System and methods of organ segmentation and applications of same

• US 20060013482A1
• Filed: 06/23/2005
• Published: 01/19/2006
• Est. Priority Date: 06/23/2004
• Status: Active Grant

• Current Assignee: Vanderbilt University
• Original Assignee: Vanderbilt University
• Inventors: Dawant, Benoit M., Cao, Zhujiang
• Granted Patent: US 7,519,209 B2
• Time in Patent Office: Days
• US Class Current: 382/173
• CPC Class Codes: G06T 2207/10081 Computed x-ray tomography [CT]
• CPC Class Codes: G06T 2207/10088 Magnetic resonance imaging [MRI]
• CPC Class Codes: G06T 2207/20104 Interactive definition of region of interest [ROI]
• CPC Class Codes: G06T 2207/20161 Level set
• CPC Class Codes: G06T 2207/30056 Liver; Hepatic
• CPC Class Codes: G06T 7/12 Edge-based segmentation
• CPC Class Codes: G06T 7/149 involving deformable models, e.g. active contour models

Abstract

A method for segmentation of an organ of a living subject with a variable shape and boundary and surrounded by structures and tissues in connection with an image containing the organ. In one embodiment, the method includes the steps of initializing a contour inside the organ in the image, introducing a speed function that is capable of accumulating spatial and temporal information of a propagating front of the contour, and evolving the contour toward the boundary of the organ using the introduced speed function so as to segment the organ.

Claims

1. A method for segmentation of an organ of a living subject with a variable shape and boundary and surrounded by structures and tissues in connection with an image containing the organ, wherein the boundary of the organ is embedded as a zero level set of an embedding function, φ

, comprising the steps of;

a. initializing a contour inside the organ in the image;

b. introducing a speed function that is capable of accumulating spatial and temporal information of a propagating front of the contour, wherein the speed function has a term, g₀;

c. defining an image-dependent static term, g_base;

d. setting the term g₀=g_base;

e. computing {(x,y,z)|Φ

(x,y,z)=0} at iteration n, so as to obtain a set of points in the zero level set of the embedding function φ

, wherein n=1, 2, 3, . . . , and coordinates (x, y, z) represent a point on the propagating front of the contour;

f. retrieving the static term g_base (x, y, z) for each of the set of points in the zero level set of the embedding function φ

;

g. extending the retrieved static term g_base (x, y, z) to a narrow band in which the embedding function φ

is computed so as to generate an extended term g_ext;

h. updating the term g₀=g₀g_ext so as to update the speed function;

i. computing the embedding function φ

at iteration (n+1) using the updated speed function; and

j. iteratively repeating steps (e)-(i) for a predetermined number of iterations or until the propagating front of the contour does not move,

wherein the front of the contour corresponds to the boundary of the organ.

2. The method of claim 1, wherein the extending step comprises the step of computing the extended term g_ext that satisfies an equation of ∇

g_ext·

∇

θ

=0, ∇

θ

being a standard signed distance function computed from the zero level set of the embedding function φ

.

3. The method of claim 2, wherein the computing step is performed with a fast marching method.

4. The method of claim 3, wherein the extended term g_ext(x, y, z)=g_base(c(x, y, z)) for points (x,y,z) close to the zero level set, c(x, y, z) being the closest point in the zero level set of the embedding function φ

.

5. The method of claim 1, wherein the embedding function φ

is governed by a level set equation, φ

_t+F|∇

Φ

|=0, wherein the speed function F=g₀(1−

ε

κ

).

6. The method of claim 1, wherein the embedding function φ

is governed by a level set equation, Φ

_t−

Sign(g_base)((|g₀|−

ε

κ

)|∇

Φ

|)=0, wherein the speed function F=−

Sign(g_base)(|g₀|−

ε

κ

) and Sign(g_base) is a sign function of g_base.

7. The method of claim 6, wherein the static term g_base is in the form of g_base=g_gradg_gray wherein g_grad and g_grey comprise intensity gradient information and gray value information of the image, respectively.

8. The method of claim 1, further comprising the step of localizing an inner boundary of the structures surrounding the organ as a shape constraint for the propagating front of the contour.

