Building Prostate Statistical Atlas using Large-Deformation Image Registration

1. Building Prostate Statistical Atlasusing Large-Deformation Image Registration Eric Huierichui@alumni.uwaterloo.ca University of Waterloo – MIAMI Bi-weekly MeetingMarch 31, 2003 at 10:30am in DC 2564

2. Outline • Motivation • Overall Design • Fluid Landmarks • Resulting Prostate Statistical Atlas • Conclusions • Questions

3. Motivation Ultrasound image of a prostate (from University of Western Ontario)

4. Motivation Outline of the prostate (by Dr. Downey)

5. Motivation Benign Prostatic Hyperplasia (BPH) Cancerous Benign Identified regions of the prostate (by Dr. Downey)

6. Motivation • Features: • Grey-level: dark vs. bright; • Texture: textured vs. homogeneous; • Spatial location w.r.t. the prostate.

7. Motivation • Regions closer to the anus has a higher probability of being cancerous.

8. Motivation (x,y) P(cancerous)=0.6 P(BPH) = 0.1 P(benign) = 0.3 • The idea is to build a statistical atlas. • The spatial location (x,y) is mapped to a probability of cancerous, BPH, or benign.

9. Motivation • Prostates come in different sizes and shapes!!! Image Registration

10. Overall Design Deform Sum over “cancerous” P(cancerous) Deform Sum over “BPH” P(BPH) Sum over “benign” Deform P(benign)

11. Large-Deformation usingFluid Landmarks • Simple affine transformations(e.g. rigid translation, rotation, scaling, shearing) • Intensity-based deformation • Small-deformation(e.g. thin-plate splines and linear-elastic models) • Large-Deformation using Fluid Landmarks

12. Large-Deformation usingFluid Landmarks • Lagrangian trajectory: • Matlab implementation: T=3 subject landmarks model landmarks Note that Matlab is one-based, so time starts at t=1.

13. Large-Deformation usingFluid Landmarks • The optimal Lagrangian trajectory can be computed as: • Using iterative gradient descent:

14. Distance Error D((x,t)) • The rate of change in distance error can be computed as:where is the a priorierror covariance, is the a priorimodel landmark location,

15. Distance Error D((x,t))

16. Quadratic Energy P((x,t)) • The rate of change in quadratic energy can be computed as:where can be thought as a measure of the distance between and .

17. Quadratic Energy P((x,t)) • Landmarks are moved “smoothly” because the velocity vectors of all other landmarks , weighted by a distance function , contribute to the quadratic energy. Consider landmark xn at t=2

18. Iteration 1

19. Iteration 2

20. Iteration 3

21. Iteration 4

22. Iteration 10

23. Iteration 20

24. Interpolate Velocity Vectors • Velocity vectors at any location can be interpolated by a weighted sum of the optimal velocity vectors of all landmarks.

25. Velocity Vectors at t=2 Magnitudes are normalized in this plot.

26. Velocity Vectors at t=3 Magnitudes are normalized in this plot.

27. Final Trajectories for All Points • Lagrangian trajectory: • Matlab implementation: T=3 subject landmarks model landmarks

28. Deformation Result deform • The intensity values between the discrete pixels of the original image are interpolated using triangle-based linear interpolation.

29. Recall: Overall Design Deform Sum over “cancerous” P(cancerous) Deform Sum over “BPH” P(BPH) Sum over “benign” Deform P(benign)

30. Resulting Prostate Statistical Atlas Cancerous Benign BPH Results based on 10 images.

31. Conclusions • Spatial location of a ROI can also be a useful feature in classification. • In order to build a prostate statistical atlas, each prostate must be deformed to a common shape (e.g. circle). • Large-deformation based on fluid landmarks can be used for such deformation.

32. Questions • How to define the landmarks? • e.g. equally spaced vs. curvature-based. • Is circle a good shape for the model? • e.g. circle vs. ellipse vs. “walnut” shape. • How to handle the imperfection of the result (i.e. not a perfect circle)? • e.g. more landmarks vs. additional class called “undefined”. • Further improvements or extensions? • e.g. dynamic knowledge base.

33. References • G.E. Christensen, P. Yin, M.W. Vannier, K.S.C. Chao, J.F. Dempsey, and J.F. Williamson, “Large-Deformation Image Registration using Fluid Landmarks”. • S.C. Joshi and M.I. Miller, “Landmark Matching via Large Deformation Diffeomorphisms”, IEEE Transactions on Image Processing, Vol. 9, No. 8, August 2000.