Experiment 2 – Robust SSM and MRF Local Modeling

5.5.3.1 Robust SSM Performance

Skoˇcaj et al. [SLB07] demonstrated that a robust PCA outperformed conventional PCA when using corrupted data, as the latter was unable to handle erroneous data. However, many of the tests they conducted only underpinned the good Specificity of the robust SSM. The performance of an SSM in the context of segmentation cannot be explained only by the statistical model, as there are many factors, such as appearance priors and evolution strategies, which come into play.

We therefore devised this experiment to investigate whether the mixing of non-corruptedS^○and corruptedS^●shapes into a robust SSM (Section4.3.2) would result in better segmentation results compared to those obtained with an SSM only built from S^○. Ten VB datasets were randomly chosen as the testing data, and the remaining 33 datasets were used to build 3 different SSMs:

– A “full-SSM” built using all 33 reference shapes.

– A “sub-SSM” built from 12 shapes randomly chosen among the 33 reference shapes.

– A “mixed-SSM” created from the 12 reference shapes of the sub-SSM and 21 corrupted shapes.

The corrupted shapes were obtained from the segmentation of the cVB datasets in the previous experiment (Section5.5.2.2), in which all points out of FOV were not reliable. These shapes were aligned using the weighted alignment described in Sec. 4.3.2.2.

For the mixed-SSM, we chose the mdEM robust PCA approach as it produced the best results in our evaluation experiments (Sec. 4.5.4). The initialization process described in Sec. 4.3.2.2 was used as a start to the robust PCA. The configuration IP+SSS was chosen since it exhibited excellent performance in the previous experiment (Sec. 5.5.2.1) with VB datasets. Furthermore, exactly the same landmark-based initialization was used, i.e. with identical landmarks place-ment. This provided a fair comparison with the previous experiment results.

Table5.4compares the performances of the segmentation on the VB dataset using full-, mixed-and sub-SSM performed after the lmixed-andmark-based initialization. The table shows that the seg-mentation results with 33 complete shapes (ASSD 1.29±0.32 mm) were slightly worse than those of previous experiment (Sec. 5.5.2.1) in which 43 full shapes were considered (ASSD 1.21±0.35 mm, see Table 5.1). Although no statistical difference was established, this observation is con-sistent with the idea that larger training sets usually improve the SSM’s segmentation efficiency.

This idea is also supported by the results of the sub-SSM where the use of a smaller training set (12 shapes) produced significantly worse results compared to the full-SSM (p-value<0.04 for each bone type and side). As expected, the Generality of the sub-SSM was too weak to efficiently segment the shapes. The most interesting result is the comparison of mixed- and full-SSMs re-sults which are not differentiable from a statistical viewpoint. This strongly suggests that the proposed combination of complete and corrupted shapes in the construction of SSM can be very robust and efficient.

Table 5.4: Segmentation results on VB dataset with full-, mixed- and sub-SSM after landmark-based initial-ization on 10 datasets (average±standard deviation). F: femurs, HB: hip bones. ASSD, ASRSD, MSD are in mm, VOE in %.

5.5.3.2 MRF Local Modeling Evaluation

We studied the performance of forces based on the local shape variation modeling by MRF as presented in Sec. 5.3.3.4. Two situations were investigated. In the first case, the MRF prior was coupled with a PDM trained with all available training samples (except the current one being

tested) whose efficiency was demonstrated in IP+SSS experiments. For comparison purposes, the IP+SSS configuration without MRF was run on the same data with identical conditions (ini-tialization, training data, etc.). In the second case, we used the previous sub-SSM only composed of 12 training samples, whose segmentation results were mitigated due to the relative small size of the training set. All experiments were conducted with the same 10 subjects of the previous experiment evaluating the robust SSM performance.

As presented in Sec. 5.3.3.4, the exploitation of MRF priors is equivalent to a MAP problem which can be solved with a dynamic evolution using image f^im and regularization f^mrf forces.

When MRF priors are used it is no longer necessary to simultaneously use shape (f^smemor f^pdm) or smoothing forces, since the force f^mrf already achieves smoothing and shape regularization.

In our experiments, we used MRF-based forces in an interleaved manner with the SSM multi-resolution approach: after all the scheduled iterations of a multi-resolution level, the current model state was set as the reference shape X and only MRF forces f^mrf and image forces (IP-based and gradient forces as in the IP+SSS configuration) were used to drive the model evolution (Sec.

5.3.3.4). The iteration schedule for the MRF evolution was set to 50/20/5. The last resolution level did not rely on MRF priors to better capture fine details not expressed by the priors. Values of MRF parameters (Sec. 5.3.3.4) were 1/η² = 1 and 1/σ² = 0.25 as suggested in the work of Kervrann and Heitz [KH98]. The weighting parameter β=α^mrf was progressively modified to give an increasing importance to local variations based on the shape resolution, by adopting the schedule 1.5/2/3. Results are reported in Table5.5(a)for both scenarios.

Bone ASSD ASRSD MSD VOE Time

IP + SSS (SSM built with 42 shapes)

F 1.30±0.26 2.03±0.33 9.02±1.78 17.16±2.11 –

Table 5.5:(a)Segmentation results on 10 VB datasets with MRF-based priors (average±standard deviation).

F: femurs, HB: hip bones. ASSD, ASRSD, MSD are in mm, VOE in %. Mean times are in sec for left and right pairs of bones (i.e. 4 bones), and include model loading time.(b)An example of before (top) and after (bottom) MRF-based evolution, where white arrows indicate a better delineation of fine details.

In the first scenario involving a large training shape set, the use of MRF-based priors does not seem not to be beneficial as a sensible increase of the errors was observed (e.g., ASSD: 1.28±0.34 to 1.29±0.26) although this difference could not be statistically proven. However, in the case

where the training dataset was not very big (12 shapes), the MRF-based evolution significantly improved the results. In fact, the ASSD for both bone types decreased from 1.49±0.35 (Sub-SSM results in Table 5.4) to 1.35±0.29, where statistical difference was only detected for femurs (p-value < 3.8E-3). It was noticed that MRF often refined the delineation of anatomical features, such as the femoral head or the acetabulum (Fig.5.5(b)), thanks to its local modeling of variations.

Timing results showed a higher computational cost of the MRF-based approaches which was mostly explained by a higher number of iterations and the additional computation of energy terms related to the MRF local modeling.