## 3 Results and Discussion
### Reasons behind the Failures of the Contemporary Approaches
#### 3.2.2 Samples with Less Divergence
We suspect that this failure occurs because the deep CNN was only trained to learn the locations of the pores and fractures situated at the corners of the image samples (mainly, the locations of the green boxes) and can only detect the pore and fracture locations at the corners of the testing images; hence, it is a case of mode collapse. This failure could also be due to the unusual dissimilarity between the training dataset locations, shapes, sizes and orientations of the pores and fractures (Figure 10a) and the testing dataset (Figure 10b). Moreover, the divergence between the training and the testing sets was significant, whereas the divergence within the training and testing sets was quite low. These findings might point to the existence of visually similar images in the training (\(\mathcal{E}\)) set as well as in the testing (\(\mathcal{J}\)) set, i.e., the images of \(\mathcal{E}\) and \(\mathcal{J}\) are highly statistically and visually dissimilar. For example, the average similarity/dissimilarity between the images of the training set (\(\mathcal{E}\)) shown in Figure 10a is quite low, with \(\mathcal{D}_{\mathrm{KL}}(\mathcal{E}_{i}||\mathcal{E}_{r})\approx 0.799\), where \(\mathcal{E}_{i},\mathcal{E}_{r}\in\mathcal{E}\subseteq\mathcal{M};i\
eq r\) (see Section 2.2). Hence, the Custom Object CNN model learnt the locations of the pores and fractures of the training set and finally failed to identify the pores and fractures in the testing samples (see Figure 10b). Additionally, the average similarity/dissimilarity between the images in \(\mathcal{E}\) and \(\mathcal{J}\) is calculated to be quite high \(\mathcal{D}_{\mathrm{KL}}(\mathcal{E}_{i}||\mathcal{J}_{r})\approx 9.89\), where \(\mathcal{E}_{i}\in\mathcal{E}\) and \(\mathcal{J}_{r}\in\mathcal{J}\subseteq\mathcal{M}\). This result could be another reason behind the poor performance in the current case and might be extremely specific to the current problem in the present dataset. 2. To combat these problems, we prepared a training set incorporating more statistically dissimilar images (partially shown in Figure 11a) and found better detection accuracy than the previous one, although still unsatisfactory (see Figure 11b). This performance improvement is mainly due to the diversity of the training samples, which helps the Custom Object CNN model to learn about more diverse locations of the pores and fractures (the locations of the green boxes), situated in the corners, middle and several other portions in the micro-images. In this case, the average dissimilarity within \(\mathcal{J}\) was increased to \(\mathcal{D}_{\mathrm{KL}}(\mathcal{J}_{i}||\mathcal{J}_{r})\approx 4.799\) (higher than the previous case) while the average dissimilarity between the images of \(\mathcal{E}\) and \(\mathcal{J}\) was reduced to \(\mathcal{D}_{\mathrm{KL}}(\mathcal{E}_{i}||\mathcal{J}_{r})\approx 6.193\); \(\mathcal{E}_{i}\in\mathcal{E};\mathcal{J}_{r}\in\mathcal{J};i,r\in\mathbb{Z}^{+}\). Quite expectedly, the resulting identification accuracy was better than the previous attempt (see Figure 10). In the current study, however, it is impracticable to increase the dissimilarity within the training samplesdue to the limited size of the image sample and experimental constraint of sequential images. This result aligns with the well-accepted notion that deep learning needs a large dataset to achieve its famed accuracy. 3. Another reason for the poor identification accuracy of the Custom Object CNN model could be the irregular shape-related features of any \(\mathcal{H}_{i}\) from the training dataset. The irregular shapes of all \(\mathcal{H}_{i}\)'s make it difficult for model developers to identify the suitable supervised deep CNN features for their accurate classifications. \(\checkmark\) However, this problem might be handled well using capable unsupervised deep CNN counterparts, which can automatically and intelligently identify the features required to recognise the irregular objects with higher accuracy.