# 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  
Using the estimated _shapelet_ and the 61 classical wavelets, 175,584 runs were performed, resulting in detecting six embedded mass-like patterns in 118 images from INbreast. When using shapelets and classical wavelets for detection, the average IoU mean was reported as 0 with a median of 0, indicating many cases with little to no overlap between detected and actual patterns  
When _shapelets_ were used to detect the masses in images that actually had such anomalies inserted (472 images), 431 zeros of the IoU measure were obtained, with a mean of 0.01 (\(SD=0.08\)) and a maximum value of 0.92. If the images did not contain the mass-like pattern (2360), this measure reached 2181 zeros, a mean of 0.01 (\(SD=0.07\)), and a maximum value of 0.92. Figure 12 shows that when using the estimated _shapelets_ for each pattern, a very high sensitivity of 0.96 (i.e., most of the inserted mass-like patterns were detected correctly) and a low specificity of 0.04 (i.e., if the anomaly was not in the signal, it is not detected by the  
Figure 11: Successful pattern detection in image 53580858. From left to right and top to bottom: the original image, the pattern to be detected, the region given by the algorithm based on _shapelets_, and the measure \(\mathbb{S}\) of the diagonal detail coefficients. algorithm) were reached. In addition, a high positive predictive value of 0.83 (i.e., knowing that the algorithm detected the anomaly, what is the probability that it actually occurs in the signal) and a low negative predictive value of 0.16 (i.e., knowing that if the algorithm did not detect the anomaly, what is the probability that it really is not there) were obtained. Figure 13 shows, from top to bottom, the best and worst detection results according to the IoU measure. From left to right, the mammography image with the mass-like pattern inserted (in a red rectangle) by fusion of the S-LIP model; the image of the mass to be detected; and the detection results (red rectangles) according to the measurement \(\mathbb{S}\) on the diagonal detail coefficients of the DST-II 2 are shown. The detection with the highest value of the said measurement is colored yellow. The last column of the graph shows the values of the measure \(\mathbb{S}\) for the diagonal coefficients. Figure 13a,b show the most accurate detection results. It can be noted that there are several predictions of the pattern detection with value of \(\mathbb{S}>0.7\), and very accurate pattern detection was reached (IoU = 0.92 and 0.64, respectively), with a high value of the measure (\(\mathbb{S}=0.73\) and 0.75, respectively). Many of the predictions are located within the breast and near the position where the mass-like abnormality pattern was inserted. However, some are at the edge of the breast, near the pectoral, or entirely outside the breast. On the other hand, Figure 13c,d shows the least-accurate results in pattern detection. A dispersion of the predictions can be noticed, and even the most accurate does not detect the anomaly, as expected, since it was not inserted into the image. Note that in these cases, despite the fact that high values of the \(\mathbb{S}\) measure are obtained, similar to those obtained in the most precise detection, the IoU metric reached low values. Figure 12: Confusion matrix on the effectivity for detecting 2D patterns using the corresponding _s shapelets_. Figure 13: Best (**a,b**) and worst (**c,d**) results, according to the measure IoU, of 2D detection (in yellow) using the estimated _shapelet_ for each pattern inserted in the image. From left to right: the original image, the pattern to be detected, the region given by the algorithm based on _shapelets_, and the measure \(\mathbb{S}\) of the diagonal coefficients of detail. (**a**) Detection of the pattern pat21598072 inserted in the image 20587466, IoU = 0.92, \(\mathbb{S}=0.73\). (**b**) Detection of the pattern pat22580192 inserted in the image 50996228, IoU = 0.64, \(\mathbb{S}=0.75\).