System and method for tracing rib posterior in chest CT volumes
View Patent ↗A method for tracing, rib posteriors includes providing an incomplete rib tracing comprising a digitized 3-dimensional representation of a rib and a digital image from which said rib tracing was extracted, initializing, a tracing direction for a remainder of said rib, detecting a plurality of ridge points in a sub-volume of said digital image about said initial tracing direction, and deforming a closed curve in a plane perpendicular to said tracing direction until a rib-edge contour is obtained, using said ridge points as constraints.
1. A method for tracing rib posteriors comprising the steps of:
providing an incomplete rib tracing comprising a digitized 3-dimensional representation of a rib and a digital image from which said rib tracing was extracted, said image comprising a plurality of intensities corresponding to a domain of points on a 3-dimensional grid;
initializing a tracing direction for a remainder of said rib;
detecting a plurality of ridge points in a sub-volume of said digital image about said initial tracing direction, wherein a ridge point is a point in a high intensity edge; and
deforming a closed curve in a plane perpendicular to said tracing direction until a rib-edge contour is obtained, using said ridge points as constraints, wherein said incomplete rib tracing is extended by incorporating points on said rib-edge contour.
2. The method of claim 1 , further comprising calculating a center point of a cross section enclosed by said rib-edge contour, reinitializing said tracing direction from said center point, and repeating said steps of detecting a plurality of ridge points and deforming a closed curve until a rib end has been reached.
3. The method of claim 1 , wherein said tracing direction is initialized from a plurality of preceding tracing directions from said incomplete rib tracing using double exponential smoothing.
4. The method of claim 3 , wherein said double exponential smoothing uses equations equivalent to
S t =αy t +(1−α)( S t−1 +b t−1 ),
and
b t =γ( S t − S t−1 )+(1−γ) b t−1 ,
over a pre-determined number of previous iterations of said incomplete rib tracing, wherein S t is an estimated tracing direction at iteration time t, b t is a smoothing term, α and γ satisfy 0≦α≦1 and 0≦γ≦1, respectively, and y t is a rib cross-section center point at iteration time t.
5. The method of claim 1 , wherein detecting a plurality of ridge points comprises using a steerable filter on a sub-region of the image about the tracing direction whose output is a list of points in a plane perpendicular to said tracing direction at different directional orientations with respect to said tracing direction.
6. The method of claim 1 , wherein deforming a closed curve comprises minimizing an energy function of a plurality of points representing said closed curve, wherein said minimization is constrained by said ridge points.
7. The method of claim 6 , wherein said energy function comprises a first term that is a function of the distance between a point on said closed curve and a corresponding ridge point, a second term representing a force that causes the closed curve to expand outward, and a third term that causes the curve to contract if a curve point has advanced beyond the ridge points, and helps the curve expand if a curve point is within the ridge points.
8. The method of claim 7 , wherein said first term is represented by a form equivalent to
α
l
(
V
)
v
j
′
-
δ
×
(
v
j
-
1
+
v
j
+
1
)
2
wherein α is a pre-determined constant,
δ
=
1
2
cos
(
2
π
/
n
)
,
v
j
′
is a point on the curve being deformed, v j+1 and v j−1 are ridge points, l(V) is the length of the curve, and n is the number of the plurality of points.
9. The method of claim 7 , wherein said second term represents a constant outward force.
10. The method of claim 7 , wherein said third term has a negative value when a curve point is within said ridge points and a positive value otherwise.
11. A method for tracing rib posteriors comprising the steps of:
providing a digital image comprising a plurality of intensities corresponding to a domain of points on a 3-dimensional grid;
locating a starting point for a posterior portion of a rib in said digital image;
initializing a tracing direction for said posterior portion of said rib;
detecting a plurality of ridge points by convolving a sub-region of an image slice perpendicular to the tracing direction with orientable basis functions to obtain a direction and strength of a dominant orientation for each point in said sub-region, wherein a ridge point is a point in a high intensity edge; and
minimizing an energy function of a plurality of points representing a closed curve in a plane perpendicular to said tracing direction until a rib-edge contour is obtained, wherein said minimization is constrained by said ridge points; and
incorporating points from said rib-edge contour into a rib posterior tracing.
