Automated lung nodule segmentation using dynamic programming and EM based classification

1. A method for automatically segmenting lung nodules in a three-dimensional (3D) Computed Tomography (CT) volume dataset, comprising the steps of:

receiving an input corresponding to a user-selected point near a boundary of a nodule;

constructing a model of the nodule from the user-selected point, the model being a deformable circle having a set of parameters β that represent a shape of the nodule;

estimating continuous parts of the boundary and discontinuities of the boundary until the set of parameters β converges, using dynamic programming and Expectation Maximization (EM); and

segmenting the nodule, based on estimates of the continuous parts of the boundary and the discontinuities of the boundary.

2. The method of claim 1 , wherein the set of parameters β=[O, s] T , O being a position of the model, s being a scale of the model, and T being a transpose of a vector corresponding to the position O and the scale s of the model.

3. The method of claim 2 , further comprising the step of representing the boundary as a sum B, where B=(∪ i B ci )∪(∪ i B dj ), B ci represents continuous parts of the boundary and B dj represents discontinuities of the boundary.

4. The method of claim 3 , wherein said estimating step includes the steps of;

estimating the continuous parts B ci of the boundary based on a Maximum A-posteriori (MAP) estimate according to an equation B ci =arg maxB ci p(B ci ξI, β), I being a slice from the 3D CT volume dataset;

estimating a MAP density as p(B ci ξI, β)=1/z exp(E β (B ci )), E β (B ci ) being a sum of internal shape and external image energies, and z being a normalization constant;

minimizing the sum of internal shape and external image energies E β (B ci ) using a time-delayed discrete dynamic programming method;

connecting the continuous parts B ci of the boundary to obtain an estimate of the discontinuities B dj of the boundary; and

updating the set of parameters β, based upon a circle fitting method being applied to the continuous parts B ci and the discontinuities B dj of the boundary.

5. The method of claim 1 , wherein said constructing step comprises the step of increasing a radius of the deformable circle until the radius contacts high gradient points in the 3D CT volume dataset.

6. The method of claim 5 , further comprising the step of pre-processing a region-of-interest that encompasses the user-selected point using an Expectation Maximization (EM) based method, so as to classify and remove a calcification from the region-of-interest.

7. The method of claim 6 , wherein said pre-processing step removes the high gradient points that result from the calcification of the nodule.

8. A method for automatically segmenting lung nodules in a three-dimensional (3D) Computed Tomography (CT) volume dataset, comprising the steps of:

receiving an input corresponding to a user-selected point near a boundary of a nodule;

constructing a model of the nodule from the user-selected point, the model being a deformable circle having a set of parameters β that represent a shape of the nodule, where β=[O, s] T , O being a position of the model, s being a scale of the model, and T being a transpose of a vector corresponding to the position O and the scale s of the model;

representing the boundary as a sum B, where B=(∪ i B ci )∪(∪ i B dj ), B ci represents continuous parts of the boundary and B dj represents discontinuities of the boundary;

estimating the boundary, wherein said estimating step includes the steps of;

estimating the continuous parts B ci of the boundary based on a Maximum A-posteriori (MAP) estimate according to an equation B ci =arg maxB ci p(B ci ξI, β), I being a slice from the 3D CT volume dataset;

estimating a MAP density as p(B ci ξI, β)=1/z exp(E β (B ci )), E β (B ci ) being a sum of internal shape and external image energies;

minimizing the sum of internal shape and external image energies E β (B ci ) using a time-delayed discrete dynamic programming method;

connecting the continuous parts B ci of the boundary to obtain an estimate of the discontinuities B dj of the boundary;

updating the set of parameters β, based upon a circle fitting method being applied to the continuous parts B ci and the discontinuities B dj of the boundary;

repeating said step of estimating the boundary until the set of parameters β converges; and

segmenting the nodule, based on estimates of the continuous parts of the boundary and the discontinuities of the boundary.

9. The method of claim 8 , wherein said constructing step comprises the step of increasing a radius of the deformable circle until the radius contacts high gradient points in the 3D CT volume dataset.

10. The method of claim 9 , further comprising the step of pre-processing a region-of-interest that encompasses the user-selected point using an Expectation Maximization (EM) based method, so as to classify and remove a calcification from the region-of-interest.

11. The method of claim 10 , wherein said pre-processing step removes the high gradient points that result from the calcification of the nodule.

12. A program storage device readable by machine, tangibly embodying a program of instructions executable by the machine to perform method steps for automatically segmenting lung nodules in a three-dimensional (3D) Computed Tomography (CT) volume dataset, said method steps comprising:

receiving an input corresponding to a user-selected point near a boundary of a nodule;

constructing a model of the nodule from the user-selected point, the model being a deformable circle having a set of parameters β that represent a shape of the nodule;

estimating continuous parts of the boundary and discontinuities of the boundary until the set of parameters β converges, using dynamic programming and Expectation Maximization (EM); and

segmenting the nodule, based on estimates of the continuous parts of the boundary and the discontinuities of the boundary.

13. The program storage device of claim 12 , wherein the set of parameters β=[O, s] T , O being a position of the model, s being a scale of the model, and T being a transpose of a vector corresponding to the position O and the scale s of the model.

14. The program storage device of claim 13 , further comprising the step of representing the boundary as a sum B, where B=(∪ i B ci )∪(∪ i B dj ), B ci represents continuous parts of the boundary and B dj represents discontinuities of the boundary.

15. The program storage device of claim 14 , wherein said estimating step includes the steps of;

estimating the continuous parts B ci of the boundary based on a Maximum A-posteriori (MAP) estimate according to an equation B ci =arg maxB ci p(B ci ξI, β), I being a slice from the 3D CT volume dataset;

estimating a MAP density as p(B ci ξI, β)=1/z exp(E β (B ci )), E β (B ci ) being a sum of internal shape and external image energies, and z being a normalization constant;

minimizing the sum of internal shape and external image energies E β (B ci ) using a time-delayed discrete dynamic programming method;

connecting the continuous parts B ci of the boundary to obtain an estimate of the discontinuities B dj of the boundary; and

updating the set of parameters β, based upon a circle fitting method being applied to the continuous parts B ci and the discontinuities B dj of the boundary.

16. The program storage device of claim 12 , wherein said constructing step comprises the step of increasing a radius of the deformable circle until the radius contacts high gradient points in the 3D CT volume dataset.

17. The program storage device of claim 16 , further comprising the step of pre-processing a region-of-interest that encompasses the user-selected point using an Expectation Maximization (EM) based method, so as to classify and remove a calcification from the region-of-interest.

18. The program storage device of claim 17 , wherein said pre-processing step removes the high gradient points that result from the calcification of the nodule.