# Cascaded Regression-Based Segmentation of Cardiac CT under Probabilistic Correspondences
## 4 Discussion  
Multi-objects modeling in cascaded regression is under development. In the correspondence construction of the GMM-based method, the dependence of multi-objects must be considered, although training procedure is performed in combined shape. If the vertex number of 3D model \(n_{M}\) is increased to cover many objects, computation resources will increase rapidly. There is a trade-off between memory problems and shape loss in separate and combined constructions of correspondences.  
Segmentation accuracy depends on the quality of tetrahedron set \(T_{a}\) since the final segmentation region is calculated by checking inside of the tetrahedron set. In the proposed method, several heuristics rules are adapted to tetrahedron statistics calculations. A more systemic rule must be developed to increase the quality of segmentation shape from the found point set.  
Separate operation of correspondence construction is made from the input sort array of training points. Since statistics of sorts is calculated accurately by using \(\sum\limits_{i\in U_{k}^{H}}E_{kij}\), we apply this sort of information to statistical analysis of tetrahedron \(T_{a}\). Tetrahedron between LA and LV can have noises since the topology between LA and LV is complex. More fine control is needed, especially in the region between LA and LV.  
The separate shape model of duplicate eigenvectors gave more freedom in shape change and produced a slightly better evaluation result than the proposed method. But since the conflict between LA and LV could occur, a check of conflict must be performed to use this model. Since this conflict check between objects needs an additional computation, the combined shape model can be used instead.  
Figure 6: The median case in the dimension of DC. The red resultant mask is true positive, the blue mask is false negative, and the green resultant mask is false positive. SSD, HD, and DC are presented as the (LV SSD, LA SSD, LH SSD, LV HD, LA HD, DC) set, which is (1.79 mm, 2.16 mm, 1.98 mm, 11.29 mm, 19.91 mm, 81.88%). **(a)** Axial view. **(b)** Sagittal view. **(c)** Coronal view.  
Figure 7: The worst case in the dimension of DC. The red resultant mask is true positive, the blue mask is false negative, and the green resultant mask is false positive. SSD, HD, and DC are presented as the (LV SSD, LA SSD, LH SSD, LV HD, LA HD, DC) set, which is (2.79 mm, 2.09 mm, 2.44 mm, 16.80 mm, 17.43 mm, 67.58%). **(a)** Axial view. **(b)** Sagittal view. **(c)** Coronal view.  
Since unit-vector normalization makes the contents of appearance too small, z-score normalization is applied to the appearance input of ridge regression. Furthermore, ridge regression is not scale-invariant. If the scales used to express the individual appearance variables are changed, then the ridge coefficients do not alter in inverse proportion to the changes in the variable scales [39]. Therefore, z-score normalization is assumed to produce better scaling in terms of data size.  
In the future, the segmentation model for dealing with every phases of the heart must be developed, since the statistics of the systole phase make DC be comparatively low value. If an extensive database is applied, memory problems and many technical problems will occur since cascaded regression needs texture modeling compared with an active shape model. To improve the segmentation result, then many cases must be applied to construct the heart anatomical model. Finally, readjustment of segmentation surfaces by using boundary normal direction can be developed to increase the segmentation performance by including this post-processing in active appearance framework.