A Computationally Efficient Approach for 2D-3D Image

Registration

Juri Minxha Medical Image Analysis

Professor Benjamin KimiaSpring 2011

Brown University

Problem Statement2 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)

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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)

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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. GradientGauss-Newton, steepest descent, Levenberg-Larquardt, simplex method etc.

The main challenge is:Minimize computation time

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Approach Outlined in this paper

1. Similarity Measure: Sum of Conditional Variances

2. Optimization Algorithm: Gauss-Newton

1. Requires computation of gradient2. Fast convergence

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Similarity Metric: SoCVI0 Ro

R0 =100·ln(256-I0)-300

1. Quantize images to 64 possible values2. 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

Similarity Metric: SoCV

What happens if I0 is translated to the right?

For each value of R, we have a range of values in I’

Similarity Metric: SoCV

Compute the conditional expectation/mean of this distribution

Replace each value in R with the conditional mean

Similarity Metric: SoCV

Optimization: Gauss-NewtonGoal: Find values of 3D rigid-body transform that minimize S

Initial Testing (Matlab MRI data)

Rotation aboutz –axis (25o)

So far…Similarity metric: Sum of Conditional

VariancesOptimization StepThe optimization step only converges for

certain casesOptimization over 1 variable only (needs to

be debugged)Testing with MRI data built into Matlab

Plan of Action

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Fix optimization over all 6 parameters [rx ry rz

tx ty tz ]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

ReferencesA computationally efficient approach for 2D-3D image

registrationHaque, M.N.; Pickering, M.R.; Biswas, M.; Frater, M.R.; Scarvell, J.M.; Smith, P.N.; 2010 Annual International Conference of the IEEEEngineering 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 multimodalsimilarity measure for fast gradient-based 2D-3D imageregistration," in Proc. IEEE Int. Conf. on Engineering in Medicineand Biology (EMBC), Minneapolis, USA, 2009, pp. 5821-5824.

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