Image-based extraction for vascular trees

Abstract

An accurate analysis of the spatial distribution and intravascular pattern of blood flow in any organ must be based on interpolated gradient located within back plane detailed morphometry (diameters, lengths, of cube defined by neighboring voxels vessel numbers, branching pattern, branching angles, etc.) of the organ vasculature. Despite the significance of detailed morphometric data, there is relative scarcity of database on vascular anatomy, mainly because the process is extremely labor intensive. Novel methods in the form of a segmentation algorithm for semi-automation of morphometric data extraction are provided. The extraction algorithm is based on a topological analysis of a vector field generated by the normal vectors of the extracted vessel wall. With this approach, special focus is made on achieving the highest accuracy of the measured values, with excellent results when compared to manual measurements of the main trunk of the coronary arteries with microscopy.

1 . A method for extracting a curve-skeleton from a volumetric image of a vessel having a local center and a boundary, the method comprising the steps of:
 segmenting vessels within the volumetric image to identify a plurality of points;   determining a boundary of the plurality of points by moving the points along a gradient direction so that the points are located at a maximal gradient;   computing a tetrahedrization of the plurality of points located at the maximal gradient along the boundary;   computing a vector field of the plurality of points so that the vectors within the vector field point inwards toward the local center of the vessel;   computing points using topological analysis of the vector field to identify center points within the vessel; and   connecting the center points based upon topology of the tetrahedrization to create a centerline of the vessel within the volumetric image.   
     
     
         2 . The method of  claim 1 , wherein the segmentation step is performed based on volumetric image gradients. 
     
     
         3 . The method of  claim 1 , whereby the step of computing a tetrahedrization of a plurality of points utilizes the implementation of a Delaunay tetrahedrization algorithm. 
     
     
         4 . The method of  claim 3 , wherein the step of computing a tetrahedrization of a plurality of points further utilizes tri-linear interpolation within one or more tetrahedra generated by the tetrahedrization of a plurality of points. 
     
     
         5 . The method of  claim 1 , wherein the step of computing a vector field of the plurality of points determines a repulsive force field utilizing points on the boundary of the vessel, the repulsive force field generated by a force field within the vessel by electrically charging the boundary of the vessel. 
     
     
         6 . The method of  claim 1 , wherein the step of computing a vector field of the plurality of points defines a vector by using an identified point and points neighboring the identified point to define a plane approximated by the identified point and points neighboring the point. 
     
     
         7 . The method of  claim 6 , wherein the plane comprises a normal, the normal defining an orthogonal vector corresponding to the identified point. 
     
     
         8 . The method of  claim 1 , whereby the step of computing a vector field of the plurality of points utilizes a vector field defined by three vectors located at the vertices of a triangle. 
     
     
         9 . The method of  claim 8 , whereby the step of computing a vector field of the plurality of points computes barycentric coordinates of a point within a triangle. 
     
     
         10 . The method of  claim 9 , wherein the barycentric coordinates are used as weights for linearly combining the three vectors to compute an interpolated vector. 
     
     
         11 . The method of  claim 1 , wherein the step of computing a vector field of the plurality of points utilizes a computation so that the vectors within the vector field are orthogonal to the boundary of the vessel. 
     
     
         12 . The method of  claim 11 , wherein the step of computing a vector field of the plurality of points further utilizes a computation to linearly interpolate the vectors within the vector field. 
     
     
         13 . The method of  claim 1 , whereby the step of computing a vector field of the plurality of points utilizes an analysis of a matrix, whereby the matrix and a vector from the vector field describe a linear map. 
     
     
         14 . The method of  claim 13 , wherein the vector field is a linear vector field of type 1 and the matrix is diagonalizable. 
     
     
         15 . The method of  claim 14 , wherein the vector field is selected from the group consisting of saddle singularity, node singularity, and focus singularity. 
     
     
         16 . The method of  claim 13 , wherein the vector field is a linear vector field of type 2. 
     
     
         17 . The method of  claim 16 , wherein the vector field is selected from the group consisting of center singularity and spiral singularity. 
     
     
         18 . The method of  claim 13 , wherein the vector field is a linear vector field of type 3. 
     
     
         19 . The method of  claim 18 , wherein the vector field is an improper node singularity. 
     
     
         20 . The method of  claim 1 , whereby the step of computing points using topological analysis of the vector field to identify center points within the vessel comprises the computation of a topology of a vector field defined on the faces of a tetrahedralized set of points. 
     
