Seed localization system and method in ultrasound by fluoroscopy and ultrasound fusion

• US 6,549,802 B2
• Filed: 06/07/2001
• Issued: 04/15/2003
• Est. Priority Date: 06/07/2001
• Status: Expired due to Term

• Current Assignee: Varian Medical Systems Incorporated (Siemens AG)
• Original Assignee: Varian Medical Systems Incorporated (Siemens AG)
• Inventors: Thornton, Kenneth B
• Primary Examiner(s): Jaworski, Francis J.
• Application Number:
  US09/875,031
• Publication Number:
  US 20020193677A1
• Time in Patent Office: 677 Days
• Field of Search: 600/407, 600/409, 600/426, 600/437, 600/439, 600/427, 382/131
• US Class Current: 600/426
• CPC Class Codes: A61B 6/12 Arrangements for detecting or locating foreign bodies
• CPC Class Codes: A61B 6/5247 combining images from an ionising-radiation diagnostic technique and a non-ionising radiation diagnostic technique, e.g. X-ray and ultrasound
• CPC Class Codes: A61B 8/0833 involving detecting or locating foreign bodies or organic structures
• CPC Class Codes: A61B 8/0841 for locating instruments
• CPC Class Codes: A61B 8/4416 related to combined acquisition of different diagnostic modalities, e.g. combination of ultrasound and X-ray acquisitions
• CPC Class Codes: A61N 2005/1012 Templates or grids for guiding the introduction of sources
• CPC Class Codes: A61N 5/1027 Interstitial radiation therapy
• CPC Class Codes: A61N 5/1048 Monitoring, verifying, controlling systems and methods

Abstract

A seed localization system and method in which a computer-based system is used to determine the three-dimensional (3D) position of radiotherapy seeds with respect to an area of affected tissue, such as the prostate, using ultrasound (US) and fluoroscopy (FL) imaging, so that a radiotherapy dose may be calculated. One embodiment the present invention may be used to determine the 3D position of implanted brachytherapy seeds. An alternative embodiment of the invention may be used to determine the 3D position of implanted objects other than brachytherapy seeds. The seed localization system and method includes a graphical user interface useful for assisting a user of the seed localization system in its operation.

Claims

1. A system for determining a position of at least one implanted object in a body, comprising:

an ultrasound imager configured to forming an ultrasound image of a portion of the body containing the at least one implanted object;

a fluoroscopy imager configured to form a plurality of fluoroscopic images of the portion of the body; and

a computer system coupled to said ultrasound imager and to said fluoroscopy imager, said computer system processing the ultrasound image and the plurality of fluoroscopic images to calculate the position of the at least one implanted object in the body.

2. The system of claim 1, wherein said computer system includes:

a processor for processing the ultrasound image and the plurality of fluoroscopic images; and

a monitor coupled to said processor and configured to display a three-dimensional image of the portion of the body showing the position of the at least one implanted object in the body.

3. The system of claim 2, wherein said computer system further includes a graphical user interface coupled to said processor, said graphical user interface enabling a user to interact with said processor.

4. The system of claim 3, wherein said graphical user interface includes:

a first data input adapted to receive data regarding the ultrasound image;

a second data input adapted to receive data regarding the plurality of fluoroscopic images; and

a data analyzer coupled to said first data input and to said second data input and adapted to calculate from the ultrasound image a series of three-dimensional coordinates Q₁, Q₂, . . . , Q_M associated with M markers placed in the portion of the body and visible in the ultrasound image and the plurality of fluoroscopic images, wherein M≧

4.

5. The system of claim 4, wherein said data analyzer is further adapted to calculate:

at least one set of two-dimensional coordinates for the at least one implanted object in each of the plurality of fluoroscopic images; and

M sets of two-dimensional coordinates for the M markers in each of the plurality of fluoroscopic images.

