# A Fast Method of Visually Lossless Compression of Dental Images
## 3 Basic Dependences
Analysis of these curves shows the following:  
1. ADCTC provides sufficiently better results than both JPEG2000 and SPIHT: Larger PSNR and PSNR-HVS-M values for CR in the range of interest for both test images;  
Figure 2: The 512 \(\times\) 512 pixel fragment with two partition schemes obtained for quantization step (QS) = 3 (a) and QS = 13 (b). 2. These dependences can be treated in another way--a larger CR is provided for a given quality (fixed values of PSNR or PSNR-HVS-M); the benefit in CR can reach 20%. Figure 3: _Cont_. One can argue that ADCTC uses DCT and the metric PSNR-HVS-M also employs DCT. Due to this, a comparison of ADCTC with JPEG2000 and SPIHT coders, both based on wavelets, in terms of PSNR-HVS-M might not seem fair. Because of this, we also carried out a similar analysis using the feature similarity (FSIM) index [39], which is a low-level feature-based image quality assessment metric. The basic principle of FSIM is that human vision perceives images based on their salient low-level features. Two types of features are employed, the phase congruency and the gradient magnitude. The phase congruency is used to weight the contribution of each point to the similarity of distorted and reference images. FSIM values vary from 0 to 1, where the latter one corresponds to the perfect quality. The dependences are given in Figure 4 and their analysis confirms that the performance of ADCTC is superior according to the metric FSIM as well. Figure 4: _Cont_. Figure 3: Dependences of Peak signal-to-noise ratio (PSNR) (**a,b**) and Peak Signal-to-Noise Ratio using Human Visual System and Masking (PSNR-HVS-M) (**c,d**) on compression ratio (CR) for complex structure (**a,c**) and simple structure (**b,d**) images. As it was mentioned above, larger QS values correspond to larger compression ratios. To demonstrate this, we show the plots obtained for integer values of QS varying in the limits from 1 to 40 for twenty \(512\times 512\) image fragments of different complexity (Figure 5a). All dependences (CR on QS for a given image fragment) are monotonous. Meanwhile, for a given QS, CR values vary in the wide limits depending on image fragment context. For example, for QS = 10, CR varies from 6 to 22, whilst, for QS = 20, CR varies from 12 to 78. That is, CR can differ by one order or even more. Figure 4: Dependences of A Feature Similarity Index (FSIM) on compression ratio (CR) for simple structure (**a**) and complex structure (**b**) image fragments. Figure 5: Dependences of compression ratio (CR) (**a**) and Peak signal-to-noise ratio (PSNR) (**b**) on quantization step (QS) for many image fragments for ADCTC. PSNR decreases monotonously if QS increases (Figure 4b). If QS \(\leq\) 5, PSNR values for the same QS are almost the same for all fragments. Meanwhile, for larger QS, PSNR values for the same QS can vary a lot. For example, for QS = 20, PSNR values are in the limit of 34 to 40 dB (i.e., they vary in wide limits). This means that setting a given QS leads to a wide variation of CR and PSNR if QS is large. In other words, by setting some QS it is not easy to provide a desired quality of compressed images, at least, according to the metric PSNR and for large QS. For example, QS = 20 leads to invisibility of distortions for some images and their visibility for other images (note that, according to [23], distortions are, with high probability, invisible if PSNR > 36 dB).