# A New Adaptive Spatial Filtering Method in the Wavelet Domain for Medical Images
## 3 Results and Discussions
The proposed algorithm leads both in the invariant approach to translation and in the simple one to good results both in terms of PSNR and C coefficient, as well as visually, as it can be seen in Figure 5 (Comparative Performance in Standard Images). Table 6 compares the two correction methods based on the hierarchical correlation map. It can be seen that in the case of continuous type correction, better results are obtained in terms of PSNR than in the case of switched type correction, especially for higher noise levels. However, this is done at the cost of poor preservation of the contours in the image, which is highlighted by lower values of the C coefficient. Currently, imaging is present in all branches of science, and the acquisition of images that are not disturbed by external factors arouses interest in the field of scientific research. Digital images unaffected by disturbing elements, such as noise, contrast and uneven lighting, allow a correct understanding of its content. Following the research of the specialized literature and the implemented applications, in this article we will confer a benefit in the extraction of useful information from medical images. The objectives of the research are to model, process and extract useful information from digital medical images using image segmentation and fusion methods. These techniques generate higher quality images than the original ones. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Image**} & \multirow{2}{*}{\(\sigma\)} & \multirow{2}{*}{**Initial**} & \multicolumn{3}{c}{**Method A**} & \multicolumn{3}{c}{**Method B**} \\  & & & \multicolumn{3}{c}{**(Integral Application of the Algorithm in Invariant Form to Translation and Performing the Correction on This Result)**} \\ \cline{4-9}  & & & & **Algorithm in Invariant** & & & **Algorithm in Invariant** \\ \cline{4-9}  & & & & **Form to Translation** & & & **Algorithm in Invariant** \\ \cline{4-9}  & & & & **Form to Translation** & & & **Algorithm in Invariant** \\ \cline{4-9}  & & & & **Form to Translation** & & & **Algorithm in Invariant** \\ \cline{4-9}  & & & & **Form to Translation** & & & **Algorithm in Invariant** \\ \cline{4-9}  & & & & **Form to Translation** & & & **Algorithm in Invariant** \\ \cline{4-9}  & & & & **Form to Translation** & & & **Algorithm in Invariant** \\ \cline{4-9}  & & & & **Form to Translation** & & & **Algorithm in Invariant** \\ \hline \multirow{2}{*}{_Lena_} & 0.05 & 26.00 & 63.94 & 31.07 & **66.70** & 31.14 & 66.47 & 30.96 & 66.83 \\ \cline{2-9}  & 0.1 & 20.08 & 47.64 & 27.55 & **50.77** & 27.59 & 48.69 & 27.35 & 51.02 \\ \cline{2-9}  & 0.05 & 26.07 & 63.73 & 28.08 & **63.89** & 28.14 & 63.03 & 28.01 & 63.84 \\ \cline{2-9}  & 0.1 & 20.17 & **48.02** & 24.17 & 46.44 & 24.17 & 45.25 & 24.03 & 46.66 \\ \hline \multirow{2}{*}{_Aerial_} & 0.05 & 26.01 & 69.43 & 29.00 & **70.50** & 29.09 & 69.46 & 28.88 & 70.55 \\ \cline{2-9}  & 0.1 & 20.10 & 53.90 & 25.27 & **56.47** & 25.32 & 54.23 & 25.02 & 56.07 \\ \hline \multirow{2}{*}{_Bout_} & 0.05 & 26.03 & 64.12 & 31.97 & **67.28** & 32.03 & 67.18 & 31.82 & 67.18 \\ \cline{2-9}  & 0.1 & 20.03 & 47.58 & 28.19 & **51.26** & 28.25 & 50.15 & 27.94 & 51.12 \\ \hline \multirow{2}{*}{_House_} & 0.05 & 26.05 & 65.47 & 32.68 & **68.70** & 32.75 & 68.28 & 32.54 & 68.41 \\ \cline{2-9}  & 0.1 & 20.13 & 55.13 & 29.16 & **56.95** & 29.21 & 55.13 & 28.91 & 56.28 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Application of the proposed algorithm in invariant approach to displacement, in the two approaches discussed. Four circular trips were made. The test images were \(256\times 256\) pixels and were degraded with white Gaussian additive noise.