     
         21 . The method of  claim 1 , whereby the step of computing points using topological analysis of the vector field is performed by computing singularities within the vector field interpolated within each faces of one or more tetrahedra generated by the tetrahedrization of a plurality of points. 
     
     
         22 . The method of  claim 1 , wherein the step of computing points using topological analysis of the vector field is performed by identifying focus singularities and/or spiral singularities within one or more faces of one or more tetrahedral generated by the tetrahedrization of a plurality of points. 
     
     
         23 . The method of  claim 1 , whereby the step of computing points using topological analysis of the vector field is performed after the vectors within the vector field are projected onto one or more faces of one or more tetrahedra generated by the tetrahedrization of a plurality of points. 
     
     
         24 . The method of  claim 23 , whereby the vectors within the vector field are projected onto one or more faces of one or more tetrahedra at the vertices of the triangles comprising one or more tetrahedral, and whereby the step of computing points using topological analysis of the vector field comprises linear interpolation. 
     
     
         25 . The method of  claim 1 , wherein the diameter of the vessel at a particular location is computed as the distance between a center point and a first vessel boundary multiplied by two. 
     
     
         26 . The method of  claim 25 , further comprising the step of comparing the diameter of the vessel at a particular location is computed by the method to a diameter of the vessel identified by optical measurements to determine any potential statistical variations between the two diameters. 
     
     
         27 . The method of  claim 1 , further comprising the step of filling gaps occurring between center points within the vessel. 
     
     
         28 . The method of  claim 27 , whereby the filling step is performed by identifying tetrahedral close to a gap having a center point at each end, and by determining individual fractions of a line contained within one or more tetrahedra. 
     
     
         29 . The method of  claim 28 , whereby the gap is filled if the sum of the individual fractions equals one. 
     
     
         30 . The method of  claim 1 , wherein the diameter of the vessel at a particular location is computed as the distance between a center point and a first vessel boundary plus the distance between the same center point and a second vessel boundary opposite the first vessel boundary. 
     
     
         31 . A method for extracting a curve-skeleton, the method comprising the steps of:
 obtaining a volumetric image of a vasculature; and   extracting a boundary of the volumetric image using a gradient threshold, the boundary comprising a plurality of points.   
     
     
         32 . The method of  claim 31 , further comprising the step of moving the plurality of points along a gradient direction. 
     
     
         33 . The method of  claim 32 , further comprising the step of determining a plurality of vectors orthogonal to a surface of the boundary from the plurality of points. 
     
     
         34 . The method of  claim 33 , whereby the step of determining a plurality of vectors is determined by deriving a least-square fit of a plurality of neighboring points to the plurality of points and utilizing a plurality of vectors. 
     
     
         35 . A method for determining a curve-skeleton of an object, the method comprising the steps of:
 extracting a boundary of the object, the boundary having a surface;   computing a vector field, the vector field being orthogonal to the object's boundary surface; and   determining the curve-skeleton by applying topological analysis to the vector field.   
     
     
         36 . The method of  claim 35 , further comprising the step of automatically closing gaps between segments of the curve-skeleton. 
     
     
         37 . The method of  claim 35 , wherein the extracting step involves the extraction of a vasculature of a specimen. 
     
     
         38 . The method of  claim 37 , whereby the extracting step occurs only after the specimen has been perfused and CT-scanned. 
     
     
         39 . The method of  claim 37 , whereby the vasculature is defined by a volumetric image, the volumetric image consisting of voxels aligned along a three-dimensional grid. 
     
     
         40 - 46 . (canceled) 
     
     
         47 . A system for extracting a curve-skeleton from a volumetric image of a vessel having a local center and a boundary, the system comprising:
 a processor;   a storage medium operably connected to the processor, the storage medium capable of receiving and storing morphometric data;   wherein the processor is operable to:
 segment vessels within the volumetric image to identify a plurality of points; 
 determine a boundary of the plurality of points by moving the points along a gradient direction so that the points are located at a maximal gradient; 
 compute a tetrahedrization of the plurality of points located at the maximal gradient along the boundary; 
 compute a vector field of the plurality of points so that the vectors within the vector field point inwards toward the local center of the vessel; 
 compute points using topological analysis of the vector field to identify center points within the vessel; and 
 connect the center points based upon topology of the tetrahedrization to create a centerline of the vessel within the volumetric image. 
   
     
     
         48 . The system of  claim 47 , wherein the segmentation is performed based on volumetric image gradients. 
     
     
         49 . The system of  claim 47 , whereby the computation of a tetrahedrization of a plurality of points utilizes the implementation of a Delaunay tetrahedrization algorithm. 
     
