# Adversarial Data Augmentation on Breast MRI Segmentation
## 2 Methods
### Evaluation Metrics
#### 2.3.2 Metrics Analysis  
The particularity of FID not having an upper bound and the fact of values being domain specific, motivated further study. To do so, we performed an analysis of the metrics' outcomes when applied between a reference image and that same image tampered with specific artifacts. We seized the opportunity to also evaluate which types of artifacts influenced the SSIM the most. Concretely, we transformed one image, from our breast MRIdataset, using an array of processing algorithms. The tamperings chosen reflect some of the issues that may be found in artificial images, which are the following:  
* T\({}_{1}\)--horizontal flip;
* T\({}_{2}\)--horizontal translation (20 pixels);
* T\({}_{3}\)--zoom (140%) and crop;
* T\({}_{4}\)--rotation (10%);
* T\({}_{5}\)--gamma correction (\(\gamma=2.5\)), resulting in a lower intensity distribution;
* T\({}_{6}\)--gamma correction (\(\gamma=0.5\)), resulting in a higher intensity distribution;
* T\({}_{7}\)--median blur (size \(15\times 15\));
* T\({}_{8}\)--downsampling (\(\frac{1}{4}\) factor) with aliasing, and resize, resulting in a blurry image;
* T\({}_{9}\)--Gaussian blur (\(\sigma=2\), kernel \(13\times 13\));
* T\({}_{10}\)--salt and pepper noise. Figure 4 show the reference and tampered MRI images. Respective FID and SSIM values are presented in Table 1.  
Table 1 shows FID scores between a range of 49 to 370, approximately. Against the MRI reference, the horizontal flip (T\({}_{1}\)), horizontal translation (T\({}_{2}\)) and zoom (T\({}_{3}\)) transformations produce FID values under 100, which we find low considering the observable FID range. On the other hand, the SSIM for the same transformation resulted in values below 0.65. \begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline  & **T\({}_{1}\)** & **T\({}_{2}\)** & **T\({}_{3}\)** & **T\({}_{4}\)** & **T\({}_{5}\)** & **T\({}_{6}\)** & **T\({}_{7}\)** & **T\({}_{8}\)** & **T\({}_{9}\)** & **T\({}_{10}\)** \\ \hline FID\(\downarrow\) & 49.84 & 69.89 & 92.63 & 129.4 & 107.2 & 133.3 & 229.0 & 273.1 & 293.8 & 367.1 \\ SSIM\(\uparrow\) & 0.615 & 0.528 & 0.547 & 0.582 & 0.744 & 0.766 & 0.814 & 0.845 & 0.838 & 0.117 \\ \hline \end{tabular} SSIM—Structural Similarity Index, range \(-\)1 to 1, best is max, negative is inverted; FID—Frechet Inception Distance, range 0 to Inf, best is 0.  
\end{table} 
Table 1: Reference metrics values for transformations: T\({}_{1}\)—H-flip, T\({}_{2}\)—H-offset, T\({}_{3}\)—zoom in, T\({}_{4}\)—rotation, T\({}_{5}\)—2.5 gamma, T\({}_{6}\)—0.5 gamma, T\({}_{7}\)—Med. blur, T\({}_{8}\)—Down sampling, T\({}_{9}\)—Gauss blur, T\({}_{10}\)—Salt&Pepper. Figure 4: Reference and tampered MRI images. This is not surprising as SSIM is sensitive to the structure of the data and performing flipping, translation, cropping or rescaling affects the co-variance matrix, and thus, those properties. In fact, the 10% slight rotation (T\({}_{4}\)) also strongly influences SSIM (0.582) while the increase in FID does not seem that substantial (129.4). The gamma corrections (T\({}_{5}\) and T\({}_{6}\)), that homogeneously alter the full image, have considerably less of an impact on the SSIM than the previous affine changes (T\({}_{1}\) to T\({}_{4}\)). This may result from the fact that SSIM tries to normalize for overall image luminance, focusing on the impact of localized distortions. Conversely, FID is slightly worse, as the squashing or expansion of the pixel intensities changes more considerably than SSIM. However, this T\({}_{5}\)-T\({}_{6}\) impact on FID is comparable to the rotation test (T\({}_{4}\)), which leads to believe that both SSIM and FID may not be rotation invariant. We can also observe that the best SSIM values (T\({}_{7}\) to T\({}_{9}\)) also correspond to higher, and among the worst, FID scores. These different kinds of blur effects change very little the structure of the data, hence also do not affect as much on the SSIM. Conversely, the FID shows significant alterations (over 4 times the lowest FID) for this blurring sub-set.