6. The system of claim 5, wherein said graphical user interface further includes a coordinate reconstructor coupled to said data analyzer and adapted to determine:

a series of three-dimensional coordinates R₁, R₂, . . . , R_N associated with N implanted objects; and

a series of three-dimensional coordinates P₁, P₂, . . . , P_M associated with the M markers.

7. The system of claim 6, wherein said graphical user interface further includes a coordinate correlator adapted to associate each of the series of three-dimensional coordinates P_i with each of the series of three-dimensional coordinates Q_i for each of the M makers, wherein 1≦

i≦

M.

8. The system of claim 7, wherein said coordinate correlator is further adapted to determine a 3×

3 matrix T and a 3×

1 vector t by solving an optimization problem.

9. The system of claim 8, wherein:

an initial estimate for (T,t) is found by solving a first optimization problem $\underset{T,t}{\min }<br><br>\underset{i=1}{\overset{M}{\sum <br><br>}}<br><br>{<br><br>Q_i-{\mathrm{TP}}_i-t<br><br>}^2;<br><br>$

a subsequent estimate for (T,t) is found by solving a second optimization problem $\underset{T,t}{\max }<br><br>\underset{j=1}{\overset{N}{\sum <br><br>}}<br><br>I<br><br>\left({\mathrm{TR}}_j+t\right),$

 

wherein I(X) is a scalar intensity of point X in the ultrasound image; and

if the second optimization problem has no unique solution, the subsequent estimate for (T,t) is found through a locally optimal solution.

10. The system of claim 8, wherein said coordinate correlator is further adapted to map each of the series of three-dimensional coordinates R₁, R₂, . . . , R_N to a series of three-dimensional coordinates S₁,S₂, . . , S_N by a transformation S_j=TR_j+t, wherein 1≦

j≦

N.

11. The system of claim 1, wherein the at least one implanted object includes a plurality of brachytherapy seeds used in a radiation treatment of affected tissue.

14. The system of claim 6 wherein said graphical user interface further comprises:

a coordinate reconstructor adapted to determine a series R₁, R₂, . . . , R_N and P₁, P₂, . . . , P_M where R_i and P_i correspond to a unique set of derived three dimensional coordinates associated with each implanted seed and marker, respectively, appearing in said plurality of two dimensional fluoroscopic images.

12. A system for determining the three dimensional position of implanted objects, comprising:

a computer system adapted to receive a three dimensional ultrasound image of a region containing the implanted objects and a plurality of two dimensional fluoroscopic images of the region, said computer system being adapted to form from said three dimensional ultrasound image and said plurality of two dimensional fluoroscopic images an improved three dimensional image of the region, said improved three dimensional image capable of indicating the location of each of the implanted objects; and

a graphical user interface for determining the three dimensional position of the implanted objects with respect to the region, wherein said graphical user interface prompts and coordinates execution of a sequence of steps performed cooperatively by a user and said computer system and further comprises;

a data input adapted to receive a number M corresponding to a number of implanted markers and a number N corresponding to a number of the implanted objects; and

a data analyzer adapted to;

locate the M highly visible implanted markers within the three dimensional ultrasound image, where M≧

4; and

store on a computer-readable medium a series Q₁, Q₂, . . . , Q_M for 1≧

i≧

M wherein Q_i corresponds to a unique set of three dimensional coordinates associated with each of the M highly visible markers.

13. The system of claim 12 wherein said data analyzer is further adapted to:

locate each implanted seed and marker appearing in each image of said plurality of two dimensional fluoroscopic images; and

store on a computer-readable medium a unique set of two dimensional coordinates corresponding to the location of each implanted seed and marker appearing in each of said two dimensional fluoroscopic images.

15. The system of claim 13 wherein said graphical user interface further comprises:

a coordinate correlator adapted to associate each said unique set of three dimensional FL coordinates P₁ for 1≦

i≦

M corresponding to the location of each of the M highly visible markers with each said unique set of identified three dimensional US coordinates Q_i for 1≦

i≦

M corresponding to the same marker.

