Step 7: Image B: Point (P_Xt, P_Yt, P_Zt)_B in Table coordinates

In this step, the table has moved from image A to image B. The table coordinates of the object of interest are the same on image A and image B because it is assumed that the patient is fixed on the table.

(P_Xt, P_Yt, P_Zt)_B = (136.99, -95.41, -32.48) in mm.

Step 8: Image B: Point (P_X, P_Y, P_Z)_B in Isocenter coordinates

In this step, the isocenter coordinates (P_X, P_Y, P_Z)_B are calculated from the table coordinates (P_Xt, P_Yt, P_Zt)_B by taking into account the table position and angles of the image B in the Isocenter coordinate system:

Tx =Table X Position to Isocenter = 20.0 mm

Ty =Table Y Position to Isocenter = 100.0 mm

Tz =Table Z Position to Isocenter = 0.0 mm

At₁ = Table Horizontal Rotation Angle = 0.0 deg

At₂ = Table Head Tilt Angle = 10.0 deg

At₃ = Table Cradle Tilt Angle = 0.0 deg

(P_X, P_Y, P_Z)^T= (R₃ · R₂ · R₁)^T· (P_Xt, P_Yt, P_Zt)^T+ (T_X, T_Y, T_Z)^T

(P_X, P_Y, P_Z)_B = (156.99, -12.11, -48.55) in mm.

Step 9: Image B: Point (P_Xp, P_Yp, P_Zp)_B in positioner coordinates

In this step, the positioner coordinates (P_Xp, P_Yp, P_Zp)_B are calculated from the isocenter coordinates (P_X, P_Y, P_Z)_B by taking into account the positioner angles of the image B in the Isocenter coordinate system:

Ap₁ = Positioner Isocenter Primary Angle = -30.0 deg

Ap₂ = Positioner Isocenter Secondary Angle = 0.0 deg

Ap₃ = Positioner Isocenter Detector Rotation Angle = 0.0 deg

(P_Xp, P_Yp, P_Zp)^T= R₃ · ((R₂ · R₁) · (P_X, P_Y, P_Z)^T)

(P_Xp, P_Yp, P_Zp)_B = (142.01, 68.00, -48.55) in mm.

Step 10: Image B: Point ( P_u, P_v)_B in positioner coordinates

In this step, the (P_u, P_v)_B coordinates in mm are calculated from the positioner coordinates (P_Xp, P_Yp, P_Zp)_B by taking into account the Distance Source to Detector and the Distance Source to Isocenter of the image B:

SID = Distance Source to Detector = 1000 mm

ISO = Distance Source to Isocenter = 800 mm

Magnification ratio = SID / (ISO - P _Yp ) = 1200/(800-68) = 1.366

Pu = P _Xp * Magnification ratio = 142.01 * 1.64 = 194.00 mm

Pv = P _Z p * Magnification ratio = -48.55 * 1.64 = -66.33 mm

( P_u, P_v)_B = (194.00, -66.33) in mm.

Step 11: Image B: Point (i, j)_B in physical detector coordinates

In this step, the physical detector coordinates (i, j)_B are calculated from the positioner coordinates ( P_u, P_v)_B by taking into account the projection of the Isocenter in physical detector coordinates, and the Detector Element Spacing of the image B:

ISO_P_idet = Position of Isocenter Projection (column) = 1024.5

ISO_P_jdet = Position of Isocenter Projection (row) = 1024.5

D_idet =Detector Element Spacing between two adjacent columns = 0.2

D_jdet =Detector Element Spacing between two adjacent rows = 0.2

i = ISO_P_idet + Pu / D_idet = 1024.5 + 194.00 / 0.2 = 1994.5

j = ISO_P_idet - Pv / D_idet = 1024.5 - (-66.33) / 0.2 = 1356.2

(i, j)_B = (1994.5, 1356.2) in detector elements.

Step 12 : Image B: Point (i, j)_B in FOV coordinates

In this step, the FOV coordinates are calculated from the physical detector coordinates by taking into account the FOV origin and the ratio between Imager Pixel Spacing and Detector Element Spacing of the image B:

D_i = Imager Pixel Spacing (column) = 0.4 mm

D_j = Imager Pixel Spacing (row) = 0.4 mm

D_idet = Detector Element Spacing between two adjacent columns = 0.2 mm

D_jdet = Detector Element Spacing between two adjacent rows = 0.2 mm

Zoom Factor (column) = D_i / D_idet = 2.0

Zoom Factor (row) = D_j / D_jdet = 2.0

FOV Origin (column) = FOV_idet = 25.0

FOV Origin (row) = FOV_jdet = 25.0

new i = (i - FOV_idet).D_idet / D_i - (1 - D_idet / D_i) / 2 = (1994.5 - 25.0) / 2.0 - 0.25 = 984.5

new j = (j - FOV_jdet).D_jdet / D_j - (1 - D_jdet / D_j) / 2 = (1356.2 - 25.0) / 2.0 - 0.25 = 665.35

(i, j)_B = (984.50, 665.35) in stored pixel data.

Step 13 : Image B: Point (i, j)_B in Pixel Data

In this step, the position (i, j)_B of the projection of the object of interest in the Pixel Data of the image B is calculated from the FOV coordinates by taking into account the FOV rotation and Horizontal Flip applied to the FOV matrix when the Pixel Data were created:

1.1: Horizontal Flip : NO

new i = i = 984.50

new j = j = 665.35

1.2: Image Rotation : 180 (clockwise)

new i = (columns -1) - i = 1000 - 1 - 984.50 = 14.50

new j = (rows -1) - j = 1000 - 1 - 665.35 = 333.65

(i, j)_B = (14.50, 333.65) in stored pixel data.