1. A Computationally Efficient Approach for 2D-3D Image Registration Juri Minxha Medical Image Analysis Professor Benjamin Kimia Spring 2011 Brown University

2. Problem Statement  2 Signal Sources - 3D volumetric data (CT scan, MRI) - 2D images (ex. frame from fluoroscopy video)  Project 3D data onto a 2D plane and compare it to existing 2D image. The projected image is also known as the digitally reconstructed radiograph (DRR) Brown University

3. Why do we need this? Image guided surgery Pre-operative data (CT/MRI acquisitions) Good resolution 3D data Slow Acquisition Intra-operative data (fluoroscopy images) Can be quickly acquired Poor resolution, more noise (ex. temporal blurring) Brown University

4. Typical Approach to Registration Similarity Metric Optimization 1. Similarity Metric Mutual Information, Cross-Correlation, Correlation Ratio, Cross Correlation Residual Entropy 2. Optimization, Non-gradient vs. Gradient Gauss-Newton, steepest descent, Levenberg-Larquardt, simplex method etc. The main challenge is: Minimize computation time Brown University

5. Approach Outlined in this paper 1.Similarity Measure: Sum of Conditional Variances 2.Optimization Algorithm: Gauss-Newton 1.Requires computation of gradient 2.Fast convergence Brown University

6. Similarity Metric: SoCV I0I0 RoRo R 0 =100·ln(256-I 0 )-300 1.Quantize images to 64 possible values 2.Each pixel in the image on the left corresponds to a bin in the histogram (64 x 64 bins) 3.Notice the non-linear relationship between I and R

7. Similarity Metric: SoCV What happens if I 0 is translated to the right? For each value of R, we have a range of values in I’

8. Similarity Metric: SoCV Compute the conditional expectation/mean of this distribution

9. Replace each value in R with the conditional mean Similarity Metric: SoCV

10. Optimization: Gauss-Newton Goal: Find values of 3D rigid-body transform that minimize S

11. Initial Testing (Matlab MRI data) Rotation about z –axis (25 o )

12. So far… Similarity metric: Sum of Conditional Variances Optimization Step The optimization step only converges for certain cases Optimization over 1 variable only (needs to be debugged) Testing with MRI data built into Matlab

13. Plan of Action Brown University Fix optimization over all 6 parameters [r x r y r z t x t y t z ] Test on a real data set Implement the computationally efficient approach to this algorithm from their follow up paper Test on real data set and compare computation speed to original April 28 - May 2 May 2 – May 10 May 10 - May 14

14. References A computationally efficient approach for 2D-3D image registration Haque, M.N.; Pickering, M.R.; Biswas, M.; Frater, M.R.; Scarvell, J.M.; Smith, P.N.; 2010 Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Issue Date: Aug. 31 2010-Sept. 4 2010, On page(s): 6268 – 6271 M. Pickering, A. Muhit, J. Scarvell, and P. Smith, "A new multimodal similarity measure for fast gradient-based 2D-3D image registration," in Proc. IEEE Int. Conf. on Engineering in Medicine and Biology (EMBC), Minneapolis, USA, 2009, pp. 5821-5824. Brown University