# SA-GAN: Stain Aclimation Generative Adversarial Network for Histopathology Image Analysis
## 4 Experimental Results
### Structure Analysis  
Evaluation metrics: The Pearson correlation-coefficient (PCC) [37][1], structural similarity index (SSIM) [37] and peak signal-to-noise ratio (PSNR) [42] are taken to evaluate structural analysis. Texture properties of histology images are related to spatial distribution of image intensity values. We quantified the texture similarity between the original and processed images by computing PCC metric. A PCC of value 1 implies that intensity distributions of original image are exactly preserved in the processed image, which is highly desirable in color normalization. On the contrary, PCC of value 0 denotes that no similarity occurs between the images. PCC is described as:  
\[PCC=\frac{\sum\limits_{i}{(a_{i}-\mu_{a})(b_{i}-\mu_{b})}}{\sqrt{\frac{\sum \limits_{i}{(a_{i}-\mu_{a})^{2}}\sqrt{\sum\limits_{i}{(b_{i}-\mu_{b})^{2}}}}}} \tag{8}\]  
where \(a_{i}\) and \(b_{i}\) represent source and processed images, respectively. \(\mu_{a}\) and \(\mu_{b}\) represent the mean of source and processed images, respectively. Similarly, the SSIM [37] metric is calculated to measure structural, contrast, and luminance differences between two images. For robust normalization, SSIM value should be close to one. SSIM is described as:  
\[SSIM(a,b)=(\frac{2\mu_{a}\mu_{b}+x_{1}}{\mu_{a}^{2}+\mu_{b}^{2}+x_{1}})(\frac{ 2\sigma_{ab}+x_{2}}{\sigma_{a}^{2}+\sigma_{b}^{2}+x_{2}}) \tag{9}\]  
where \(\sigma_{a}\) and \(\sigma_{b}\) are the standard deviation of source and processed images, respectively. \(\sigma_{ab}\) is the correlation between source and processed images. \(x_{1}\) and \(x_{2}\) are the constants used to stabilize \(SSIM\) when its value approaches zero. Furthermore, to analyze the perceptual quality of stain transferred image, \(PSNR=20\log MAX_{I}/\sqrt{MSE}\) score is computed, where \(MAX_{I}\) is the maximum intensity value in the image and \(MSE\) is the mean squared error between stain transferred image and target (test) image. Qualitative and quantitative performance: In this analysis, we discussed the qualitative and quantitative normalized performance of proposed method. The qualitative results of the proposed SA-GAN and other state-of-the-art methods are given in Figure 3. Visual inspection depicts that when the images are processed with stain color descriptor (SCD) [16] method, white luminance part is not well preserved but structural details are maintained to some extent. Results obtained with Macenko [20] method show that color from target image is not transferred correctly and the white background of source image is fraught with fade color. Nevertheless, the Macenko method effectually avoided structural artifacts. [PERSON] et al. [17] method maintained the structural details of the source image; however, color contents are not transferred properly from source to processed image. The SCD [16] method does not maintain the structure and color details in processed images. Compared to all other benchmark methods, in SCD method, loss of information is high, and more structural defects occur for all datasets that can be particularly seen in Figure 3. In contrast, results obtained with the adoptive color normalization (ACD) [26] method preserve the structure details. However, the color information is not exactly transferred to processed images, and the background of images is also affected. Staining of the bright background luminance, tint, or discoloration of nuclei appears in many normalized images across all the datasets. For instance, the SCD and Macenko method stains bright backgrounds, and color characteristics of target domain are copied to normalized colon cancer images and also are seen in the breast cancer ICIAR dataset images. Artifacts such as stained bright background or improper color in nuclei appear in the results of the StainGan [28] method. The processed images with accurate stain representations and structural details are considered the best results. Hematoxylin appears as the predominant color in the nuclei, while eosin appears in the stroma or other organs.