# Image Quality Assessment for Gibbs Ringing Reduction
## 4 Region of Interest  
As we noted earlier, it has been suggested that \"For image quality assessment, it is useful to apply the SSIM index locally rather than globally\" [23]. Gibbs ringing is the most severe around discontinuities. We therefore speculate that applying metrics to a limited region near edges could enhance their sensitivity to ringing, which could overcome the problems we identified previously. This approach of identifying the region of interest (RoI) means that the spatial information of each pixel is taken into account. Will the performances of the metrics increase with the use of an RoI? In this section, we propose a method to identify the RoI based on high pass filtering, binarization, and erosion and dilation. We then evaluate 16 metrics on this region of the test image. The steps we used to calculate the RoI are shown in Figure 5. For space reasons, we limit the example to the phantom, though we have also tested it on the other two test images. It is assumed that the ground truth is known. In practical situations, the RoI might have to be estimated from a Fourier reconstruction. Figure 5a shows the original Shepp-Logan phantom (i.e., without ringing). Figure 4: The optimal reconstructions of the Shepp–Logan phantom from the different metrics. For reference, we also show the ground truth without ringing and the Fourier reconstruction with added ringing. Figure 3: Evaluation of different Gaussian filters using \(\ell_{e}^{0}\), SSIM, MS-SSIM, MAE, Huber loss and entropy. In all sections of the figure, we plot the results for the ideal square test image (blue), the Shepp–Logan phantom (red) and an MR head section (yellow). The dotted vertical lines of the same colour indicate a peak/nadir of the three metrics. The image is normalized to have maximum value 1. A Laplacian of Gaussian (LoG) filter with rotational symmetry, kernel size of 4 \(\times\) 4 and standard deviation \(\sigma\) = 0.2. The image is then binarized with threshold 0.5. Image erosion is applied with a flat morphological structuring element object of size 3 \(\times\) 3. Image dilation is applied with a flat morphological structuring element object of size 20 \(\times\) 20. Steps 1-3 highlight the regions where intensity changes rapidly. Figure 4(b) shows the result after passing the original image through the LoG filter and binarization. It can be seen that the locations of edges were extracted from the original image. Step 4 is shown in Figure 4(c). Image erosion removes small objects. Step 5 then dilates the resulting edges to go from a representation of the edges to one of the region around edges. The final results are shown in Figure 4(d). The parameters of the image erosion and dilation were chosen empirically. Figure 6 shows the 200 th row of the Shepp-Logan phantom (with ringing) and the corresponding RoI. The red line shows the RoI and the blue line shows the remainder of the signal. It is evident that the RoI includes the parts of the image where the ringing is strongest. Figure 5: The process of determining the RoI. (**a**) Original Shepp–Logan phantom. (**b**) After LoG filter and binarization. (**c**) Image erosion of (**b**). (**d**) Image dilation of (**c**). Figure 6: 1D slice of the Shepp–Logan phantom with ringing. The RoI is in red. The excluded regions are in blue. Next, we apply \(\ell_{e}^{0}\), SSIM, MS-SSIM, Huber loss, MAE, entropy and all 12 metrics discussed in [17] to the RoI. Unfortunately, almost all of the metrics show no significant changes. \(\ell_{e}^{0}\), SSIM, Huber loss, MAE and entropy show peaks or nadirs for similar values of \(\sigma\) when applied to the RoI or to the whole image. All other metrics but one show no peak with or without RoI. The exception is PSR. Figure 7 shows the behaviour of PSR with and without the RoI. It can be seen that, applied to the whole image, PSR shows a monotonic upward trend. Applied to the RoI, PSR shows a peak and a local minimum. The peak is for very small \(\sigma\), which would introduce an unreasonable amount of blurring.