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A Bayesian Approach for Transformation Estimation

A Bayesian Approach for Transformation Estimation. Landmark Detection in brain MRI. Camille Izard and Bruno Jedynak. Laboratoire Paul Painlevé Université des Sciences et Technologies de Lille. Center for Imaging Science Johns Hopkins University. Image Registration. Comparing structures

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A Bayesian Approach for Transformation Estimation

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  1. A Bayesian Approachfor Transformation Estimation Landmark Detection in brain MRI Camille Izard and Bruno Jedynak Laboratoire Paul Painlevé Université des Sciences et Technologies de Lille Center for Imaging Science Johns Hopkins University

  2. Image Registration • Comparing structures • Time evolution • Between patients • Comparing different image modalities • MRI, CT • General Approach for registration • Define the mean image • Define the norms • Different types of  • Affine transformation • Diffeomorphisms

  3. Image Registration • Use of landmarks • Characterize the underlying shape • Rough analysis of the shape (Bookstein, 1991) • Corresponding point for registration algorithm • Manual Landmarking HT SCC HoH

  4. Image Model Let’s denote v2I the voxels of an image Graylevels modeled with a mixture of Gaussian, Zv the matter at voxel v, unknown random variable. We define  : R3R3. Matter in the new coordinate system: The template: Generating an image For all u,

  5. Matter Distribution Template obtained when  is a translation, considering the landmark SCC CSF GM WM

  6. With a new image

  7. Unkonwn : • Caracterize the photometry • Learned for each image by EM algorithm • Estimating the transformation = locating the landmarks • Contains the geometry of the images • Includes the variation of geometry • Learned offline on a training set

  8. Comparison • Data term • No needs to define the mean image • Adjustable weight depending on the law distribution • Use of the matter and not gray level • Regularity constraints • Prior on the transformation parameters

  9. Estimating Photometry distributions Mixture of 6 Gaussian distributions: - Pure Voxels : CSF, GM , WM • Mixed Voxels : CSF+GM, GM+WM • Outliers Use EM to learn the distributions

  10. Matter Distribution Estimation

  11. The Template The Template obtained with  a translation and HoH as a landmark CSF GM WM

  12. Recovering the Transformation HoH SCC Information Map : Information contained at each voxel with  a translation, left: with SCC, right: with HoH.

  13. Results translation, 38 training images, 9 images for testing

  14. Using more complex transformations If  has more parameters , Gradient descent on the transformation parameters:

  15. Current extensions • Affine Transformations • Able to deal with several landmarks simultaneously • Estimation by gradient descent in the parameter space • Uniqueness issues • C. Izard, B. Jedynak, Bayesian Registration for Landmark detection, ISBI, april 2006 • Splines transformations • Able to deal with several landmarks at the same time, • Flexibility of the model to various number of landmarks, • Unicity of the transformation • Estimation by gradient descent in the parameter space

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