Method, device, and system for calculating a geometric system model using an area-simulating-volume algorithm in three dimensional reconstruction

1. A method for calculating distance ratios used to calculate a geometric probability between a voxel and a tube-of-response (TOR) defined by two crystals within a reconstruction space of a medical imaging apparatus, the method comprising:

determining a first edge line connecting respective left endpoints of the two crystals in an X-Y plane of the medical imaging apparatus, the first edge line including a first middle point located midway between the left endpoints;

determining a second edge line connecting respective right endpoints of the two crystals in the X-Y plane, the second edge line including a second middle point located midway between the right endpoints;

determining a middle line of the TOR in the X-Y plane as a line intersecting the first middle point and the second middle point;

projecting, in the X-Y plane, a first center point of a first surface of the voxel to the middle line along a direction of the first edge line to define a first projected point;

projecting, in the X-Y plane, a second center point of a second surface of the voxel to the middle line along a direction of the second edge line to define a second projected point;

calculating a first distance between one of the first and second middle points and the first projected point, and a second distance between the one of the first and second middle points and the second projected point; and

determining a first distance ratio in the X-Y plane based on the first distance and the second distance.

2. The method of claim 1 , further comprising:

determining a center on each of the two crystals defining a line of response.

3. The method of claim 2 , further comprising:

determining the first center point of the first surface of the voxel and the second center point of the second surface of the voxel based on an angle between the line of response and a positive X-axis in the X-Y plane.

4. The method of claim 1 , further comprising:

determining a third edge line connecting respective front endpoints of the two crystals in a Y-Z or X-Z plane of the medical imaging apparatus, the third edge line including a first z-line point;

determining a fourth edge line connecting respective rear endpoints of the two crystals in the Y-Z or X-Z plane, the fourth edge line including a second z-line point;

determining a z-line of the TOR parallel to a Z-axis in the Y-Z or X-Z plane as a line intersecting the first z-line point and the second z-line point;

projecting, in the Y-Z or X-Z plane, a third center point of a third surface of the voxel to the z-line along a direction of the third edge line to define a third projected point;

projecting, in the Y-Z or X-Z plane, a fourth center point of a fourth surface of the voxel to the z-line along a direction of the fourth edge line to define a fourth projected point;

calculating a third distance between one of the first and second z-line points and the third projected point, and a fourth distance between the one of the first and second z-line points and the fourth projected point; and

determining a second distance ratio in the Y-Z or X-Z plane based on the third distance and the fourth distance.

5. The method of claim 4 , further comprising:

calculating an intersected volume by multiplying the first distance ratio by the second distance ratio.

6. The method of claim 4 , wherein

the third surface of the voxel and the fourth surface of the voxel are on opposite sides of the voxel.

7. The method of claim 1 , wherein

the first surface of the voxel and the second surface of the voxel are on opposite sides of the voxel.

8. A reconstruction device for calculating distance ratios used to calculate a geometric probability between a voxel and a tube-of-response (TOR) defined by two crystals within a reconstruction space of a medical imaging apparatus, the reconstruction device comprising:

a determining unit configured to

determine a first edge line connecting respective left endpoints of the two crystals in an X-Y plane of the medical imaging apparatus, the first edge line including a first middle point located midway between the left endpoints,

determine a second edge line connecting respective right endpoints of the two crystals in the X-Y plane, the second edge line including a second middle point located midway between the right endpoints, and

determine a middle line of the TOR in the X-Y plane as a line intersecting the first middle point and the second middle point;

a projecting unit configured to project, in the X-Y plane, a first center point of a first surface of the voxel to the middle line along a direction of the first edge line to define a first projected point, and to project, in the X-Y plane, a second center point of a second surface of the voxel to the middle line along a direction of the second edge line to define a second projected point;

a calculating unit configured to calculate a first distance between one of the first and second middle points and the first projected point, and a second distance between the one of the first and second middle points and the second projected point; and

a distance ratio determining unit configured to determine a first distance ratio in the X-Y plane based on the first distance and the second distance.

9. The reconstruction device of claim 8 , wherein

the determining unit is further configured to determine a center on each of the two crystals defining a line of response.

10. The reconstruction device of claim 9 , wherein

the determining unit is configured to determine the first center point of the first surface of the voxel and the second center point of the second surface of the voxel based on an angle between the line of response and a positive X-axis in the X-Y plane.

11. The reconstruction device of claim 8 , wherein

the determining unit is further configured to

determine a third edge line connecting respective front endpoints of the two crystals in a Y-Z or X-Z plane of the medical imaging apparatus, the third edge line including a first z-line point,

determine a fourth edge line connecting respective rear endpoints of the two crystals in the Y-Z or X-Z plane, the fourth edge line including a second z-line point, and

determine a z-line of the TOR parallel to a Z-axis in the Y-Z or X-Z plane as a line intersecting the first z-line point and the second z-line point;

the projecting unit is further configured to project, in the Y-Z or X-Z plane, a third center point of a third surface of the voxel to the z-line along a direction of the third edge line to define a third projected point, and to project, in the Y-Z or X-Z plane, a fourth center point of a fourth surface of the voxel to the z-line along a direction of the fourth edge line to define a fourth projected point;

the calculating unit is further configured to calculate a third distance between one of the first and second z-line points and the third projected point, and a fourth distance between the one of the first and second z-line points and the fourth projected point; and

the distance ratio determining unit is further configured to determine a second distance ratio in the Y-Z or X-Z plane based on the third distance and the fourth distance.

12. The reconstruction device of claim 11 , further comprising:

an intersected volume calculating unit configured to calculate an intersected volume by multiplying the first distance ratio by the second distance ratio.

13. The reconstruction device of claim 11 , wherein

the third surface of the voxel and the fourth surface of the voxel are on opposite sides of the voxel.

14. The reconstruction device of claim 8 , wherein

the first surface of the voxel and the second surface of the voxel are on opposite sides of the voxel.

15. A Positron Emission Tomography (PET) system for calculating distance ratios used to calculate a geometric probability between a voxel and a tube-of-response (TOR) defined by two crystals within a reconstruction space of the PET system, the PET system comprising:

a determining unit configured to

determine a first edge line connecting respective left endpoints of the two crystals in an X-Y plane of the PET system, the first edge line including a first middle point located midway between the left endpoints,

determine a second edge line connecting respective right endpoints of the two crystals in the X-Y plane, the second edge line including a second middle point located midway between the right endpoints, and

determine a middle line of the TOR in the X-Y plane as a line intersecting the first middle point and the second middle point;

a projecting unit configured to project, in the X-Y plane, a first center point of a first surface of the voxel to the middle line along a direction of the first edge line to define a first projected point, and to project, in the X-Y plane, a second center point of a second surface of the voxel to the middle line along a direction of the second edge line to define a second projected point;

a calculating unit configured to calculate a first distance between one of the first and second middle points and the first projected point, and a second distance between the one of the first and second middle points and the second projected point; and

a distance ratio determining unit configured to determine a first distance ratio in the X-Y plane based on the first distance and the second distance.