9. The method of claim 8, wherein the structures comprise a set of ribs.

10. The method of claim 9, wherein the localizing step comprises the steps of;

a. converting the image into a binary image;

b. localizing a skin surface from the converted binary image, wherein the localized skin surface comprises a skin circumference;

c. identifying a set of candidate pixels, P_candidate={P_candidate(j)}, from the converted binary image, j=1, 2, . . . , N_c, N_c being the number of the set of candidate pixels P_candidate;

d. determining a set of rib pixels, P_rib={P_rib(i)}, from the set of candidate pixels P_candidate, each of the set of rib pixels P_rib corresponding to one of the set of ribs in the converted binary image, i=1, 2, . . . , N_r, N_r being the number of the set of rib pixels P_rib;

e. segmenting the set of rib pixels P_rib into a plurality of sections, S={S(k)}, along the skin circumference in the converted binary image, k=1, 2, . . . , N_s, N_s, being the number of the plurality of sections S;

f. calculating distances of each rib pixel in a segmented section S(k) to its closest skin pixels on the skin circumference in the segmented section S(k) so as to obtain the mean value {overscore (D)}_skin(k) and the standard deviation D_std(k) of these distances in the segmented section S(k), respectively, k=1, 2, . . . , N_s;

g. defining a skin-rib distance, d_skin-rib(k)={overscore (D)}_skin(k)+2D_std(k) for the segmented section S(k), k=1, 2, . . . , N_s; and

h. connecting the plurality of segmented sections S together to form the inner boundary of the plurality of ribs, P_in={(x,y)|d(x,y)=Td_skin-rib(C_Map(x,y))}, wherein d(x,y) is distance of pixel (x,y) to the skin circumference, C_Map(x,y) is the closest point of pixel (xy) on the skin circumference, and Td_skin-rib is a lookup table that stores the skin-rib distance d_skin-rib for each pixel along the skin circumference.

11. The method of claim 10, wherein the converting step comprises the step of thresholding the image with a threshold, I_skin.

12. The method of claim 11, wherein the set of rib pixels P_rib={(x, y)|(x, y)ε

P_candidate, and D_skin(x, y)<

d_{rib max}} d_ribmax being a maximum possible distance from a rib to the skin circumference.

13. The method of claim 10, wherein the connecting step is performed with an interpolation scheme.

14. The method of claim 1, further comprising the step of performing a stiff band algorithm on the propagating front of the contour.

15. The method of claim 14, wherein the performing step comprises the steps of:

a. defining a neighborhood for each of pixels {P_i} along the contour, wherein P_i represents the ith pixel on the contour, i=1, 2, . . . , N, N being the number of the pixels, such that the neighborhood includes a set of pixels that are within ±

ε

pixels, ε

being a non-zero positive number;

b. dividing the pixels of the neighborhood for P_i into a first set of pixels that are in front of pixel P_i along a propagating direction of the contour, and a second set of pixels that are behind of pixel P_i along the propagating direction of the contour;

c. defining a speed limit a to classify the neighborhood into several possible states;

d. for each state segmenting the neighborhood of P_i; and

e. iteratively repeating steps (bed) for all pixels {P_i}.

16. The method of claim 1, wherein the organ comprises at least a part of a liver, a heart, a kidney, a stomach, or a lung of a living subject.

17. The method of claim 1, wherein the image comprises a magnetic resonance image.

18. The method of claim 1, wherein the image comprises a computed tomography image.

19. Software stored on a computer readable medium for causing a computing system to perform functions that segment a region of interest of an organ in an image comprising:

a. initializing a contour inside the region of interest in the image;

b. introducing a speed function that is capable of accumulating spatial and temporal information of a propagating front of the contour, wherein the speed function has a term, g₀;

c. defining an image-dependent static term, g_base;

d. setting the term g₀=g_base;

e. computing {(x,y,z)|Φ

(x,y,z)=0} at iteration n, so as to obtain a set of points in the zero level set of an embedding function φ

, wherein n=1, 2, 3, . . . , and coordinates (x, y, z) represent a point on the propagating front of the contour;

f. retrieving the static term g_base(x, y, z) for each of the set of points in the zero level set of the embedding function b;

g. extending the retrieved static term g_base(x, y, z) to a narrow band in which the embedding function φ

is computed so as to generate an extended term g_ext;

h. updating the term g₀=g₀g_ext so as to update the speed function;

i. computing the embedding function φ

at iteration (n+1) using the updated speed function; and

j. iteratively repeating steps (e)-(i) for a predetermined number of iterations or until the propagating front of the contour does not move,

wherein the front of the contour corresponds to the boundary of the region of interest of an organ.

