# A New Method for 2D-Adapted Wavelet Construction:
## 3 Results
### Detection of 2D Mass-like Patterns in Digital Mammography Images
#### 3.2.1 Design of the Simulations Using the Proposed 2D Strategy  
As an initial step, the relevance of applying the proposed 2D strategy to detect a mass-type pattern in digital mammography images was verified. Figure 4 shows results where the detection was successful. Thus, it was decided to extend the experimentation to six mass-type patterns in 118 mammography images from the INbreast 1.0 [45] database (Figure 5). Due to the limitation of the 1D strategy that requires a _shapelet_ filter with sizes smaller than 26 samples [37; 46], the dimension of the images was reduced using the Haar-based DWT to reach 160 \(\times\) 108 resolution. Next, five different patterns of mass-like abnormalities were intentionally extracted, considering aspects such as the position of the mass, that the lesion was not in the pectoralis or near the edge of the breast, and that there was no local co-occurrence of abnormalities such as calcification within the mass, among other abnormalities. Images coded as 20588072, 20588334, 22580192, 50994354, 53580858, and 21598072 from the INbreast dataset were selected (Figure 6). The results of pattern detection in the first five images can be seen in Figures 7, 8, 9, 10, and 11, respectively. A flowchart of the simulations setup for the experiments over the proposed DST-II 2D for mass-like pattern detection is depicted in Figure 5.  
Figure 4: Locating a mass-like abnormality pattern on a digital mammogram. 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. Figure 5: Flowchart of the simulations setup for the experiments over the proposed DST-II 2D for mass-like pattern detection. Figure 6: Patterns of mass-like anomaly from the INbreast mammography database to estimate 2D _shapelets_: (**a**) 20588072; (**b**) 20588334; (**c**) 22580192; (**d**) 50994354; (**e**) 53580858; (**f**) 21598072. Figure 7: Successful pattern detection in image 20588072. 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. Figure 8: Successful pattern detection in image 20588334. 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. Figure 10: Successful pattern detection in image 50994354. 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. Figure 9: Successful pattern detection in image 22580192. 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. Since such mass-like patterns only occur once in the corresponding images, a test set including all INbreast images, where each of the five mass patterns were separately inserted, was constructed, merging the original image with the pattern image using the sum of images within a symmetric and logarithmic model for image processing (S-LIP) proposed by [47], already used in two of this papers author's own research [17; 48]. This fusion was performed around the centroid of the original mammography image, which was estimated with the function skimage.measure.regionprops of the Python library Scikit-image [49]. To detect the mass-like pattern, the algorithm described in Section 2.3 was used. Since it can happen that several rectangles are obtained where the pattern to be detected is estimated to be located, the rectangle with the highest value of the measure \(\mathbb{S}\) was taken.