# OmniSR-M: A Rock Sheet with a Multi-Branch Structure Image Super-Resolution Lightweight Method
## 3 Experimental Results and Their Analysis
### Particle Analysis  
In order to better evaluate the differences between different models, this paper introduces the semantic segmentation macro model SAM to randomly select four samples to evaluate the super-resolution results of different models [22]. It is mainly used to evaluate the reconstruction of different models at the edge of the grain. As shown in Figure 7, firstly, the rock thin section grain size statistics were attained from input HR images as well as super-resolution SR maps of each model using the image method of semantic segmentation. The Udden-Wentworth particle size classification criterion (\(\varphi\)) was then used to plot the frequency diagram of the particle size distribution. Figure 6: Different model reconstruction surface porosity calculation errors. (**a**) shows the original image, (**b**) shows a 200 \(\times\) 200 sub-image cropped from the red boxed region, and (**c**) shows the facies porosity rate for HR, LR, and the super-resolution structure of each advanced model. Figure 7: (**a**) shows the image of input SAM, and (**b**) shows the result of semantic segmentation of SAM. The detailed calculation results are shown in Table 4, and from the comparison results of the statistical indexes of particle size distribution in this table, it can be seen that the OmniSR-M model proposed in this paper shows significant advantages and stability in recovering the details of particle size and the overall distribution characteristics of different samples. Specifically, the recovery of the average particle size by each model is relatively close to each other; however, in the recovery of the maximum and minimum particle size ranges, OmniSR-M shows a small deviation from the true value of HR, while the other methods such as RDN show a large estimation bias, which is beyond the true range of values of HR. This indicates that OmniSR-M more accurately and completely recovers the full granularity interval contained in the image, preventing range reduction or expansion. Additionally, in terms of the particle size standard deviation, which is an indicator of the diversity of the particle size distribution, the OmniSR-M results are closest to the value of HR, implying that it recovers a degree of particle size variation that more closely approximates that of the original image, whereas the other methods are more or less guilty of omitting some of the particle size components. It should be noted that different sample images have their own particle size distribution characteristics, such as more or denser fine particle sizes, etc., but the OmniSR-M model always performs optimally and stably on all samples, which proves that it possesses strong adaptability and is able to flexibly deal with a wide range of particle size distribution situations. This can also be verified from the frequency map of particle size distribution in Figure 8, where the distribution of the OmniSR-M reconstruction results and the frequency map of HR's particle size distribution are basically the same, with the highest similarity. Finally, the metrics of OmniSR and its multi-branch structure version, OmniSR-M, almost completely overlap, which indicates that the introduction of the branch structure does not adversely affect the recovery of critical granularity details, and of its feature of light weight is thus validated. Figure 8: Frequency plot of particle size distribution for four samples. In addition, in this paper, the validity of the methods was verified on 130 test sets; specifically, the L version of SAM was used to segment the particles of all the method's super-resolution results. Subsequently, the number of particles and the particle size were computed statistically, and the detailed results of the computation are shown in Appendix A.