## 3 Results and Discussion
### Reasons behind the Failures of the Contemporary Approaches
#### 3.2.2 Samples with Less Divergence  
Low divergence samples accompanied by a small number of grayscale image samples constitute another issue we encounter in achieving accuracy using conventional methods. The dataset used in the current work has considerably less divergence, i.e., the visual quality (the location and shape of \(\mathcal{H}_{i}\)) of most images in the sample is very similar. The reason behind the visual similarity is given in Section 2.3, and a method for measuring the similarity between the image samples is provided in Section 2.2. Even in the presence of a formidably large number of grayscale image samples, we found deep-CNN models (including ours) were failing to identify the regions containing the pores and fractures with an accuracy as high as in Figure 10[18; 25]. This failure could be due to the poorly crafted training samples (having fewer unique images) leading to a mode-collapse problem, i.e., being stuck in local minima because of poor learning. To combat this problem, we conducted experiments using the Custom Object CNN model in two ways: (i) Learning manually identified regions containing the maximum numbers of micro-pores and fractures as training samples. We maintained higher visual dissimilarity while preparing the training samples. A comparative study considering the training sample divergence is shown in Figure 11. (ii) Learning the geometric shapes of individual micro-pores  
Figure 10: Evidence of location learning using Custom Object CNN: (**a**) Sample CT scan images with manually identified regions containing the possible pores and fractures of the rock used as training samples; (**b**) In return, the Custom Object CNN identifies the same regions (as in (**a**)), eventhough very few pores are located. This case is a classic example of mode collapse. One possible solution to the mode-collapse problem is minibatch learning; however, this approach might fail in the absence of a large and diverse sample image dataset. To combat this problem, we increased the diversity while preparing the training samples for Custom Object CNNs, but this policy fails because of the lack of variety within the current dataset. In figures, (**a,b**) the image boundaries are marked in red. and fractures to identify them correctly in the test samples. The manually identified regions of several images containing the most pores and fractures are chosen as training samples in case (i), whereas the normal shapes of the pores and fractures are taken as training samples for the latter case (ii). Each experiment strategy is described below. 1. Manually identify the regions containing the most possible pores and fractures: For this task, initially, we manually encircled (in green boxes) the regions containing the most possible pores and fractures to create a training set containing 300 images (see Figure 10a). We then used this training set to train the Custom Object CNN model in Section 3.1.2 and used the remaining images as a test dataset. High visual similarity can be observed among different grayscale images of the current sample, triggering a mode-collapse problem that forces the Custom Object CNN model to stick to a suboptimal solution due to the high degree of similarity among the extracted features. Figure 10b shows the evidence of mode collapse. 1. The training image samples in Figure 10a have visible pores at specific locations, mainly at the corners (enclosed in green boxes in Figure 10a). Initially, these samples were used to train the Custom Object CNN model, and a part of the resulting predictions is shown in Figure 10b, where we found that the model can identify only the learnt locations in the resulting images. For example, using testing samples with pores located in the middle, we found that the deep CNN failed to identify these pores (see Figure 10b).