3-D vessel tree surface reconstruction method
A method for reconstructing 3-D vessel geometry of a vessel includes: receiving a plurality of 2-D rotational X-ray images of the vessel; extracting vessel centerline points for normal cross sections of each of the plurality of 2-D images; establishing a correspondence of the centerline points; constructing a 3-D centerline vessel tree skeleton of the vessel; constructing an initial 3-D vessel surface having a uniform radius normal to the 3-D centerline vessel tree skeleton; and constructing a target 3-D vessel surface by deforming the initial vessel surface to provide a reconstructed 3-D vessel geometry of the vessel.
1. A method for reconstructing 3-D vessel geometry of a vessel, comprising:
receiving a plurality of 2-D rotational X-ray images of the vessel;
extracting vessel centerline points for normal cross sections of each of the plurality of 2-D images;
establishing a correspondence of the centerline points;
constructing a 3-D centerline vessel tree skeleton of the vessel;
constructing an initial 3-D vessel surface having a uniform radius normal to the 3-D centerline vessel tree skeleton; and
constructing a target 3-D vessel surface by deforming the initial vessel surface to provide a reconstructed 3-D vessel geometry of the vessel,
wherein the extracting vessel centerlines is accomplished in a form of ordered point sets, S i , from angiographic images, where i is the i th image, and each point set S i is a projection of a transformed 3-D centerline model M according to the following:
S i =P i T ( M,θ i ),
wherein P i is a camera projection operator corresponding to image i, and T(M, θ i ) is a defined transformation model;
wherein given M and S i , Gaussian mixture models (GMM) are employed to find transformations T(M, θ i ) that minimize the following cost function:
J ( S i ,M,θ i )=∫(GMM( S i )−GMM( P i T ( M,θ i )) p dx,
wherein J(Si,M, θ i ) is an energy function that measures a distance of two Gaussian mixture models (GMM) where pϵ[0, 2].
2. The method of claim 1 , wherein:
the vessel is a coronary artery.
3. The method of claim 1 , wherein:
the 2-D images have a same cardiac phase.
4. The method of claim 1 , wherein:
the 2-D images are received using ECG signals or ECG gated acquisition signals.
5. The method of claim 1 , wherein:
the 2-D images are angiography images.
6. The method of claim 1 , wherein:
the extracting vessel centerlines is accomplished using a technique of model-guided extraction.
7. The method of claim 1 , wherein:
the establishing the correspondence of centerline points is accomplished using a bipartite graph that corresponds to a linear assignment process that finds a matching vessel point for every projected model point in each image, wherein the bipartite graph represents a first set of vertices (i) that represent transformed, projected model points of the vessel centerline points, and a second set of vertices (j) that represent associated segment points of a prior 3-D vessel shape of the vessel segmented from a DynaCT volume and DynaCT reconstruction, wherein weights at edges, cij, of paired vertices of the first and second sets of vertices are computed using a distance of spatial locations of the respective vertices d ij according to the following:
c i,j ={d i,j if d i,j <dth ; ∞ if d i,j _ d th },
wherein d th is a defined distance threshold.
8. The method of claim 7 , wherein:
the constructing the 3-D centerline vessel tree skeleton is accomplished according to the following:
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wherein: n is a number of 3-D points that are seen in m views; camera (j) is parameterized by a vector a j ; b i is the i th centerline point; Q(a j , b i ) is the projection of 3-D point b i on image (j); x i,j is the i th 2-D centerline point measurement on image (j); d( , ) is a Euclidean distance between the associated points Q(a j , b i ) and x i,j ; and, k i,j ϵ[0, 1] is a confidence measurement of x i,j .
9. The method of claim 8 , wherein:
the constructing the initial 3-D vessel surface is accomplished by generating a point cloud of circles around and perpendicular to a tangential direction of the associated centerline, each one of the point cloud of circles having a defined radius r, and computing an initial surface mesh via a Poisson surface reconstruction method using the point cloud of circles.
