Discussion

The main advantage of the proposed method is the ability to negate the effect of PMTC tissues effectively through the proposed myocardial contour processing steps. The effectiveness is backed by the CVF-based image segmentation, which is able to detect most of the LV blood volume while being resistant to artifacts affecting the MR images such as field inhomogeneity and partial volume effect. First, we would like to discuss these two artifacts and how CVF is able to overcome them.

Method R² for EF

Lorenzo-Valdés 2004 0.92

Cocosco 2008 0.90

Cordero-Grande 2011 0.92 Constantinides 2012 0.83

Lu 2013 0.92

Hu 2013 0.938

Ours 0.942

Table 4.6 Reported coefficient of determination R² for EF.

The former, the field inhomogeneity, imposes a bias field on the afflicted MR image, resulting in non-uniform signal intensity which is observable on LV blood pool and other tissue types. As a consequence, we should not solely rely on simple histogram-based techniques (including Otsu’s thresholding, GMM-based thresholding) to classify the LV blood pool as they completely ignore the spatial relationship of the neighboring pixels (or voxels in the context of CMR volume). In CVF-based segmentation, the image is first transformed into cost volume and the label with least cost is selected after cost within every cost slice is aggregated based on spatial proximity and intensity similarity.

Therefore, CVF will return clustered group of labels. Furthermore, CVF acts like a classifier with adaptive threshold. These characteristics makes CVF ideal for combating against field inhomogeneity. See Fig. 4.4 for an example. Point A (PA) and Point B (PB) belongs to the region of LV blood pool. Due to field inhomogeneity, they apparently do not have the same signal intensity. What is interesting here is the darkest area in the blood pool is almost the same as the brightest area in the myocardium. Depending on the threshold value chosen, too high, we risk mistakenly label the myocardium as LV blood

Fig. 4.4 Robustness against field inhomogeneity

pool. Too low, then not all LV blood pool can be correctly labeled. We may need adaptive threshold for this case. Here, we choose CVF because it is more versatile: it is a general solution for refining multi-label problems. And we can alter the cost for each label in different situations. For example, in hypertrophic cases, we alter the cost so that it is easier to be classified as LV blood pool, and we have found this versatility valuable in the context of CMR image segmentation.

The latter, the partial volume effect, causes the signal of many tissue types to mix up and averaged together if the tissue are in close proximity to each other. Partial volume effect is very common in areas where the papillary muscle and trabeculae carneae are almost collapsed together with the endocardium border. It causes an ambiguity that previous methods are often failed to label correctly. We argue that CVF is effective against partial volume effect. See Fig. 4.5 for examples of two similar cases. In Fig. 4.5(a) shows the original images of the LV after polar transformation. Fig. 4.5(b) and (c) compares the segmentation result from Otsu’s thresholding and CVF-based method, respectively. The CVF-based method shows vast improvement over the popular Otsu’s method. All the

Fig. 4.5 Robustness against partial volume effect.

ambiguities caused by partial volume effect are recovered by the proposed CVF-based segmentation. All these improvements add up. Combined with the proposed endocardial processing framework, the CVF indeed returns results that show major improvements over previous methods.

For additional visual assessment of the proposed method, Fig. 4.6 demonstrates one of our best results from patients stricken by heart failure. Since the endocardium border is clearly defined in both ES and ED phases, the proposed method delineates the endocardium accurately. Fig. 4.7 and Fig. 4.8 show relatively poor performance in the case of hypertrophy. However, delineating endocardium border in hypertrophic hearts is recognized as a very challenging task, as shown in previous findings [11], [12], [17], [34], [37]. Our segmentation result is nevertheless an improvement over previous works.

With little modification to cost volume initialization, we also attempted to apply the method to LV epicardium delineation. However, preliminary result is not favorable. It is at best among the ranks of average performers. And since it is only experimental, we do not publish the exact results here. One reason for the proposed method to fall short on epicardium delineation is the intrinsic limitation of CVF: that CVF relies on intensity similarity to gather costs from corresponding neighbors. Since the signal intensity difference between the myocardium and its neighboring tissues is not as clearly defined as that between the myocardium and blood pool, it is very easy to mislabel the nearby tissues. Given this finding, it might not be suitable to use intensity similarity for epicardium delineation. Gradient-based methods, such as active appearance model or active contour model, could be more promising. It will need more investigation to see whether gradient information can be used in CVF to prevent such mislabel problems.

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Fig. 4.6 Selected results from patient SC-HF-I-06.

ES phase

ED phase

— Solid line: auto - - Dashed line: manual

ES phase

ED phase

Fig. 4.7 Selected results from patient SC-HYP-37. The proposed algorithm still manage to find the endocardium border even when PMTC tissues collapse together.

— Solid line: auto - - Dashed line: manual

ES phase

ED phase

Fig. 4.8 Selected results from patient SC-HYP-38. The PMTC tissues collapse together and obscure the endocardium border at ES; segmentation error can be observed.

— Solid line: auto - - Dashed line: manual