1. Model-based Symmetric Information Theoretic Large Deformation
Multi-modal Image Registration
Peter Lorenzen1, Brad Davis1 and Sarang Joshi1,2
Departments of 1Computer Science and 2Radiation Oncology, University of North Carolina, Chapel Hill, NC 27599,
Symmetric Registration
We introduce an independent coordinate system W from which the transformations h1 and h2 are estimated.
The registration framework is inherently inverse consistent as f o g = g o f = the identity map.
Bayesian Information Theoretic Framework
Assume that the underlying anatomy consists of tissue classes, such as grey matter, white matter, and cerebrospinal fluid.
The data likelihoods characterize the intensity response of the underlying tissues in the various imaging modalities.
To drive the registration, a symmetric form of Kullback-Leibler divergence is used as a dissimilarity metric between the class posterior densities for images I1 and I2.
The dissimilarity metric can be expressed in terms not involving the independent coordinate system, W.
Introduction
Goal: Find a mapping between the underlying anatomical structures in two multi-modal image sets I1 and I2.
Approach: Use a Bayesian framework in which the information about the anatomical structures is captured by class posterior densities.
Registration is estimated to minimize the symmetric Kullback-Leibler divergence.
An image set is a collection of co-registered images of different modalities.
Image Set I1 under f
Image Set I2 under g
Grid under f
Grid under g
Grid under f o g
Grid under g o f
Image Set I1
Image Set I2
Results
BrainWeb brain database is used to simulate two multi-modal image sets.
The second image set, I2, was subjected to an artificial sinusoidal transformation.
The algorithm is run and the transformations f:W1 -> W2 and g:W2 -> W1 are estimated.
Final transformed image sets
An image of a regular grid under f, g, and their compositions provides a qualitative understanding of the inverse invariance.
Due to the inherent symmetric formulation the consistency error can be made arbitrarily small.
The registration is estimated within the framework of large deformation fluid diffeomorphisms.
The transformations and their inverses are generated by integrating velocity fields forward and backwards in time.
Fluid Deformation Framework