# A Photometric Stereo Using Re-Projected Images for Active Stereo Vision System
## 4 Experimental Results and Evaluation
Figure 9b shows 3D scan data obtained from [PERSON]'s algorithm with the normal vector from traditional photometric stereo method ((P\({}^{\text{sv}}\)), (N\({}^{\text{ps}}\))\({}^{\text{[PERSON]}}\); this shows more surface details, and the high-frequency noise is removed. Figure 9c shows 3D scan data obtained from/via [PERSON]'s algorithm with the normal vector from the re-projection method proposed in this paper ((P\({}^{\text{sv}}\)), (N\({}^{\text{TP}}\)))\({}^{\text{[PERSON]}}\). The result also shows more surface details, and the high-frequency noise is removed, while it is not significantly different from the 3D scan data obtained from the method which uses an external light source. Figure 8: Normal maps. (**a**) Normal vector obtained by stereo vision; (**b**) Normal vector obtained by traditional photometric stereo; (**c**) Normal vector obtained by photometric stereo using re-projection images. Figure 9: 3D rendering comparisons. (**a**) 3D scan data obtained by active stereo vision; (**b**) 3D scan data applying [PERSON]’s algorithm using traditional photometric stereo method; (**c**) 3D scan data applying [PERSON]’s algorithm using re-projection method. For quantitative comparison analysis, high-quality 3D scan data obtained by measuring a target object with a high-precision 3D scanner (Identica Hybrid, Medit Company, Seoul, Republic of Korea) which has 7 \(\upmu\)m accuracy was defined as ground truth. This ground truth was compared with the 3D scan data measured previously using the Geomagic Control X (3D Systems, Rock Hill, SC, USA) [19]. Figure 10 shows the point distance deviation comparison to the ground truth. Table 1 shows the root mean square (RMS) error and standard deviation. Applying [PERSON]'s algorithm to the 3D scan data from active stereo vision resulted in a decrease in RMS error. A comparison between normal vectors is also needed to see how much the surface detail is improved. Figure 11 shows the angular deviation between the normal vector of the ground truth and the other normal vector. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Error (mm)** & **Active Stereo Vision** & **Nehab’s Configuration** & **Ours** \\ \hline RMS (root mean square) Estimate & 0.0490 & 0.0450 & 0.0454 \\ Standard deviation & 0.0489 & 0.0450 & 0.0454 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Distance deviation of point data. Figure 11: Angular deviation of the normal vector to the ground truth. (**a**) Normal vector obtained by stereo vision; (**b**) Normal vector after applying [PERSON]’s algorithm, which uses normal vector from the traditional photometric stereo method; (**c**) Normal vector after applying [PERSON]’s algorithm, which uses normal vector from the re-projection method. Figure 10: Distance deviation of the points from ground truth. (**a**) Points obtained by active stereo vision; (**b**) Points after applying [PERSON]’s algorithm, which uses normal vector from the traditional photometric stereo method; (**c**) Points after applying [PERSON]’s algorithm, which uses normal vector from the re-projection method. Figure 12 shows the angular deviation with the normal vector in terms of the number of points per deviation. Both [PERSON]'s configuration with external light sources and our configuration without external light sources show an increase in the number of points, with the angular deviation under \(12^{\circ}\), thereby showing that the surface detail has improved, compared to the original stereo vision scan data. To use [PERSON]'s algorithm, an external light source is required, increasing the size and complexity of the equipment. However, our configuration does not require any external light source in order to use [PERSON]'s algorithm, which improves the quality of the 3D scan data.