Accelerated image volume segmentation using minimal surfaces given a boundary
View Patent ↗A method for image volume segmentation includes receiving an input image, obtaining an oriented closed contour on one or more slices of the input image, determining a minimum-weight surface from the oriented closed contour using a minimum-cost circulation network flow, and outputting the minimum-weight surface as a segmentation of the input image.
1. A computer readable medium embodying instructions executed by a processor to perform a method for image volume segmentation, the method steps comprising:
receiving an input image;
forming a primal 6-connected lattice of edges and a dual 6-connected lattice of faces defining an object in the input image, wherein the faces in the dual 6-connected lattice correspond to edges in the primal 6-connected lattice, wherein the edges in the primal 6-connected lattice connect voxels of the input image;
obtaining one or more oriented closed contours on respective slices of the input image;
defining a face weight for each of the faces of the dual 6-connected lattice based on a function of image intensities of the voxels of a corresponding edge;
identifying a surface of the input image having an initial boundary based on the face weights;
determining a three-dimensional minimum-weight surface including the initial boundary as a set of saturated edges in the primal 6-connected lattice of edges corresponding to a minimum-cost circulation network flow, wherein the minimum-weight surface is a three-dimensional segmentation of a portion of the object with the one or more oriented closed contours defining a boundary of the three-dimensional minimum-weight surface determination; and
outputting the three-dimensional minimum-weight surface as a segmentation of the input image.
2. The computer readable medium of claim 1 , further comprising obtaining a series of closed contours.
3. The computer readable medium of claim 1 , wherein the oriented closed contour is represented by a vector r in the determination of the three-dimensional minimum-weight surface given by:
min
z
Q
(
z
)
=
∑
i
w
i
z
i
,
subject
to
Bz
=
r
,
where z is an indicator vector indicating whether a face is present in the three-dimensional minimum weight surface and w i indicates the weights of a face.
4. The computer readable medium of claim 1 , wherein the oriented closed contour is obtained by a two-dimensional segmentation method.
5. The computer readable medium of claim 1 , wherein the face weights include an arbitrary value for outside faces.
6. A system for image volume segmentation comprising:
a memory device storing a plurality of instructions embodying the system for image volume segmentation;
a processor for receiving an input image and executing the plurality of instructions to perform a method comprising:
forming a primal 6-connected lattice of edges and a dual 6-connected lattice of faces defining an object in the input image, wherein the faces in the dual 6-connected lattice correspond to edges in the primal 6-connected lattice;
obtaining an oriented closed contour on one or more slices of the input image;
defining a face weight for each of the faces of the dual 6-connected lattice based on a function of image intensities of the voxels of a corresponding edge;
identifying a surface of the input image having an initial boundary based on the face weights;
determining a three-dimensional minimum-weight surface including the initial boundary as a set of saturated edges in the primal 6-connected lattice of edges corresponding to a minimum-cost circulation network flow, wherein the minimum-weight surface is a three-dimensional segmentation of a portion of the object with the one or more oriented closed contours defining a boundary of the three-dimensional minimum-weight surface determination; and
outputting the three-dimensional minimum-weight surface as a segmentation of the input image.
7. The system of claim 6 , further comprising obtaining a series of closed contours.
8. The system of claim 6 , wherein the oriented closed contour is represented by a vector r in the determination of the three-dimensional minimum-weight surface given by:
min
z
Q
(
z
)
=
∑
i
w
i
z
i
,
subject
to
Bz
=
r
,
where z is an indicator vector indicating whether a face is present in the three-dimensional minimum weight surface and w i indicates the weights of a face.
9. The system of claim 6 , wherein the oriented closed contour is obtained by a two-dimensional segmentation method.
10. The system of claim 6 , wherein the face weights include an arbitrary value for outside faces.