     
         50 . The system of  claim 49 , wherein the computation of a tetrahedrization of a plurality of points further utilizes tri-linear interpolation within one or more tetrahedra generated by the tetrahedrization of a plurality of points. 
     
     
         51 . The system of  claim 47 , wherein the computation of a vector field of the plurality of points determines a repulsive force field utilizing points on the boundary of the vessel, the repulsive force field generated by a force field within the vessel by electrically charging the boundary of the vessel. 
     
     
         52 . The system of  claim 47 , wherein the computation of a vector field of the plurality of points defines a vector by using an identified point and points neighboring the identified point to define a plane approximated by the identified point and points neighboring the point. 
     
     
         53 . The system of  claim 52 , wherein the plane comprises a normal, the normal defining an orthogonal vector corresponding to the identified point. 
     
     
         54 . The system of  claim 47 , whereby the computation of a vector field of the plurality of points utilizes a vector field defined by three vectors located at the vertices of a triangle. 
     
     
         55 . The system of  claim 54 , whereby the computation of a vector field of the plurality of points computes barycentric coordinates of a point within a triangle. 
     
     
         56 . The system of  claim 55 , wherein the barycentric coordinates are used as weights for linearly combining the three vectors to compute an interpolated vector. 
     
     
         57 . The system of  claim 47 , wherein the computation of a vector field of the plurality of points utilizes a computation so that the vectors within the vector field are orthogonal to the boundary of the vessel. 
     
     
         58 . The system of  claim 57 , wherein the computation of a vector field of the plurality of points further utilizes a computation to linearly interpolate the vectors within the vector field. 
     
     
         59 . The system of  claim 47 , whereby the computation of a vector field of the plurality of points utilizes an analysis of a matrix, whereby the matrix and a vector from the vector field describe a linear map. 
     
     
         60 . The system of  claim 59 , wherein the vector field is a linear vector field of type 1 and the matrix is diagonalizable. 
     
     
         61 . The system of  claim 60 , wherein the vector field is selected from the group consisting of saddle singularity, node singularity, and focus singularity. 
     
     
         62 . The system of  claim 59 , wherein the vector field is a linear vector field of type 2. 
     
     
         63 . The system of  claim 62 , wherein the vector field is selected from the group consisting of center singularity and spiral singularity. 
     
     
         64 . The system of  claim 59 , wherein the vector field is a linear vector field of type 3. 
     
     
         65 . The system of  claim 64 , wherein the vector field is an improper node singularity. 
     
     
         66 . The system of  claim 47 , whereby the computation of points using topological analysis of the vector field to identify center points within the vessel comprises the computation of a topology of a vector field defined on the faces of a tetrahedralized set of points. 
     
     
         67 . The system of  claim 47 , whereby the computation of points using topological analysis of the vector field is performed by computing singularities within the vector field interpolated within each faces of one or more tetrahedra generated by the tetrahedrization of a plurality of points. 
     
     
         68 . The system of  claim 47 , wherein the computation of points using topological analysis of the vector field is performed by identifying focus singularities and/or spiral singularities within one or more faces of one or more tetrahedral generated by the tetrahedrization of a plurality of points. 
     
     
         69 . The system of  claim 47 , whereby the computation of points using topological analysis of the vector field is performed after the vectors within the vector field are projected onto one or more faces of one or more tetrahedra generated by the tetrahedrization of a plurality of points. 
     
     
         70 . The system of  claim 69 , whereby the vectors within the vector field are projected onto one or more faces of one or more tetrahedra at the vertices of the triangles comprising one or more tetrahedral, and whereby the step of computing points using topological analysis of the vector field comprises linear interpolation. 
     
     
         71 . The system of  claim 47 , wherein the diameter of the vessel at a particular location is computed as the distance between a center point and a first vessel boundary multiplied by two. 
     
     
         72 . The system of  claim 71 , whereby the processor is further operable to compare the computed diameter of the vessel at a particular location to a diameter of the vessel identified by optical measurements to determine any potential statistical variations between the two diameters. 
     
     
         73 . The system of  claim 47 , whereby the processor is further operable to fill gaps occurring between center points within the vessel. 
     
     
         74 . The system of  claim 73 , whereby the filling step is performed by identifying tetrahedral close to a gap having a center point at each end, and by determining individual fractions of a line contained within one or more tetrahedra. 
     
     
         75 . The system of  claim 74 , whereby the gap is filled if the sum of the individual fractions equals one. 
     