16. The system of claim 15 wherein said coordinate correlator is further adapted to:

map each said unique set of derived three dimensional FL coordinates R_i. corresponding to an implanted seed to the three dimensional US coordinates S_icorresponding to the same implanted seed by the transformation S_i=TR_i+t.

17. The system of claim 16 wherein said coordinate correlator is further adapted to determine a solution to an optimization problem.

18. The system of claim 16 wherein said coordinate correlator is further adapted to:

determine a solution 3×

3 matrix Tand a 3×

1 vector t wherein;

an initial estimate for (T,t) is found by determining the unique solution to the optimization problem $\underset{T,t}{\min }<br><br>\underset{i=1}{\overset{M}{\sum <br><br>}}<br><br>{<br><br>Q_i-T<br><br>\text{\hspace{1em}<br><br>}<br><br>P_i-t<br><br>}^2;<br><br>$

a final estimate is found by solving the optimization problem $\underset{T,t}{\max }<br><br>\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br>I<br><br>\left(T<br><br>\text{\hspace{1em}<br><br>}<br><br>R_i+t\right);<br><br>$

and if the maximization problem has no unique solution, a locally optimal solution is determined.

19. A method for locating a plurality of implanted seeds, comprising the steps of:

obtaining a three-dimensional ultrasound image of a region containing the plurality of implanted seeds;

obtaining a plurality of two-dimensional fluoroscopic images of the region;

matching the plurality of implanted seeds in the three-dimensional ultrasound image with corresponding ones in the plurality of two-dimensional fluoroscopic images; and

calculating a plurality of three-dimensional coordinates of the plurality of implanted seeds by analyzing the three-dimensional ultrasound image and the plurality of two-dimensional fluoroscopic images.

20. The method of claim 19, further comprising the step of implanting a plurality of brachytherapy seeds used in a radiotherapy as the plurality of implanted seeds.

21. The method of claim 19, further comprising the step of placing M markers in the region, the M markers being visible in the three-dimensional ultrasound image and in the plurality of two-dimensional fluoroscopic images.

22. The method of claim 21, further comprising the steps of:

locating the M markers within the three-dimensional ultrasound image, wherein M≧

4; and

calculating a series of three-dimensional coordinates Q₁, Q₂, . . . , Q_M of the M markers by analyzing the three-dimensional ultrasound image.

23. The method of claim 22, further comprising the steps of:

locating the plurality of implanted seeds and the M markers in each of the plurality of two-dimensional fluoroscopic images;

calculating a first plural sets of two-dimensional coordinates for the plurality of implanted seeds appearing in the plurality of two-dimensional fluoroscopic images;

calculating a second plural sets of two-dimensional coordinates for the M markers appearing in the plurality of two-dimensional fluoroscopic images;

determining a first series of three-dimensional coordinates R₁, R₂, . . . , R_N of the plurality of implanted seeds from the first plural sets of two-dimensional coordinates, wherein N is a number of the plurality of implanted seeds; and

determining a second series of three-dimensional coordinates P₁, P₂, . . . , P_M of the M markers from the second plural sets of two-dimensional coordinates.

24. The method of claim 23, further comprising the step of associating each P_i with a corresponding Q_i, wherein 1≦

i≦

M.

25. The method of claim 24, further comprising the step of finding a series of three-dimensional coordinates S₁, S₂, . . . , S_N of the N implanted seeds by a transformation S_j=TR_j+t, wherein 1≦

j≦

N.

26. The method of claim 25, wherein the step of associating includes finding a 3×

3 matrix T and a 3×

1 vector t by determining a solution to an optimization problem.

27. A method for determining the three dimensional position of implanted seeds, comprising the steps of:

inputting a number M corresponding to a number of implanted markers and a number N corresponding to a number of implanted seeds;

obtaining a three dimensional ultrasound image of a region of implanted seeds;

obtaining a plurality of two dimensional fluoroscopic images of the region of implanted seeds;

forming an improved three dimensional image of the region of implanted seeds by analyzing data from said three dimensional ultrasound image in combination with data from said plurality of two dimensional fluoroscopic images; and

identifying the location of each implanted seed in the region by analysis of said improved three dimensional image.

