# A Fast Method of Visually Lossless Compression of Dental Images
## 4 Invisibility Threshold and Compression  
There are several approaches to visually lossless compression of images. For the case of noise-free or near noise-free images, one of the main approaches is presented in [40], according to which:  
1. One must choose an adequate metric that characterizes well a visual quality;
2. In addition, a distortion invisibility threshold for the chosen metric must be a priori known or determined;
3. Finally, a way to provide this threshold value for the chosen metric at image compression stage must be found and the corresponding algorithm needs to be fast enough. Since there are numerous visual quality metrics [41], it is difficult to choose the best among them. Meanwhile, for the grayscale images considered here, we decided to analyze two visual quality metrics mentioned above--PSNR-HVS-M and FSIM, for the following reasons. These metrics have rank correlations with mean opinion scores for many image databases [23; 41] among the largest for the known metrics. For these metrics, there exists threshold values of distortion invisibility [23]. These metrics are based on DCT and wavelets; thus, if the conclusions drawn from the analysis of these metrics are in a good agreement, then one can be confident that these conclusions are correct with a high probability. What concerns the visibility thresholds are: Experimental data presented in the paper [23] show that distortions are practically invisible when the PSNR-HVS-M value is above 41 dB or FSIM > 0.99. One additional condition is that distortions shall be \"uniformly\" distributed across a compressed image. Finally, efficient noniterative methods to provide a desired visual quality of compressed images have been proposed recently [31; 42]. This is important for ADCTC, since it is computationally more demanding than JPEG due to a partition scheme optimization and use of DCTs of different sizes. Note that by \"fast method\" with application to ADCTC, we mean an efficient noniterative compression method. Let us consider the dependences of PSNR-HVS-M and FSIM on QS. They are presented for image fragments in Figure 6. As one can see from this figure, curve points are placed compactly. It is practically guaranteed that PSNR-HVS-M > 40 dB and FSIM > 0.99 if QS \(\leq\) 12. The exceptions are image fragments with very simple structure. This can be supported also by other results. In [31] it was found that \(\text{MSE}_{\text{HVS-M}}=0.02896\text{-QS}^{1.976}\). This expression was obtained for a different coder, but it is also approximately valid for ADCTC. Then one has \(\text{QS}_{\text{des}}\approx\text{MSE}_{\text{HVS-Mdes}}/0.02896)^{1/2}\), where \(\text{MSE}_{\text{HVS-Mdes}}\) is the desired \(\text{MSE}_{\text{HVS-M}}\) (for PSNR-HVS-M about 41 dB it corresponds to 5) one gets \(\text{QS}_{\text{des}}\approx 13\)We have already discussed a noise filtering effect if a lossy compression is applied to a noisy image. Recent study shows that people practically do not detect changes in a noise level if these changes are one order smaller than the level of an original noise [43] (i.e., in our case, if the introduced losses have to be by one order smaller than noise \(\delta_{\text{eq}}^{2}\) in original images). Then, for \(\delta_{\text{eq}}^{2}\) value around 50, one needs to provide PSNR at the level of 40 dB. This happens if QS is around 11 (see data in Figure 5b). Thus, we can generally set QS to 12. In the next Section, we verify this conclusion for image fragments. But first, let us compare the performance of the proposed method to other approaches. Coder efficiency can be analyzed and compared in many ways. In our case, we would like a lossy compression method to guarantee a lossy compression with invisible distortions in one iteration (i.e., to be fast) and with high values of CR. ADCTC with a selected QS = 12 was applied to the set of dental image fragments. Then, mean PSNR-HVS-M (PHVSM\({}_{\text{mean}}\)) and root mean square (RMSE\({}_{\text{PHVSM}}\)) of its deviation were determined.