Author: D Yoan L Mekontchou Yomba
This repository contains a matlab implementation of the Viscous Fluid model for Image Registration.
Nonlinear registration is the warping of one object onto another, using measures of image similarity or corresponding features extracted from the images to guide the deformation. It is widely used in brain imaging for computational anatomy studies. Tensor-based morphometry (TBM), for example, identifies systematic differences in brain structure by statistically analyzing deformations that align images from many subjects to a common template.
Registration methods commonly combine two terms: a similarity measure (distance or measure of agreement between two images) that drives the transformation and a regularizer that ensures its smoothness. This extra term is added to the registration function being optimized, to enforce desirable transformation properties such as smoothness, invertibility and inverse-consistency. For instance, the similarity criterion is regarded as a body force introduced into mechanical equations that govern linear elastic motion (Hooke’s Law) in or viscous fluid equations (Navier-Stokes equation) in. Other algorithms rely on Gaussian filtering or enforce particular properties of the deformation such as diffeomorphic trajectories.
When registering structural magnetic resonance brain images, the information available (voxel intensity, pre-defined landmarks) is rather limited and correspondence mappings are not unique. Consequently, a realistic model is needed to achieve deformations that are closer to an independently defined ground truth. This can be done for instance, as we chose to do here, by incorporating statistical information on the data set into the deformation.
The goal of fluid registration is to determine a mapping from one image (the target) to another image (the source) in the form of a displacement field, u, defined throughout the target volume. The way this problem is set up has been described in some detail in previous publications (Christensen et al 1996, Freeborough and Fox 1998, Crum et al 2001) to which we refer the interested reader for more detail. Briefly though, the displacement field is modelled as a time-dependent viscous fluid flow on the target image, driven by image-derived forces that act to improve a measure of image similarity. The response of the fluid to the applied forces at an instant is obtained by solving the Navier–Stokes equation for a compressible viscous fluid. Such a fluid does not exist in nature but is a convenient transformation model for registration.
Contained in this repository is a sample solution of the PDE driving this model and serves as a reference for any one currently performing research in the field.
- Implementation of a cost function utilizing jacobian maps to preserve topology
- Implementation of vector fields based off of bspline coefficients
- Implementation of alterations to the navier stockes equation
- Further Work On Parameter Optimization
- Implementation of Deep Learning Techniques