# A New Method for 2D-Adapted Wavelet Construction:
## 3 Results
### Detection of 2D Mass-like Patterns in Digital Mammography Images
#### 3.2.2 Results of 2D Detection
(**c**) Detection of the pattern pat21598072 inserted in the image 22670832, IoU = 0.116, \(\mathbb{S}=0.73\). (**d**) Detection of the pattern pat21598072 inserted in the image 22579916, IoU = 0.012, \(\mathbb{S}=0.74\). When comparing the detection of these 2D patterns using classical wavelets instead of _shapelets_, high precision was not obtained. Figure 14 shows that very high sensitivity (0.99) and very low specificity (0.006) were reached. On the other hand, a high positive predictive value (0.83) and a low negative predictive value (0.18) were obtained. Table 1 shows a summary of the measures obtained from the confusion matrix when detecting 2D shapes using shapelets and classical wavelets. The proposed strategy to detect specific 2D patterns showed effectiveness in artificial patterns and, in some cases, in patterns of mass-like abnormalities in digital mammography. When performing the simulation on this type of images, a high sensitivity and positive predictive value in detection was achieved, but not a high specificity or negative predictive value, contrary to what occurred in the 1D strategy. This means that the proposed algorithm presents a high number of false negatives, which can be explained by the high self-similarity of the regions in the breast tissue, the slow intensity variations of the pixels in these images, and the presence of fuzzy edges, aspects pointed out by authors such as [1], as well as the modification of the resolution made in order to apply the proposed 2D strategy. Sensitivity and specificity are inversely related; as sensitivity increases, specificity tends to decrease, and vice versa. When a test's sensitivity is high, only few cancers are likely to be missed. Specificity is the proportion of healthy women who are correctly identified as not having breast cancer. A test with low specificity is more likely to produce a high number of false positives and may incorrectly identify disease or illness in individuals when it is not present. Understanding how sensitivity and specificity impact test results and test interpretation \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline  & **Sensibility** & **Specificity** & **Precision** & **Recall** & **PPV** & **NPV** \\ \hline Shapelets & 0.96 & 0.04 & 0.83 & 0.96 & 0.83 & 0.162 \\ \hline Classical Wavelets & 0.99 & 0.006 & 0.83 & 0.99 & 0.83 & 0.18 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparative table of the results obtained when using shapelets and classical wavelets to detect the pattern in images. See Figures 12 and 14, respectively. Figure 14: Confusion matrix on the effectivity of detecting 2D patterns using classical wavelets. can help to inform clinical decision-making. If the radiologist is knowledgeable about the sensitivity and specificity values of the algorithm, he or she can request an opinion from more experienced people to analyze false positives, or he or she can guide other tests for this subset of the analyzed population. Another aspect to consider is the \"stiffness\" of the detection conditions of the proposed 2D extension, which was based on the DST-II detection constraints for 1D. The detection conditions are stiff in the sense that these conditions seek a perfect match between the shapelet filter and the pattern to be detected. This fact struggles to manifest in the case of mammographic images, given the high self-similarity of the regions in the breast tissue, the slow variations of pixel intensity in these images, and the presence of fuzzy edges. This opens the door for further research where fuzzy constraints or a probabilistic and Bayesian approach can be used to model such correspondence. Also, it is know that the detection with DST-II is sensitive to noise in 1D signals, so it is recommend to apply some denoising method before the detection. It is necessary to undertake further research on this issue, considering the different noise types present in mammographic images, such as Poisson noise.