Toma de postura

The third set of experiments consists of utilising the three methods implemented in the symmetric warping manner. Similar as the previous assessments, first the exper- iments were conducted with the synthetically generated data, then the different real data sets were used to quantify the performance of the aforementioned symmetric

algorithms in the particular biomedical applications. In general, the deformation fields estimated by utilising the image registration with the symmetric warping are more accurate in terms of the distance to the ground truth deformation fields. Also the distance to the true Jacobian is reduced (except the steepest-like method).

Synthetic data

The symmetrisation incorporated into the registration algorithms was found to pro- vide many interesting observations when applied to the synthetic data.

Firstly, the image registration algorithms perform significantly better in terms of the SSDI when compared to their original versions. The algorithms have also

faster convergence for this criterion. The harmonic energy (HE) of the image regis- tration with the symmetric warping is always worse than in the case of the original registration techniques. It is mostly due to double forces that register images in two independent ways by providing more information into registration.

Brain MRI data

The results of the carried out experiments are shown in Figure 4.11e for the con- sistent Demon approach, in Figure 4.10e for the consistent Newton’s iteration ap- proach, and in Figure 4.9e for the consistent steepest-like approach.

The results obtained by the image registration with symmetric warping on the MRI brain images are characterised by the significant minimisation of the SSDI

between registered images. The SSDI obtained by the symmetric Demon approach

is 26.5% better than in that case of the original Demon, for the symmetric Newton’s iteration and the symmetric steepest-like approach the SSDI is reduced by 20.6%

and 12.7% when compared to the original methods.

Contrary to the other assessed approaches, the image registration with symmetric warping increases the value of the harmonic energy. Thus, the HE for the symmetric Demon is twice worse than that of the original Demon approach. The HE for the symmetric version of the Newton’s and the steepest-like method is increased by about 20% when compared to their original versions.

The image registration with symmetric warping increases on the average the values of the ROs for the brain structures up to 4.0 for the symmetric Demon, to 2.2 for the Newton’s iteration method, and only about 1.1 for the symmetric steepest- like method when compared to their original versions. The best improvements are observed for the structure such as dura matter (17.2% for the Demon, 15.7% for the Newton’s method, 11.3% for the steepest-like method), CSF (14.6% for the Demon, 8.8% for the Newton’s method, 6.2% for the steepest-like method), white mater (12.8% for the Demon, 6.6% for the Newton’s method, 3.1% for the steepest-like

method) and grey matter (10.7% for the Demon, 5.8% for the Newton’s method, 3.6% for the steepest-like method). These structures (except dura mater) occupy the largest area of the brain.

The image registration with symmetric warping shows an improved performance in terms of automatic labelling of the brain structures, thereby it can be considered for the practical utilisation. Although the HE is significantly worse than that pro- duced by any other approaches, the results suggest that it does not decrease overall robustness of the symmetric framework.

Pelvic-area MRI data

The results of the experiments performed on the MRI pelvic-area data using the image registration with symmetric warping are shown in the following figures: Figure 4.14e shows the results for the Demon approach, Figure 4.13e for the Newton’s iteration method, and Figure 4.12e for the steepest-like method.

All the image registration algorithms with the symmetric warping reduce the

SSDI. The maximum reduction is gained by symmetric Demon approach and it is

21.3% better than that of the original version. For the symmetric Newton’s iteration and the symmetric steepest-like method, the SSDI is better by about 9.1% and

4.5%, respectively.

The harmonic energy is increased for all methods. For the symmetric Demon approach, the HE is twice worse than that of the original Demon. For the Newton’s and the steepest-like method, the HE is worse only by 9.5% and 49.0%, respectively. Although, there is a significant reduction of the SSDIbetween registered images,

the values of the RO for the prostate stays at the same level, while the RO for the bladder is better by only about 3.7%, 2.0% and 0.5% for the Demon, the Newton’s iteration and the steepest-like method when compared to their original versions.

The presented results suggest that the benefits of using the symmetric warping approach for the MRI pelvic-area data is negligible.

Lung CT data

The results of the assessment conducted on the CT of lungs for the images registra- tion with the warping based on the Demon approach is shown in Figure 4.17e, on the Newton’s iteration approach in Figure 4.16e and on the steepest-like approach in Figure 4.15e.

Similar to the previous cases, the image registration algorithms with the sym- metric warping, produces the significantly better SSDI between registered images

10.7%, and 10.8% for the symmetric version of the Demon, the Newton’s iteration and the steepest-like method.

Also the harmonic energy has similar patterns. The HE is twice worse for the symmetric Demon, whereas the symmetric Newton’s iteration and the steepest-like method produce the deformation fields with the HE being 38.4% and 21.1% worse than that of the original methods.

The distances between the manually selected landmarks for the Demon method and the steepest-like method with symmetric warping stays at the same level as that of the original methods, while for the Newton’s iteration method the T RE is slightly worse (the T RE is worse by about 0.1mm). The differences are not significant.

Altogether, the symmetrisation of the image registration does not have the prac- tical advantages on the respiratory motion estimation. Although, the SSDI between

registered images is reduced, it does not lead to further improvement of the land- marks positions estimation.

Observations on the symmetrisation of the registration

The significant improvement of the image registration with symmetric warping in terms of the SSDI is not surprising. Indeed, this registration takes the advantage

of the double forces to warp the moving image to the mean image and simultane- ously the reference image to the same mean image. In addition, the increased HE is somehow linked to this double forces by providing more deformation in every it- eration. The final composition of two half-way velocity field (half-way deformation fields) has a minor impact on the final velocity field (deformation field) [17].

The presented results of the image registration with symmetric warping show symmetrisation improves the performance of the registration only in some cases. The experimental evidence was found for the MRI brain data set, where some struc- tures were better labelled than those by utilising either the original or diffeomorphic algorithms. Further investigations on other data sets do not show similar improve- ment of the image registration in terms of the RO of prostate or the T RE between selected landmarks in the lungs. The results achieved for the pelvic-area do not con- firm the statement from [53] where the symmetric image registration was claimed as having better performance than the log-domain registration. The presented results for the brain labelling are consistent with the results reported in [10], where regis- tration with symmetric warping was shown as producing slightly better ROs of the different areas of brain.