Robust vessel tree modeling
View Patent ↗A method for extracting a local center-axis representation of a vessel, includes: placing first and second seed points in an image that includes the vessel, wherein the first and second seed points are placed near a beginning and an end of a centerline of the vessel; representing the image as a discrete graph having nodes and edges, wherein the first seed point is a source node and the second seed point is a goal node; and finding a minimum-cost path between the first and second seed points by computing a cost of edges between the first and second seed points, wherein the cost of each edge is reciprocal to a vesselness measure of the edge.
1. A method for computing a vesselness measure, comprising:
initializing a plurality of rays from a center point of a vessel and collecting an intensity profile of the vessel and a background of the vessel along each ray;
modeling each intensity profile by dividing the intensity profile into first, second and third intervals, wherein the first interval represents an intensity value inside the vessel, the second interval represents an intensity value outside the vessel and the third interval represents an intensity value between a boundary of the vessel and the background;
for each ray, obtaining a difference between an originally measured intensity profile of the vessel and the background and the originally measured intensity profile's corresponding modeled intensity profile, wherein the difference is a fit measure of the ray, the fit measure is given by
ƒ i =arg min R,σ
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where ƒ(x)=u(I v −I(x)), g(x)=u(I(x)−I o ), u(x) is a step function, γ 1 , γ 2 , and γ 3 are weights for the first to third intervals, respectively, V i is a vessel model along the ray, R is the radius of the ray, I v is the intensity value inside the vessel and I o is the intensity value outside the vessel; and
summing the fit measures for each ray, wherein the total sum is the vesselness measure.
2. The method of claim 1 , wherein the vesselness measure along a ray is strong near a center of the ray, drops rapidly near a boundary of the ray and is weak in a non-vascular area between the ray and another ray.
3. The method of claim 1 , wherein the vessel is a blood vessel.
4. A system for computing a vesselness measure, comprising:
a memory device for storing a program;
a processor in communication with the memory device, the processor operative with the program to:
initialize a plurality of rays from a center point of a vessel and collect an intensity profile of the vessel and a background of the vessel along each ray;
model each intensity profile by dividing the intensity profile into first, second and third intervals, wherein the first interval represents an intensity value inside the vessel, the second interval represents an intensity value outside the vessel and the third interval represents an intensity value between a boundary of the vessel and the background;
for each ray, obtain a difference between an originally measured intensity profile of the vessel and the background and the originally measured intensity profile's corresponding modeled intensity profile, wherein the difference is a fit measure of the ray, the fit measure is given by
ƒ i =arg min R,σ ,
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γ
1
∑
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=
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V
i
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x
,
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,
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where ƒ(x)=u(I v −I(x)), g(x)=u(I(x)−I o ), u(x) is a step function, γ 1 , γ 2 , and γ 3 are weights for the first to third intervals, respectively, V i is a vessel model along the ray, R is the radius of the ray, I v is the intensity value inside the vessel and I o is the intensity value outside the vessel; and
sum the fit measures for each ray, wherein the total sum is the vesselness measure.
5. The system of claim 4 , wherein the vesselness measure along a ray is strong near a center of the ray, drops rapidly near a boundary of the ray and is weak in a non-vascular area between the ray and another ray.