Building Prostate Statistical Atlas using Large-Deformation Image Registration Eric Hui University of Waterloo – MIAMI Bi-weekly Meeting March 31, 2003 at 10:30am in DC 2564

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

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

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

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

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

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

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

11 Large-Deformation using Fluid 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 Large-Deformation using Fluid Landmarks

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

13 Large-Deformation using Fluid Landmarks The optimal Lagrangian trajectory can be computed as: The optimal Lagrangian trajectory can be computed as: Using iterative gradient descent: 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 priori error covariance, is the a priori model landmark location, The rate of change in distance error can be computed as: where is the a priori error covariance, is the a priori model 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. 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. Landmarks are moved “smoothly” because the velocity vectors of all other landmarks, weighted by a distance function, contribute to the quadratic energy. Consider landmark x n 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 The intensity values between the discrete pixels of the original image are interpolated using triangle-based linear interpolation. deform

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

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

31 Conclusions Spatial location of a ROI can also be a useful feature in classification. 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). 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. Large-deformation based on fluid landmarks can be used for such deformation.

32 Questions How to define the landmarks? How to define the landmarks? e.g. equally spaced vs. curvature-based. e.g. equally spaced vs. curvature-based. Is circle a good shape for the model? Is circle a good shape for the model? e.g. circle vs. ellipse vs. “walnut” shape. e.g. circle vs. ellipse vs. “walnut” shape. How to handle the imperfection of the result (i.e. not a perfect circle)? How to handle the imperfection of the result (i.e. not a perfect circle)? e.g. more landmarks vs. additional class called “undefined”. e.g. more landmarks vs. additional class called “undefined”. Further improvements or extensions? Further improvements or extensions? e.g. dynamic knowledge base. 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”. 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 S.C. Joshi and M.I. Miller, “Landmark Matching via Large Deformation Diffeomorphisms”, IEEE Transactions on Image Processing, Vol. 9, No. 8, August 2000.