     
         76 . The system of  claim 47 , wherein the diameter of the vessel at a particular location is computed as the distance between a center point and a first vessel boundary plus the distance between the same center point and a second vessel boundary opposite the first vessel boundary. 
     
     
         77 . The system of  claim 47 , further comprising a program stored upon the storage medium, said program operable by the processor upon the morphometric data. 
     
     
         78 . The system of  claim 47 , wherein the system comprises a user system and a server system, and wherein the user system and the server system are operably connected to one another. 
     
     
         79 . A system for extracting a curve-skeleton, the system comprising:
 a processor;   a storage medium operably connected to the processor, the storage medium capable of receiving and storing morphometric data;   wherein the processor is operable to:
 obtain a volumetric image of a vasculature; and 
 extract a boundary of the volumetric image using a gradient threshold, the boundary comprising a plurality of points. 
   
     
     
         80 . The system of  claim 79 , whereby the processor is further operable to move the plurality of points along a gradient direction. 
     
     
         81 . The system of  claim 80 , whereby the processor is further operable to determine a plurality of vectors orthogonal to a surface of the boundary from the plurality of points. 
     
     
         82 . The system of  claim 81 , whereby the determination of a plurality of vectors is determined by deriving a least-square fit of a plurality of neighboring points to the plurality of points and utilizing a plurality of vectors. 
     
     
         83 . The system of  claim 79 , further comprising a program stored upon the storage medium, said program operable by the processor upon the morphometric data. 
     
     
         84 . The system of  claim 79 , wherein the system comprises a user system and a server system, and wherein the user system and the server system are operably connected to one another. 
     
     
         85 . A system for extracting a curve-skeleton from a volumetric image of a vessel, the system comprising:
 a processor;   a storage medium operably connected to the processor, the storage medium capable of receiving and storing morphometric data;   wherein the processor is operable to:
 extract a boundary of the object, the boundary having a surface; 
 compute a vector field, the vector field being orthogonal to the object's boundary surface; and 
 determine the curve-skeleton by applying topological analysis to the vector field. 
   
     
     
         86 . The system of  claim 85 , whereby the processor is further operable to automatically closing gaps between segments of the curve-skeleton. 
     
     
         87 . The system of  claim 85 , wherein the extraction of a boundary of the object involves the extraction of a vasculature of a specimen. 
     
     
         88 . The system of  claim 87 , wherein the extraction of a boundary of the object occurs only after the specimen has been perfused and CT-scanned. 
     
     
         89 . The system of  claim 87 , whereby the vasculature is defined by a volumetric image, the volumetric image consisting of voxels aligned along a three-dimensional grid. 
     
     
         90 . The system of  claim 87 , further comprising a program stored upon the storage medium, said program operable by the processor upon the morphometric data. 
     
     
         91 . The system of  claim 87 , wherein the system comprises a user system and a server system, and wherein the user system and the server system are operably connected to one another. 
     
     
         92 - 100 . (canceled) 
     
     
         101 . A program having a plurality of program steps to be executed on a computer having a processor and a storage medium to extract a curve-skeleton from a volumetric image of a vessel having a local center and a boundary, the program operable to:
 segment vessels within the volumetric image to identify a plurality of points;   determine a boundary of the plurality of points by moving the points along a gradient direction so that the points are located at a maximal gradient;   compute a tetrahedrization of the plurality of points located at the maximal gradient along the boundary;   compute a vector field of the plurality of points so that the vectors within the vector field point inwards toward the local center of the vessel;   compute points using topological analysis of the vector field to identify center points within the vessel; and   connect the center points based upon topology of the tetrahedrization to create a centerline of the vessel within the volumetric image.   
     
     
         102 . The program of  claim 101 , wherein the processor is further capable of calculating the vessel radius at any given point as the distance between the centerline of the vessel and the boundary. 
     
     
         103 . A program having a plurality of program steps to be executed on a computer having a processor and a storage medium to extract a curve-skeleton from a volumetric image of a vessel having a local center and a boundary, the program operable to:
 obtain a volumetric image of a vasculature; and   extract a boundary of the volumetric image using a gradient threshold, the boundary comprising a plurality of points.   
     
     
         104 . A program having a plurality of program steps to be executed on a computer having a processor and a storage medium to extract a curve-skeleton from a volumetric image of a vessel having a local center and a boundary, the program operable to:
 extract a boundary of the object, the boundary having a surface;   compute a vector field, the vector field being orthogonal to the object's boundary surface; and   determine the curve-skeleton by applying topological analysis to the vector field.   
     
     
         105 . (canceled)