10. The method of claim 9 , wherein:
the constructing the target 3-D vessel surface is accomplished using 2-D information through 3-D to 2-D projection to deform the initial 3-D vessel surface according to the following:
T={S ( v i )| i= 1 . . . L},
wherein T represents the initial 3-D vessel surface having radius r, where L is the number of vertices (v i ), i is an iterative parameter, and S(v i ) is a sampling point along a searching profile for (v i ), wherein a minimum-surface cost function w(v i , S(v i )), subject to smoothness constraints |S(v i )−S(v j )|≤Δ, is solved via the following:
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wherein T* represents the target 3-D vessel surface, and Δ is a smoothness constraint that requires that the surface's position between neighboring vertices (v i ) and (v j ) does not change more than a constant distance Δ.
11. The method of claim 10 , wherein the cost function w(v i , S(v i )) describes the unlikeliness that a node is on the target vessel surface and is resolved according to the following:
w ( v i ,S ( v i ))=(α)( w e ( v i ,S ( v i )))+(1−α)( w r ( v i ,S ( v i ))),
wherein αϵ[0, 1] is a weighting (balance) parameter between a boundary-based cost w e (v i , S(v i )) and region-based cost w r (v i , S(v i )), the boundary-based cost being defined as follows:
w e ( v i ,S ( v i ))=(1− p e ( v i ,S ( v i ))),
wherein p e ϵ[0, 1] is the probability that a node belongs to a vessel boundary, wherein the probability p e is a normalized value depicting the likeliness of the vessel boundary, wherein the region-based cost is defined as follows:
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wherein p v ϵ[0, 1] is the probability that a node belongs to a vessel, and p nv ϵ[0, 1] is the probability that a node does not belong to a vessel.
12. The method of claim 11 , wherein:
probability p e is defined by the following:
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wherein u S(vi),j denotes a visibility of a 3-D surface point S(vi) on image j, and p j e denotes a vessel boundary probability map of view j, wherein u S(vi),j is a binary value of 1 or 0, where a value of 1 means the point u S(vi),j is visible on the vessel boundary in image j, and a value of 0 means otherwise;
wherein a soft visibility value is utilized as follows:
u S(vi),j =exp((∠( n S(vi) ,v j )−π/2)/σ u ),
wherein ∠(n S(vi) , v j ) is an angle between a normal direction n S(vi) at a predicted surface point S(v i ) and view direction v j of camera j, and σ u is a standard deviation;
wherein p j e is either: a probability map generated using a machine learning based vessel boundary detector; a normalized gradient map; or, both gradient magnitude and direction are considered as follows:
p j e ( Q ( a j ,S ( v i )))={0, if [ n Q(aj,S(vi)) ·g j dir ( Q ( a j ,S ( v i )))]<0, g j mag ( Q ( a j ,S ( v i ))); if otherwise},
wherein g j dir (Q(a j , S(v i ))) and g j mag (Q(a j , S(v i ))) are a gradient direction and gradient magnitude at 2-D location Q(a j , S(v i )) in image j, respectively, wherein n Q(aj, S0(vi)) is defined as follows:
n Q(aj,S0(vi)) = < Q ( a j ,S 1 ( v i )), Q ( a j ,S ( v i )) {right arrow over (>)},
wherein S 1 (v i ) is any point on searching profile of vertex v i below S(v i ).
13. The method of claim 1 , wherein:
the establishing the correspondence of centerline points is accomplished using a prior 3-D vessel shape segmented from a DynaCT volume and DynaCT reconstruction.
14. The method of claim 1 , wherein:
the establishing the correspondence of centerline points is accomplished using vessel centerline tangents and normals.
15. The method of claim 1 , wherein:
the constructing the 3-D centerline vessel tree skeleton is accomplished using 2-D points of the extracted vessel centerlines using a bundle adjustment based approach.
16. The method of claim 1 , wherein:
the constructing the target 3-D vessel surface is accomplished using a polynomial-time implementation.
17. A computer program storage medium comprising a non-transitory computer readable medium having program code executable by a processing circuit for implementing the method according to claim 11 .
18. An apparatus for reconstructing 3-D vessel geometry of a vessel, comprising:
a computer controlled machine comprising a processing circuit;
computer readable executable instructions, which upon loading into the processing circuit causes the machine to be responsive to the executable instructions to facilitate implementation of the method according to claim 11 .