Method for tracking blood vessels

1. A method for tracking images of a blood vessel, comprising:

Providing user indication of the source and terminus of an image of the blood vessel; and finding the shortest path along a current established from a steady-state circuit model with a current source and a current sink given by user-placed seeds on the image;

wherein the finding of the shortest path comprises determining change in the current.

2. The method recited in claim 1 the finding of the shortest path comprises using the Dijkstra algorithm.

3. A method for tracking images of a blood vessel, comprising:

providing a digitized image of the blood vessel comprising a plurality of intensities corresponding to a domain of points on a graph;

obtaining two labeled ones of the points on the graph from a user, one of such labeled points being a vessel source, v s , and the one of such labeled points being a vessel terminus, v t ;

building a weighted graph from the plurality of intensities;

determining a potential function; from the weighted graph;

obtaining steady-state electrical current flowing through the weighted graph from the determined potential function;

obtaining a new set of weights for the graph from the obtained steady-state electrical current; and

applying finding the shortest path between v s and v t .

4. A method for tracking images of a blood vessel, comprising:

obtaining a digitized image of the blood vessel comprising a plurality of intensities corresponding to a domain of points on a graph;

obtaining two labeled ones of the points on the graph from a user, one of such labeled points being a vessel source, v s , and the one of such labeled points being a vessel terminus, v t ;

determining differences in the intensities between neighboring ones of the plurality of points to build a weighted graph;

obtaining a new set of weights for the graph from the determined differences; and

applying a new set of weights to find the shortest path between v s , and v t .

5. The method recited in claim 4 wherein the finding of the shortest path comprises using the Dijkstra algorithm.

6. A method for tracking images of a blood vessel, comprising:

(A) providing a digitized image of the blood vessel comprising a plurality of intensities corresponding to a domain of points on a graph;

(B) obtaining two labeled ones of the points on the graph from a user, one of such labeled points being a vessel source, v s , and the one of such labeled points being a vessel terminus, v t ;

(C) building a weighted graph using w ij =exp−β(g i −g j ) 2 where g i indicates the image intensity at point v i on the graph and g j is the image intensity at point v j on the graph and β is a free parameter;

(D) minimizing Q(x)=x T Lx, where x is a function taking one value on every one of the points, subject to the constraints that the x values corresponding to v s and v t are fixed to 1 and 0 respectively, and L is a matrix and wherein the discrete Laplacian matrix is:

Lv

i

⁢

v

j

=

{

d

i

if

i

=

j

-

w

ij

if

v

i

⁢

⁢

and

⁢

⁢

⁢

v

j

⁢

⁢

are

⁢

⁢

adjacent

⁢

⁢

nodes

0

otherwise

where v i is a point on the graph;

where L vi;vj is used to indicate that the matrix L is indexed by points v i and v j and d i is the degree of vertex v i , defined as d i =Σw(e ij ) for all edges e ij incident on v i ;

where e ij is an edge between point v i and another point on the graph, v j and

wherein the summation is taken over all neighboring edges v j ;

using y=C A e ij v k x where C is a diagonal matrix having zeros off-diagonal and the weights, w ij , along the diagonal, where A e ij v k , an incidence matrix, is

A e ij v k =1 if i=k; =−1 if j=k or =0 otherwise

for every vertex v k and edge e ij , where e ij has been arbitrarily assigned an orientation; and

A e ij v k is used to indicate that the matrix is indexed by edge e ij and node v k ;

(E) obtaining a new set of weights for the graph, using r=abs(A e ij v k T )abs(y), and w ij =(r i +r j )exp−a(r i −r j ) 2 -β(g i −g j ) 2 , where a is a free parameter;

(F) applying an algorithm to the graph with the new weights to find the shortest path between v s and v t .

7. The method recited in claim 6 wherein the applied algorithm is Dijkstra's algorithm.