# An Application of Manifold Learning in Global Shape Descriptors
## 4 Experiments
### Robustness  
In this section, we address the robustness of the LESI shape descriptor to shape variations, including noise, scale, and down-sampling by performing another set of experiments. First, we generated the disturbed version of every model in the TOSCA dataset. Then, we tested the capability of every method mentioned above in discriminating between different classes. For this purpose, besides plotting the 2D PCA projection of shape descriptors, we also computed and plotted the pairwise Euclidean distance matrix, in every case. The distance matrix represents the dissimilarity between each pair of models in the set. It is often used to compute other evaluating metrics such as nearest-neighbor, and first and second tier, to name a few. The dissimilarity of descriptors increases from blue to red, and the more separate classes differ in color, the better they are discriminating from each other. **Resistance to noise. ** Multiple noisy versions of the TOSCA dataset were generated following the idea articulated in [57]. To this end, the surface meshes of all models were disturbed by changing the position of each point along its normal vector that was chosen randomly from an interval \((-L,L)\) with the 0 mean, where \(L\) determines the noise level and is a fraction of the diagonal length of the model bounding box. In this experiment, three noise levels \(L=\) 0.5%, \(L=1\%\), and \(L=2\%\) were tested, where the latter one represents a greater level of noise. Two-dimensional PCA projections of all descriptors with the presence of different levels of noise are plotted in Figure 7. Combining these with the results shown in Figure 3, where no noise is present, demonstrates that the LESI algorithm is highly noise-resistant while the performance of the Shape-DNA and cShape-DNA decreases as the level of noise increases. Moreover, GPS fails in separating different classes of models with the presence of noise. Figure 6: Confusion matrix obtained from linear multi-class SVM for McGill dataset using LESI descriptors. Figure 8 reflects the effect of noise on the discriminative power of the descriptors. The LESI algorithm shows consistent results as the level of noise increases from 0% (top row) to 2% (bottom row). **Scale invariance. ** To validate the insensitivity of the LESI descriptor to scale variations and compare the robustness of the proposed method with other descriptors, each model of the TOSCA dataset was scaled by a factor of 0.5, 0.875, 1.25, 1.625, or 2 randomly. Figure 9 shows that the LESI algorithm surpasses other methods in discerning different classes. Comparing the result of this experiment with the results shown in Figure 3 demonstrates the consistency of the LESI and cShape-DNA algorithms with the presence of scale variation. That is expected, as they can remove the parameter of scale and obtain scale-free descriptors. The distance matrices in Figure 10 show that the original Shape-DNA algorithm is very susceptible to scale variations. Even though the cShape-DNA has significantly improved scale sensitivity of the original Shape-DNA, it does not provide as accurate results as the LESI algorithm does. **Resistance to the sampling rate. ** To investigate the effect of sampling rates on the discriminative power of the shape descriptors, [PERSON] et al. [8] proposed to reduce the number of vertices to 20% of its original size. Accordingly, the down-sampled version of the TOSCA dataset was generated, and shape descriptors associated with them were computed. The 2D PCA projections and distance matrices of descriptors are illustrated in Figures 11 and 12, respectively. Although the original Shape-DNA shows a more accurate result than cShape-DNA, the separation of cat, dog, and wolf models is challenging. Although the performance of the LESI method is slightly affected, it still outperforms cShape-DNA and GPS methods.