28. A method for determining the three dimensional position of implanted seeds, comprising the steps of:

obtaining a three dimensional ultrasound image of a region of implanted seeds;

obtaining a plurality of two dimensional fluoroscopic images of the region of implanted seeds;

locating M highly visible implanted markers within the three dimensional ultrasound image, where M≧

4;

storing on a computer-readable medium a series Q₁, Q₂, . . . , Q_M for 1≧

i≧

M wherein Q_i corresponds to a unique set of three dimensional coordinates associated with each of the M highly visible markers;

forming an improved three dimensional image of the region of implanted seeds by analyzing data from said three dimensional ultrasound image in combination with data from said plurality of two dimensional fluoroscopic images; and

identifying the location of each implanted seed in the region by analysis of said improved three dimensional image.

29. A method for determining the three dimensional position of implanted seeds, comprising the steps of:

obtaining a three dimensional ultrasound image of a region of implanted seeds;

obtaining a plurality of two dimensional fluoroscopic images of the region of implanted seeds;

locating each implanted seed and marker appearing in each image of said plurality of two dimensional fluoroscopic images;

storing on a computer-readable medium a unique set of two dimensional coordinates corresponding to the location of each implanted seed and marker appearing in each said two dimensional fluoroscopic image;

forming an improved three dimensional image of the region of implanted seeds by analyzing data from said three dimensional ultrasound image in combination with data from said plurality of two dimensional fluoroscopic images;

identifying the location of each implanted seed in the region by analysis of said improved three dimensional image; and

determining series R₁, R₂, . . . , R and P₁, P₂, . . . , P_M where R_i and P_i correspond to a unique set of derived three dimensional FL coordinates associated with each implanted seed and marker, respectively, appearing in said plurality of two dimensional fluoroscopic images.

30. The method of claim 29 further comprising the step of:

associating each said unique set of three dimensional FL coordinates P_i for 1≦

i≦

M corresponding to the location of each of the M highly visible markers with each said unique set of identified three dimensional US coordinates Q_i for 1≦

i≦

M corresponding to the same implanted marker.

31. A method for determining the three dimensional position of implanted seeds, comprising the steps of:

obtaining a three dimensional ultrasound image of a region of implanted seeds;

obtaining a plurality of two dimensional fluoroscopic images of the region of implanted seeds;

forming an improved three dimensional image of the region of implanted seeds by analyzing data from said three dimensional ultrasound image in combination with data from said plurality of two dimensional fluoroscopic images, wherein said step of forming an improved three dimensional image further comprises mapping each said unique set of derived three dimensional FL coordinates R_i, corresponding to an implanted seed to its 3D US location S_i; and

identifying the location of each implanted seed in the region by analysis of said improved three dimensional image.

32. The method of claim 31 wherein said act of associating further comprises determining a solution to an optimization problem.

33. The method of claim 32 wherein said step of determining a solution to an optimization problem further comprises:

determining a solution 3×

3 matrix T and a 3×

1 vector t wherein;

an initial estimate for (T,t) is found by determining the unique solution to the optimization problem $\underset{T,t}{\min }<br><br>\underset{i=1}{\overset{M}{\sum <br><br>}}<br><br>{<br><br>Q_i-T<br><br>\text{\hspace{1em}<br><br>}<br><br>P_i-t<br><br>}^2;<br><br>$

a final estimate is found by solving the optimization problem $\underset{T,t}{\max }<br><br>\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br>I<br><br>\left(T<br><br>\text{\hspace{1em}<br><br>}<br><br>R_i+t\right);<br><br>$

if the maximization problem has no unique solution, a locally optimal solution is determined.