20. The software of claim 19, wherein the functions further comprise localizing an inner boundary of structures surrounding the organ as a shape constraint for the propagating front of the contour.

21. The software of claim 19, wherein the functions further comprise performing a stiff band algorithm on the propagating front of the contour.

22. A method for segmentation of an organ of a living subject with a variable shape and boundary and surrounded by structures and tissues in connection with an image containing the organ, comprising the steps of:

a. initializing a contour inside the organ in the image;

b. introducing a speed function that is capable of accumulating spatial and temporal information of a propagating front of the contour; and

c. evolving the contour toward the boundary of the organ using the introduced speed function so as to segment the organ.

23. The method of claim 22, wherein the boundary of the organ is embedded as a zero level set of an embedding function, φ

, governed by a level set equation.

24. The method of claim 23, wherein the evolving step comprises an iterative process.

25. The method of claim 24, wherein the iterative process comprises the steps of:

a. defining an image-dependent static term, g_base;

b. setting g₀=g_base, wherein g₀ is a term used in the speed fuction;

c. computing {(x, y, z)|Φ

(x, y, z)=0} at iteration n, so as to obtain a set of points in the zero level set of an embedding function φ

, wherein n=1, 2, 3, . . . , and coordinates (x, y, z) represent a point on the propagating front of the contour;

d. retrieving the static term g_base (x, y, z) for each of the set of points in the zero level set of the embedding function φ

;

e. extending the retrieved static term g_base (x, y, z) to a narrow band in which the embedding function φ

is computed so as to generate an extended term g_ext;

f. updating the term g₀=g₀g_ext so as to update the speed function;

g. computing the embedding function φ

at iteration (n+1) using the updated speed function; and

h. iteratively repeating steps (c)-(g) for a predetermined number of iterations or until the propagating front of the contour does not move.

26. The method of claim 25, wherein the extending step comprises the step of computing the extended term g_ext that satisfies an equation of ∇

g_ext·

∇

θ

=0, ∇

θ

being a standard signed distance function computed from the zero level set of the embedding function φ

.

27. The method of claim 26, wherein the computing step is performed with a fast marching method.

28. The method of claim 27, wherein the extended term e_ext(x, y, z)=g_base(c(x, y, z)) for points (x,y,z) close to the zero level set, c(x, y, z) being the closest point in the zero level set of the embedding function φ

.

29. The method of claim 25, wherein the level set equation is in the form of Φ

_t+F|∇

Φ

|=0, wherein the speed function F=g₀(1−

ε

κ

).

30. The method of claim 25, wherein the level set equation is in the form of Φ

_t=Sign(g_base)((|g₀|−

ε

κ

)|∇

Φ

|), wherein the speed function F=−

Sign(g_base)(g₀|−

ε

κ

), and Sign(g_base) is a sign function of g_base.

31. The method of claim 30, wherein g_base is defined in the form of g_base=g_gradg_gray, wherein g_grad and g_grey comprise intensity gradient information and gray value information of the image, respectively.

32. The method of claim 22, further comprising the step of localizing an inner boundary of the structures surrounding the organ as a shape constraint for the propagating front of the contour.

33. The method of claim 32, wherein the structures comprise a set of ribs.

34. The method of claim 33, wherein the localizing step comprises the steps of;

a. converting the image into a binary image;

b. localizing a skin surface from the converted binary image, wherein the localized skin surface comprises a skin circumference;

c. identifying a set of candidate pixels, P_candidate={P_candidate(j)}, from the converted binary image, j=1, 2, . . . , N_c, N_c being the number of the set of candidate pixels P_candidate;

d. determining a set of rib pixels, P_rib={P_rib(i)}, from the set of candidate pixels P_candidate, each of the set of rib pixels P_rib corresponding to one of the set of ribs in the converted binary image, i=1, 2, . . . , N_r, N_r being the number of the set of rib pixels P_rib;

e. segmenting the set of rib pixels P_rib into a plurality of sections, S={S(k)}, along the skin circumference in the converted binary image, k=1, 2, . . . , N_s, N_s being the number of the plurality of sections S;

f. calculating distances of each rib pixel in a segmented section S(k) to its closest skin pixels on the skin circumference in the segmented section S(k) so as to obtain the mean value {overscore (D)}_skin(k) and the standard deviation D_std(k) of these distances in the segmented section S(k), respectively, k=1, 2, . . . , N_s;

