Health-e-Child - IST-2004-027749 - Deliverable D.11.4

Heart Diseases

iLogDemons, Experiments on Synthetic Data

iLogDemons were tested on synthetic datasets with known ground truth. Eight 3D volume-preserving whirl transformations φα were created with whirl angles α= 10° to 80° (Saddi et al., 2007). Within the whirl domain, the L2-norm varied from 0.52mm to 4.78mm while the Jacobian determinant stayed close to one (worse value |∇φα=80°|= 1±0.04 (mean ± standard deviation SD)). A 3D isotropic Steady-State Free Precession (SSFP) MRI of the heart, cropped to focus on the heart, was warped with the φα's and altered with slight Gaussian noise (Figure 1).

Test Image Whirl (α=50°) Warped Image
Figure 1 Example of synthetic 3D images and whirl deformation fields represented by a warped grid

The eight warped images T were registered to the test image R using LogDemons and iLogDemons (σx=1mm, σ2=1mm and σf2=1mm). Relative mean square errors in grey level intensities (RMSE=||R-Toφ||L2/||R-T||L2), Jacobian determinant and distance to the true field φα (DTF = ||φ - φα||L2) are reported in Figure 2. Deformation fields estimated by iLogDemons were almost incompressible. Jacobian determinants were always equal to 1±0.02 independently of the strength of the deformation to recover. Image matching accuracy was not affected by the incompressibility constraint (0.6% decrease). But most importantly, iLogDemons significantly improved the accuracy of the deformations. Mean and SD of DTF were systematically lower (average improvements of 29% and 36% respectively). The larger the deformation, the more significant the improvement. This points out the importance of the choice of the deformation model. Regions with homogeneous grey levels provided little information to accurately estimate the underlying deformation, as illustrated in Figure 3. The incompressibility constraint coped with this limitation by ensuring that the estimated deformation was of the same type as the true field. Similar conclusions were drawn on experiments with other parameters (σx=2, σ2 = 2, σf2 = {0.5,2}).



Figure 2 Results on images warped by 3D synthetic volume-preserving whirls with increasing whirl angle.

Figure 3 Streamlines of true and estimated whirl deformations (whirl angle α = 60°). iLogDemons provided incompressible deformations and outperformed LogDemons in terms of deformation field accuracy (yellow arrow)

References

  1. Saddi, K.A., Chef d'hotel, C., Cheriet, F.: Large deformation registration of contrast-enhanced images with volume-preserving constraint. In: SPIE Medical Imaging. vol. 6512. (2007)
  2. T. Mansi, X. Pennec, M. Sermesant, H. Delingette, and N. Ayache. LogDemons Revisited: Consistent Regularisation and Incompressibility Constraint for Soft Tissue Tracking in Medical Images. In Medical Image Computing and Computer Assisted Intervention (MICCAI), Lecture Notes in Computer Science. Springer, 2010. In press.