34. A computer-generated graphical user interface for determining positions of a plurality of brachytherapy seeds with respect to an implanted region, the graphical user interface prompting and coordinating execution of a sequence of steps performed cooperatively by a user and a computer processor, said sequence of steps comprising:

obtaining a three-dimensional ultrasound image of the implanted region;

obtaining a plurality of two-dimensional fluoroscopic images of the implanted region;

forming an improved three-dimensional image of the implanted region by analyzing the three-dimensional ultrasound image in combination with the plurality of two-dimensional fluoroscopic images; and

identifying a position for each of the plurality of brachytherapy seeds in the implanted region in the improved three-dimensional image.

35. The graphical user interface of claim 34, wherein the plurality of brachytherapy seeds are used in radiotherapy treatment of an abnormal tissue in the implanted region.

36. The graphical user interface of claim 34, wherein said sequence of steps further comprises inputting a number M corresponding to a number of markers and a number N corresponding to a number of the plurality of brachytherapy seeds in the implanted region.

37. The graphical user interface of claim 36, wherein said sequence of steps further comprises:

locating the M markers within the three-dimensional ultrasound image, where M≧

4; and

storing on a computer-readable medium a series Q₁, Q₂, . . . , Q_M of three-dimensional coordinates associated with the M markers.

38. The graphical user interface of claim 37, wherein said sequence of steps further comprises:

locating the N brachytherapy seeds and the M markers appearing in each of said plurality of two-dimensional fluoroscopic images;

storing on the computer-readable medium a plural sets of two-dimensional coordinates for the N brachytherapy seeds and the M markers appearing in each of said plurality of two-dimensional fluoroscopic images; and

deriving a first series R₁, R₂, . . . , R_N of three-dimensional coordinates for the N brachytherapy seeds and a second series P₁, P₂, . . . , P_M of three-dimensional coordinates for the M markers from the plural sets of two-dimensional coordinates.

39. The graphical user interface of claim 38, wherein said sequence of steps further comprises associating each P_i with a corresponding Q_i for 1≦

i≦

M .

40. The graphical user interface of claim 39, wherein said step of associating further comprises determining a solution to an optimization problem.

41. The graphical user interface of claim 38, wherein said sequence of steps further comprises finding a matrix T and a 3×

1 vector t through an optimization process, wherein;

an initial estimate for (T,t) is found by solving a

minimization problem $\underset{T,t}{\min }<br><br>\underset{i=1}{\overset{M}{\sum <br><br>}}<br><br>{<br><br>Q_i-T<br><br>\text{\hspace{1em}<br><br>}<br><br>P_i-t<br><br>}^2;<br><br>$

a second estimate for (T,t) is found by solving a maximization $\underset{T,t}{\max }<br><br>\underset{j=1}{\overset{N}{\sum <br><br>}}<br><br>I<br><br>\left(T<br><br>\text{\hspace{1em}<br><br>}<br><br>R_j+t\right),$

 

wherein I(X) is a scalar intensity of point X in the three-dimensional ultrasound image; and

if the maximization problem has no unique solution, the second estimation for (T,t) is found through a locally optimal solution.

42. The graphical user interface of claim 41, wherein said sequence of steps further comprises calculating a series of derived three-dimensional coordinates S₁, S₂, . . . , S_N of the N brachytherapy seeds, wherein S_j=TR_j+t for 1≦

j≦

N.

43. A computer-generated graphical user interface for determining the three dimensional position of brachytherapy seeds with respect to an implanted region wherein said graphical user interface prompts and coordinates execution of a sequence of steps performed cooperatively by a user and a computer processor, said sequence of steps comprising:

inputting a number M corresponding to a number of implanted markers and a number N corresponding to the number of implanted seeds;

obtaining a three dimensional ultrasound image of a region of implanted seeds;

obtaining a plurality of two dimensional fluoroscopic images of the region of implanted seeds;

forming an improved three dimensional image of the region of implanted seeds by analyzing data from said three dimensional ultrasound image in combination with data from said plurality of two dimensional fluoroscopic images; and

identifying the location of each implanted seed in the region by analysis of said improved three dimensional image.

