# Quality Assessment of 2.5D Prints Using 2D Image Quality Metrics
## 4 Results and Discussion
### Are 2D IQMs Responsive to the Quality Variations in 2.5D Prints?
#### 4.1.2 Height Set  
The differences are expected to be in elevation and shadows because only height was changed between the prints in this set. The differences in the prints are better captured by the IQMs in the MS captures than in the SS ones for the three images, similar to the previous set. All selected IQMs are responsive to the differences (i.e., the highest response was on the edges compared to the background and the surface of the elevated parts) in both set-up captures. SSIM and MS-SSIM (both structure and contrast terms, scale 2) responded to differences in the background in the scissor image in the MS captures, although this area had not been elevated or changed between the prints. These metrics were also responsive to the edges and elevated parts' surfaces. However, this does not indicate that they are performing incorrectly in the scissor image. We assume that they are detecting halftone noise which is perceptually difficult to see at a normal viewing distance. This can explain the performance of SSIM and MS-SSIM (both terms, scale 2) on the scissor image. Figure 5 shows histograms of the mean quality maps from the MS captures for the scissor image by SSIM and iCID's lightness difference map as a comparison. The histogram of SSIM is more spread than of iCID's lightness difference map because the latter contains Contrast Sensitivity Function (CSF) which filters the halftone noise. Thus, the halftone noise becomes less visible to some degree. SSIM and MS-SSIM do not contain the CSF and thus they are calculating differences that might be not perceptible at a certain distance. As a result, we observe that iCID's lightness difference map is fairly robust to halftone noise and a model of the HVS is useful to avoid the metric calculating differences that are outside the CSF threshold (i.e., invisible to the human eye). We assume that SSIM and MS-SSIM (both terms, scale 2) in combination with the MS can be used in a quality assurance application to detect differences present between two prints/images not necessarily related to the perceptual aspects. Another reason for the behavior of SSIM and MS-SSIM (both terms, scale 2) can be the directional dependent appearance (i.e., complex) of the 2.5D prints. For instance, the histograms of (mean) quality maps of the scissor image by SSIM in both MS and  
Figure 5: The histograms of SSIM and iCID’s lightness difference mean quality maps for the scissor image with 1 mm maximum height print used as test image and 0.25 mm maximum height print used as reference image from the MS captures. The histograms show that iCID’s lightness difference map detects more differences between prints around zero whereas SSIM detects more spread differences. SS captures show that the prints are noisy, but the prints are noisier in the MS captures (Figure 6). Similar to SSIM and MS-SSIM (both terms, scale 2), iCID's lightness structure map also detected halftone noise in the scissor image from the MS captures between the prints (which was also responsive on the edges and elevated parts' surfaces). Its performance can be somewhat expected although it uses Gaussian weight distribution in its formula and the CSF was applied to the input images before calculating different maps in iCID. However, we used a lower pixels-per-degree value of a visual field, therefore simulating the HVS at a closer viewing distance when halftone noise becomes perceptible. Assigning a higher pixels-per-degree value of a visual field for the CSF filtering might improve iCID's performance [53]. Based on this, we found out that iCID is fairly robust to halftone noise at higher pixels-per-degree value (Figure 7). Figure 6: SSIM’s (mean) quality map histograms for the scissor image with 1 mm maximum height print used as test image and 0.25 mm maximum height print used as reference image from the MS (**left**) and the SS (**right**) captures. In the MS captures, the prints are noisier than in the SS ones.