## 4 Conclusions  
Previous work showed that using an AIHT-based image contrast enhancement method has two drawbacks. First, it lacks a mechanism to adjust the degree of enhancement; using the AIHT-based image contrast enhancement approach cannot retain the detail brightness distribution of the original image, thus leading to distortion. Second, this algorithm can only be applied to the image for global contrast enhancement, and cannot achieve local contrast enhancement. It is thus unable to meet the Human Visual System mapping curve, resulting in non-smooth or distorted images. This study proposes a new, effective multi-scale image enhancement approach based on the adaptive inverse hyperbolic tangent algorithm as a contrast function in order to map from the original image into a transformed image. This algorithm is a simple pixel-wise \"AIHT\" correction of the input data, by introducing a sub-band processing concept to overcome the wide dynamic range usually required for contrast enhancement, an automatic image based strength correction, and the _bias_ and _gain_ of sub-band parameters in order to avoid the contrast and color saturation loss common to contrast enhancement methods. This algorithm can improve the displayed quality of contrast in scenes, and offers efficient and fast computation. This approach has two major features: (1) a sub-processing method to achieve the local contrast enhancement; (2) an extreme case images processing method that is capable of enhancing and retaining the details of an original image. Enhanced images will be very helpful for further image analysis processes. Experimental results show that it is possible to maintain a large portion, if not all, of the perceived contrast of lightness while significantly enhancing the image contrast. The form of these curves used for \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Image Type**} & \multirow{2}{*}{**Name**} & \multicolumn{4}{c}{**2 SAIHT**} & \multicolumn{4}{c}{**4 SAIHT**} & \multicolumn{4}{c}{**8 SAIHT**} \\ \cline{3-11}  & & **MSE** & **SNR** & **PSNR** & **MSE** & **SNR** & **PSNR** & **MSE** & **SNR** & **PSNR** \\ \hline \multirow{4}{*}{Outdoor images} & Dawn & 0.029 & 29.48 & 34.67 & 0.005 & 176.0 & 207.0 & 0.006 & 143.8 & 169.2 \\  & Afternoon & 0.007 & 61.65 & 138.3 & 0.015 & 29.80 & 66.85 & 0.030 & 15.00 & 33.65 \\  & Night & 0.123 & 0.122 & 8.159 & 0.158 & 0.094 & 6.316 & 0.151 & 0.099 & 6.640 \\ \hline \multirow{4}{*}{Indoor images} & Park & 0.011 & 8.610 & 88.02 & 0.090 & 1.085 & 11.09 & 0.058 & 1.691 & 17.28 \\  & Hall & 0.016 & 22.14 & 61.44 & 0.052 & 6.888 & 19.11 & 0.058 & 6.237 & 17.31 \\ \cline{1-1}  & Studio & 0.016 & 21.06 & 63.64 & 0.079 & 4.206 & 12.71 & 0.076 & 4.328 & 13.08 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Compare results of 2 SAIHT, 3 SAIHT, 4 SAIHT and 8 SAIHT methods using MSE, SNR and PSNR. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Image Type**} & \multirow{2}{*}{**Name**} & \multicolumn{4}{c}{**HE**} & \multicolumn{4}{c}{**CLAHE**} & \multicolumn{4}{c}{**AIHT**} \\ \cline{3-11}  & & **MSE** & **SNR** & **PSNR** & **MSE** & **SNR** & **PSNR** & **MSE** & **SNR** & **PSNR** \\ \hline \multirow{4}{*}{Outdoor images} & Dawn & 0.169 & 5.027 & 5.913 & 0.043 & 10.32 & 23.143 & 0.039 & 22.11 & 25.89 \\  & Afternoon & 0.010 & 46.39 & 104.1 & 0.043 & 10.32 & 23.143 & 0.010 & 45.10 & 101.2 \\  & Night & 0.167 & 0.089 & 5.974 & 0.060 & 0.250 & 16.780 & 0.017 & 0.854 & 57.35 \\ \hline \multirow{4}{*}{Indoor images} & Park & 0.059 & 1.669 & 17.06 & 0.034 & 2.885 & 29.495 & 0.003 & 28.88 & 295.3 \\  & Hall & 0.002 & 175.2 & 486.1 & 0.049 & 7.323 & 20.323 & 0.016 & 22.14 & 61.44 \\ \cline{1-1}  & Studio & 0.027 & 12.25 & 37.01 & 0.056 & 5.897 & 17.825 & 0.016 & 21.06 & 63.64 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Compared results of HE, CLAHE and AIHT methods using Mean Square Error (MSE), Signal to Noise Ratio (SNR) and Peak Signal to Noise Ratio (PSNR).