44. A computer-generated graphical user interface for determining the three dimensional position of brachytherapy seeds with respect to an implanted region wherein said graphical user interface prompts and coordinates execution of a sequence of steps performed cooperatively by a user and a computer processor, said sequence of steps comprising:

obtaining a three dimensional ultrasound image of a region of implanted seeds;

obtaining a plurality of two dimensional fluoroscopic images of the region of implanted seeds;

locating M highly visible implanted markers within the three dimensional ultrasound image, where M≧

4;

storing on a computer-readable medium a series Q₁, Q₂, . . . , Q_Mfor 1≦

i≦

M wherein Q_i corresponds to a unique set of three dimensional coordinates associated with each of the at least four highly visible markers;

forming an improved three dimensional image of the region of implanted seeds by analyzing data from said three dimensional ultrasound image in combination with data from said plurality of two dimensional fluoroscopic images; and

identifying the location of each implanted seed in the region by analysis of said improved three dimensional image.

45. A computer-generated graphical user interface for determining the three dimensional position of brachytherapy seeds with respect to an implanted region wherein said graphical user interface prompts and coordinates execution of a sequence of steps performed cooperatively by a user and a computer processor, said sequence of steps comprising:

obtaining a three dimensional ultrasound image of a region of implanted seeds;

obtaining a plurality of two dimensional fluoroscopic images of the region of implanted seeds;

locating each implanted seed and marker appearing in each image of said plurality of two dimensional fluoroscopic images;

storing on a computer-readable medium a unique set of two dimensional coordinates corresponding to the location of each implanted seed and marker appearing in each said two dimensional fluoroscopic image;

determining a series R₁, R₂, . . . , R_N and P₁, P₂, . . . , P_M where R_i and P_i correspond to a unique set of derived three dimensional coordinates associated with each implanted seed and marker, respectively, appearing in said plurality of two dimensional fluoroscopic images;

forming an improved three dimensional image of the region of implanted seeds by analyzing data from said three dimensional ultrasound image in combination with data from said plurality of two dimensional fluoroscopic images; and

identifying the location of each implanted seed in the region by analysis of said improved three dimensional image.

46. The graphical user interface of claim 45 wherein said graphical user interface further prompts and coordinates the step of:

associating each said unique set of derived three dimensional FL coordinates P, for 1≦

i≦

M corresponding to the location of each of the M highly visible markers with each said unique set of identified three dimensional coordinates Q_i for 1≦

i≦

M corresponding to the same marker.

47. The graphical user interface of claim 45 wherein said graphical user interface further prompts and coordinates the step of:

mapping each said unique set of derived three dimensional FL coordinates R_i corresponding to an implanted seed to its 3D ultrasound coordinate S_i.

48. The graphical user interface of claim 47 wherein said step of associating further comprises determining a solution to an optimization problem.

49. The graphical user interface of claim 48 wherein said step of determining a solution to an optimization problem further comprises:

determining a solution 3×

3 matrix Tand a 3×

1 vector t wherein;

an initial estimate for (T,t) is found by determining the unique solution to the optimization problem $\underset{T,t}{\min }<br><br>\underset{i=1}{\overset{M}{\sum <br><br>}}<br><br>{<br><br>Q_i-T<br><br>\text{\hspace{1em}<br><br>}<br><br>P_i-t<br><br>}^2;<br><br>$

a final estimate is found by solving the optimization problem $\underset{T,t}{\max }<br><br>\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br>I<br><br>\left(T<br><br>\text{\hspace{1em}<br><br>}<br><br>R_i+t\right);<br><br>$

 

and

if the maximization problem has no unique solution, a locally optimal solution is determined.

