Métodos y enfoques en la enseñanza del idioma inglés como

6.4. MULTI-MODAL IMAGE REGISTRATION WITH MRF TRAINING 129

Figure 6.10: New testing CT image extracted from the CT scan of a third patient.

Figure 6.11: Result obtained with MRF training.

both modalities. Note that here we do not require that the images in the data base are co- registered, we merely require that all images are at least rigidly registered to better focus the learning process on deformed features instead of large translations and rotations.

For each modality, using the data-set we can learn the probability of a pixel in the image to belong to a given class using GentleBoost (see section6.1). More over, for the source modality we can learn the MRF parameters that yield the best segmentation results.

Figure 6.12: Boosting segmentation results (left) and MRF segmentation(right) results obtained on the testing set of figure 6.10, provided as a mean of comparison with figure

6.11

Let us denote by MRF T (J, x) the class that was given to pixel position x in source image J by the MRF segmentation scheme weighted by MRF training. Then we can use the probability of a feature vector of the target image to belong to this class as a similarity measure:

C (J(x), I(y)) = − log (PI(π(y)∈ MRF T (J, x))) (6.18) The idea behind this similarity measure for registration is for each iteration to compute the segmentation of the source image J using MRF segmentation and the coefficients learned by MRF training. Then using the probability computed using the GentleBoost coefficients learned on a set of images similar to the target image, we drive the registration by matching each sample from the source image to the sample in the target image it has the most probability to belong to.

MRF segmentation is a really fast process using FastPD [Komodakis 2008], and the estimation of the probabilities for the source image to feed the MRF segmentation is a matter of a matrix product and can be made in a really efficient fashion. Since the target image is not moving, the probability map on the target image is computed beforehand.

Plugging in this similarity criterion in the algorithm of [Glocker 2009] explained in section 2.3.2_{, we get registration results for a 2D image of size 512 × 512 in about 20}

minutes. The real limitation of this algorithm is the training stage of the MRF where sev- eral images have to be taken into consideration with quite a large Neighborhood system,

6.4. MULTI-MODAL IMAGE REGISTRATION WITH MRF TRAINING 131

if extended to 3D this Neighborhood system would become even larger and memory be- comes the limiting factor (more than 200GB of memory needed). This is why in all our experiments we use 2D images as a proof of concept of our method.

6.4.1

Experiments

Essentially the same data sets were used in the registration experiments and all the previous experiments. Only the size of the training database has grown since 3 patients were used for training and one patient was used for testing and the testing patient was alternatively changed between the testing and the training data set in a leave one out cross validation fashion. As it can be seen, only the number of iterations on the GentleBoost algorithm is a required parameter of the registration training algorithm, we used a number of iter- ations equal to 1000. The number of iterations of the MRF training algorithm could be set automatically by detecting when convergence is reached in the projected sub-gradient algorithm and as such is not discussed here.

For our experiments we used 120 image slices for training the source CT image that were randomly separated in 80 images for training the boosting algorithm and 40 for train- ing the MRF. 80 image slices from the T2-MRI images were extracted for the training of the probability distribution. Registration tests were done on 5 images in each patient re- sulting in 20 possible registration.

For the evaluation of the quality of registration we used manual segmentations of the liver in both source and target images and look at the evolution of the Dice coefficient before and after registration, the bigger the increase, the better the registration.

We expect that a criterion that was based on the learning of specific liver segmentations will yield better results on the Dice coefficient computed on the liver than a criterion that makes no distinction between organs.

As with previous sections, and since registration are only equal up to a smoothing pa- rameter, which is not comparable across similarity measure, we chose to use the invariant measure of the Harmonic Energy, on 20 different settings of the smoothing parameter. This makes for a total of 400 registration experiments. Comparison was made against Mu- tual Information criterion which was the only one to give decent results on this data set, all other commonly criteria, including Normalized Mutual information failed at registration and gave negative dice coefficient increase. We deem this data set as extremely in this regard.

Experimentation results are given in figure6.13.

We can see that our method does slightly better on the whole than mutual information however, the dice coefficient increase is not very significant, and since all other similarity measure used failed, we have reasons to believe that this is in part due to the extreme

Figure 6.13: Evolution of the Dice coefficient increase as a function the harmonic energy, 400 registration experiments were necessary for this graph. The solid line represents the average case while each end of the whiskers represent the minimum and the maximum value.

challenge posed by this data-set.