a bayesian approach for transformation estimation
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
A Bayesian Approachfor Transformation Estimation
Camille Izard and Bruno Jedynak
Landmark Detection in brain MRI
Laboratoire Paul Painlevé
Université des Sciences et Technologies de Lille
Center for Imaging Science
Johns Hopkins University
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
• Use of landmarks– Characterize the underlying shape– Rough analysis of the shape (Bookstein, 1991)– Corresponding point for registration algorithm
• Manual Landmarking
Image Registration
SCC
HoH
HT
Image Model
Generating an imageFor all u,
Let’s denote v 2 I the voxels of an imageGraylevels modeled with a mixture of Gaussian,Zv the matter at voxel v, unknown random variable. We define : RR3 R3.Matter in the new coordinate system:The template:
Matter Distribution
Template obtained when is a translation, considering the landmark SCC
CSF
GM WM
With a new image
-Contains the geometry of the images
-Includes the variation of geometry
-Learned offline on a training set
-Estimating the transformation = locating the landmarks
-Caracterize the photometry
-Learned for each image by EM algorithm
Unkonwn :
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
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
Matter Distribution Estimation
The Template
The Template obtained with a translation and HoH as a landmark
CSF
GM WM
Recovering the Transformation
Information Map : Information contained at each voxel with a translation, left: with SCC, right: with HoH.
HoH SCC
Results
Landmark Error on training set Error on testing set
SCC 1.81 mm (1.42 mm) 2.46 mm (1.92 mm)
HoH 2.75 mm (1.97 mm) 3.70 mm (1.48 mm)
HT 0.26 mm (0.51 mm) 2.19 mm (1.11mm)
translation, 38 training images, 9 images for testing
Using more complex transformationsIf has more parameters ,
Gradient descent on the transformation parameters:
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