50. A computer-readable medium on which is embodied a set of programmed instructions that causes a processor to perform a sequence of steps, said sequence of steps comprising:

obtaining a three-dimensional ultrasound image of a region containing a plurality of implanted seeds;

obtaining a plurality of two-dimensional fluoroscopic images of the region;

forming an improved three-dimensional image of the region by analyzing the three-dimensional ultrasound image in combination with the plurality of two-dimensional fluoroscopic images; and

identifying a location for each of the plurality of implanted seeds in the region by analysis of the improved three-dimensional image.

51. A process for locating a plurality of objects in a region, comprising the steps of:

placing a plurality of markers in the region, the plurality of markers being visible via a first imaging mode and a second imaging mode and being distinguishable from the plurality of objects;

forming a first image of the first imaging mode of the region;

identifying a first plurality of markings in the first image corresponding to the plurality of markers;

forming a second image and a third image of the second imaging mode of the region;

identifying a second plurality of markings in the second image corresponding to the plurality of markers;

identifying a third plurality of markings in the third image corresponding to the plurality of markers;

establishing a correlation between the first image, the second image, and the third image by matching the first plurality of markings with the second plurality of markings and the third plurality of markings;

deriving a set of object coordinates corresponding to the plurality of objects in the second image and in the third image; and

calculating a series of three-dimensional coordinates for the plurality of objects in response to the correlation between the first image, the second image, and the third image and to the set of object coordinates.

52. The process of claim 51, further comprising the step of implanting a plurality of brachytherapy seeds used in a radiation therapy into a portion of a patient'"'"'s body as the plurality of objects in the region.

53. The process of claim 51, wherein said step of placing a plurality of markers in the region includes placing at least four markers uncoplanar with each other in the region.

54. The process of claim 51, wherein:

said step of forming a first image of the first imaging mode includes forming a three-dimensional ultrasound image of the region; and

said step of forming a second image and a third image of the second imaging mode includes forming a plurality of two-dimensional fluoroscopic images of the region.

55. The process of claim 51, wherein:

said step of identifying a first plurality of markings includes deriving a first set of marker coordinates Q₁, Q₂, . . . , Q_M for the plurality of markers, wherein M≧

4 is a number of the markers;

said steps of identifying a second plurality of markings identifying a third plurality of markings include deriving a second set of marker coordinates P₁, P₂, . . . , P_M for the M markers; and

said step of deriving a set of coordinates corresponding to the plurality of objects in the second image and in the third image includes deriving a set of object coordinates R₁, R₂, . . . , R_N, wherein N is a number of the plurality of objects.

56. The process of claim 55, wherein said step establishing a correlation between the first image, the second image, and the third image includes a step of finding a 3×

3 matrix Tand a 3×

1 vector t by solving a first optimization problem $\underset{T,t}{\min }<br><br>\underset{i=1}{\overset{M}{\sum <br><br>}}<br><br>{<br><br>Q_i-T<br><br>\text{\hspace{1em}<br><br>}<br><br>P_i-t<br><br>}^2.$

57. The process of claim 56, wherein said step of finding a 3×

3 matrix Tand a 3×

1 vector t further includes solving a second optimization problem $\underset{T,t}{\max }<br><br>\underset{j=1}{\overset{N}{\sum <br><br>}}<br><br>I<br><br>\left(T<br><br>\text{\hspace{1em}<br><br>}<br><br>R_j+t\right),$

wherein I(X) is a scalar intensity at a point X in the first image.

58. The process of claim 57, wherein said step of finding a 3×

3 matrix Tand a 3×

1 vector t further includes solving a localized optimization problem in response to the second optimization problem not having a unique solution.

59. The process of claim 56, wherein said step of calculating a series of three-dimensional coordinates for the plurality of objects includes deriving the series of three-dimensional coordinates S₁, S₂, . . . , S_N of the N implanted seeds by a transformation S_j=TR_j+t, wherein 1≦

j≦

N .

60. The process of claim 51, generating a three-dimensional visual display of the region indicating the plurality of objects in accordance with the series of three-dimensional coordinates for the plurality of objects.