12. The method of claim 11 , wherein locating a starting point comprises providing an incomplete rib tracing comprising a digitized 3-dimensional representation of a rib, wherein said starting point corresponds to the ending point of said incomplete rib tracing.
13. The method of claim 11 , wherein said orientable basis functions are the separable basis functions of a second order Gaussian derivative and its Hilbert transform, and further comprising determining an angle for each point, and multiplying the strength of each point with a function of the angle wherein whether said point can be considered an edge, a ridge, or a valley is determined.
14. A non-transitory program storage device readable by a computer, tangibly embodying a program of instructions executable by the computer to perform the method steps for tracing rib posteriors, said method comprising the steps of: providing an incomplete rib tracing comprising a digitized 3-dimensional representation of a rib and a digital image from which said rib tracing was extracted, said image comprising a plurality of intensities corresponding to a domain of points on a 3-dimensional grid; initializing a tracing direction for a remainder of said rib; detecting a plurality of ridge points in a sub-volume of said digital image about said initial tracing direction, wherein a ridge point is a point in a high intensity edge; and deforming a closed curve in a plane perpendicular to said tracing direction until a rib-edge contour is obtained, using said ridge points as constraints, wherein said incomplete rib tracing is extended by incorporating points on said rib-edge contour.
15. The computer readable program storage device of claim 14 , the method further comprising calculating a center point of a cross section enclosed by said rib-edge contour, reinitializing said tracing direction from said center point, and repeating said steps of detecting a plurality of ridge points and deforming a closed curve until a rib end has been reached.
16. The computer readable program storage device of claim 14 , wherein said tracing direction is initialized from a plurality of preceding tracing directions from said incomplete rib tracing using double exponential smoothing.
17. The computer readable program storage device of claim 16 , wherein said double exponential smoothing uses equations equivalent to
S t =αy t +(1−α)( S t−1 +b t−1 ),
and
b t =γ( S t − S t−1 )+(1−γ) b t−1 ,
over a pre-determined number of previous iterations of said incomplete rib tracing, wherein S t , is an estimated tracing direction at iteration time t, b t is a smoothing term, α and γ satisfy 0≦α≦1 and 0≦γ≦1, respectively, and y t is a rib cross-section center point at iteration time t.
18. The computer readable program storage device of claim 14 , wherein detecting a plurality of ridge points comprises using a steerable filter on a sub-region of the image about the tracing direction whose output is a list of points in a plane perpendicular to said tracing direction at different directional orientations with respect to said tracing direction.
19. The computer readable program storage device of claim 14 , wherein deforming a closed curve comprises minimizing an energy function of a plurality of points representing said closed curve, wherein said minimization is constrained by said ridge points.
20. The computer readable program storage device of claim 19 , wherein said energy function comprises a first term that is a function of the distance between a point on said closed curve and a corresponding ridge point, a second term representing a force that causes the closed curve to expand outward, and a third term that causes the curve to contract if a curve point has advanced beyond the ridge points, and helps the curve expand if a curve point is within the ridge points.
21. The computer readable program storage device of claim 20 , wherein said first term is represented by a form equivalent to
α
l
(
V
)
v
j
′
-
δ
×
(
v
j
-
1
+
v
j
-
1
)
2
wherein α is a pre-determined constant,
δ
=
1
2
cos
(
2
π
/
n
)
,
v
j
′
is a point on the curve being deformed, v j+1 and v j−1 are ridge points, l(V) is the length of the curve, and n is the number of the plurality of points.
22. The computer readable program storage device of claim 20 , wherein said second term represents a constant outward force.
23. The computer readable program storage device of claim 20 , wherein said third term has a negative value when a curve point is within said ridge points and a positive value otherwise.