g. defining a skin-rib distance, d_skin-rib(k)={overscore (D)}_skin(k)+2D_std(k) for the segmented section S(k), k=1, 2, . . . , N_s; and

h. connecting the plurality of segmented sections S together to form the inner boundary of the plurality of ribs, P_in={(x, y)|d(x, y)=Td_skin-rib(C_Map(x, y))}, wherein d(x,y) is distances of pixel (x,y) to the skin circumference, C_Map(x,y) is the closest point of pixel (x,y) on the skin circumference, and Td_skin-rib is a lookup table that stores the skin-rib distance d_skin-rib for each pixel along the skin circumference.

35. The method of claim 34, wherein the converting step comprises the step of thresholding the image with a threshold, I_skin.

36. The method of claim 35, wherein the set of rib pixels P_rib={(x, y)|(x, y)ε

P_candidate, and D_skin (x, y)<

d_{rib max}}, d_ribmax being a maximum possible distance from a rib to the skin circumference.

37. The method of claim 34, wherein the connecting step is performed with an interpolation scheme.

38. The method of claim 22, further comprising the step of performing a stiff band algorithm on the propagating front of the contour.

39. The method of claim 38, wherein the performing step comprises the steps of:

a. defining a neighborhood for each of pixels {P_i} along the contour, wherein P_i represents the ith pixel on the contour, i=1, 2, . . . , N,N being the number of the pixels, such that the neighborhood includes a set of pixels that are within ±

ε

pixels, ε

being a non-zero positive number;

b. dividing the pixels of the neighborhood for P_i into a first set of pixels that are in front of pixel P_i along a propagating direction of the contour, and a second set of pixels that are behind of pixel P_i along the propagating direction of the contour;

c. defining a speed limit σ

to classify the neighborhood into several possible states;

d. for each state segmenting the neighborhood of P_i; and

e. iteratively repeating steps (b)-(d) for all pixels {P_i}.

40. The method of claim 22, wherein the organ comprises at least a part of a liver, a heart, a kidney, a stomach, or a lung of a living subject.

41. The method of claim 22, wherein the image comprises a magnetic resonance image.

42. The method of claim 22, wherein the image comprises a computed tomography image.

43. Software stored on a computer readable medium for causing a computing system to perform functions that segment a region of interest of an organ in an image comprising:

a. initializing a contour inside the region of interest in the image;

b. introducing a speed function that is capable of accumulating spatial and temporal information of a propagating front of the contour; and

c. evolving the contour toward the boundary of the organ using the introduced speed function so as to segment the organ, wherein the boundary of the organ is embedded as a zero level set of an embedding function, φ

, governed by a level set equation.

44. The software of claim 43, wherein the evolving function comprises:

a. defining an image-dependent static term, g_base;

b. setting g₀=g_base, wherein g₀ is a term used in the speed funtion;

c. computing {(x,y,z)|Φ

((x,y,z)=0} at iteration n, so as to obtain a set of points in the zero level set of the embedding function φ

, wherein n=1, 2, 3, . . . , and coordinates (x, y, z) represent a point on the propagating front of the contour;

d. retrieving the static term g_base (x, y, z) for each of the set of points in the zero level set of the embedding function φ

;

e. extending the retrieved static term g_base(x, y, z) to a narrow band in which the embedding function φ

is computed so as to generate an extended term g_ext;

f. updating the term g₀=g₀g_ext so as to update the speed function;

g. computing the embedding function φ

at iteration (n+1) using the updated speed function; and

h. iteratively repeating steps (c)-(g) for a predetermined number of iterations or until the propagating front of the contour does not move.

45. The method of claim 43, wherein the functions further comprise localizing an inner boundary of the structures surrounding the organ as a shape constraint for a propagating front of a contour.

46. The software of claim 43, wherein the functions further comprise performing a stiff band algorithm on the evolution of a contour.

47. A system for performing functions that segment a region of interest of an organ of a living subject in an image comprising a controller performing the steps of:

a. initializing a contour inside the region of interest in the image;

b. introducing a speed function that is capable of accumulating spatial and temporal information of a propagating front of the contour; and

c. evolving the contour toward the boundary of the organ using the introduced speed function so as to segment the organ, wherein the boundary of the organ is embedded as a zero level set of an embedding function, φ

, governed by a level set equation.