## 3 Results and Discussion
Figure 13 indicates the ROI to be analyzed, and the results are shown in Figure 3:3 In these cases, calcifications are more easily detected and their characterization would help to classify  
Figure 3:4 A detail of the ROI selected in Figure 3:5 (**a**) Original zoomed ROI, (**b**) Fractal convolved and contrast enhanced ROI, (**c**) XOR segmented ROI. Figure 3:6 The original and enhanced mammograms. Figure 3:7 ROI selection. Different algorithms have been applied to 40 digital mammograms to test the level of enhancement achieved by the proposed approach. The compared algorithms are: Local Contrast Enhancement (CLAHE) [32], an algorithm based on a multiscale wavelet analysis (Atrous) [33; 34], and an algorithm based on wavelet sub-band decomposition (Haar) [35]. They were selected because they are well-known and are tested ImageJ implemented plugins. In Figure 16, the processed images of an ROI sample are represented. The histograms of the original ROI and the different processed images are shown in Figure 17 for comparison purposes. Figure 3:8 ROI-processed images. (**a**) Original sample, (**b**) fractal mask, (**c**) Local Contrast Enhancement (CLAHE) algorithm, (**d**) Atrous algorithm, and (**e**) Haar algorithm. In order to quantitatively validate all these results, we calculated the contrast improvement index (CII) defined in a previous study [9]. This parameter was calculated using Formula (3):  
Figure 3:9  
C is obtained by Formula (4)  
Figure 5.0  
Figure 5.1 Histogram of ROI. (**a**) Original sample. (**b**) Processed image with a fractal mask and no contrast enhancement. (**c**) Image processed with a fractal mask and log-exp contrast enhancement. (**d**) Processed image with the CLAHE algorithm. (**e**) Processed image with the Atrous algorithm. (**f**) Processed image with the Haar algorithm. where f is the mean gray-level of a microcalcification area and b is the mean gray-level value of the background. Table 2 provides the contrast improvement index results obtained with the different algorithms cited above. The contrast (CII) of the different microcalcifications depends on the grayscale of the microcalcifications and the background, the density of the surrounding tissue, and the complexity of the background. Accordingly, Table 2 shows how the CII values vary considerably. However, in all cases, the proposed algorithm confers improvement, while the other three algorithms produce less enhancement, and in some cases, even reduced contrast. This is why most recent references [3; 22] tend to use hybrid approaches. The results shown in Table 2 agree with the values provided in Table 4 of the previous study [9], which reinforces the validity of the presented algorithm. It is noteworthy that the contrast enhancement  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**ROI** & **CII Fractal** & **CII CLAHE** & **CII Atrous** & **CII Haar** \\ \hline Mammogram1 & 9.00329385 & 0.78247068 & 2.03116094 & 1.06843971 \\ Mammogram2 & 3.56662498 & 0.79058571 & 0.41786664 & 1.40218904 \\ Mammogram3 &  
achieved by fractal mask convolution is comparable, or even better, than the results of the referenced algorithms without removing the background. Moreover, the peak signal-to-noise ratio (PSNR) and the average signal-to-noise ratio (ASNR) were calculated, and are shown in Tables 3 and 4, using Formulae (5) and (6) described in the previous study [9] for more robust comparison purposes. Figure 5.2  
where p is the maximum gray-level value of the microcalcification area and \(\sigma\) is the standard deviation in the background region. Figure 5.3