# Pattern Recognition in Dried Milk Droplets Using Lacunarity and Deep Learning
## 3 Results
### Pattern in Dried Droplets of Milk with NaCl and Added Water  
An interesting question pertains to the method's effectiveness in detecting additional water content in milk. Figure 7 illustrates the milk deposits generated with varying levels of additional water content and different NaCl concentrations. In Figure 7a, distinct deposits corresponding to whole milk and lactose-free milk without NaCl are evident, featuring varying concentrations of additional water. Both milk types display a coffee ring pattern. The deposits associated with whole milk demonstrate a consistent, uniform deposition. However, for whole milk deposits from 40% of additional water, some minor aggregates emerge. Conversely, deposits linked to lactose-free milk exhibit a uniform deposition regardless of the added water concentration. Notably, the coffee ring's clarity is enhanced as the volume of additional water increases. In Figure 7b, the depicted deposits correspond to whole milk and lactose-free milk with \(\phi_{N}=2\) wt%, featuring varying concentrations of additional water. Regardless of milk type or added water content, all deposits exhibit a distinct coffee ring. Deposits of both whole milk and lactose-free milk, lacking extra water content, display amorphous crystalline structures in the central region. Additionally, deposits of lactose-free milk showcase homogeneity between the coffee ring and crystalline structures. The addition of 20% water  
Figure 6: Accuracy of CNN-based differentiation among milk types. Classification accuracy of a convolutional neural network (CNN) model for differentiating whole milk from lactose-free milk at different NaCl concentrations, \(\phi_{N}=0\) wt%, 2 wt%, and 4 wt%. The CNN model exhibits a similar trend to the lacunarity-based approach (Figure 4), achieving the highest accuracy at \(\phi_{N}=0\) wt% and slightly improved stability across different concentrations. content in deposits of whole milk results in randomly distributed protrusions. Conversely, lactose-free milk deposits reveal branched dendritic crystal structures. At a 40% increase in water concentration, deposits of whole milk reveal scattered small aggregates, whereas lactose-free milk deposits display high-density aggregates centrally, decreasing towards the coffee ring. At a 60% increase in water, for both milk types, a palm leaf-like crystalline pattern emerges at the center. This structure features four well-defined axes stemming from a central point, capable of extending across the deposit, with perpendicular ramifications originating from these axes. This crystalline pattern is enveloped by a homogeneous region. Notably, lactose-free milk deposits showcase a well-defined coffee ring and an increased count of internal crystalline structures. At 80% additional water content, both milk deposits display an entire covering of a palm leaf-like crystalline pattern. In Figure 7c, we observe the depositions of whole milk and lactose-free milk with \(\phi_{N}=4\) wt%, at varying concentrations of added water. Notably, regardless of the milk type, the most substantial structural distinction occurs between deposits without added water and those with additional water content. Deposits containing 0% added water display an indistinct coffee ring and diverse cross-shaped aggregates dispersed throughout. It is worth highlighting  
Figure 7: Milk deposits with different NaCl and water concentrations. Dry drops of whole and lactose-free milk, each with distinct water concentrations (0, 20, 40, 60, and 80%) at \(\phi_{N}=0\) wt% (**a**), 2 wt% (**b**), and \(\phi_{N}=4\) wt% (**c**). that deposits associated with whole milk exhibit a higher density of crystalline structures. Conversely, deposits containing 20% and 40% added water exhibit a leaf-like crystalline arrangement. Furthermore, deposits with 60% and 80% additional water content, irrespective of milk type, reveal a well-defined coffee ring and a symmetrical leaf-like crystalline pattern. Notably, the main axes of these structures can span the width of the deposit.