# Use of Gradient-Based Shadow Detection for Estimating Environmental Illumination Distribution
## 3 Results
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & & **Light1** & **Light 2** & **Light 3** & **Average Absolute Deviation** \\ \hline \multirow{8}{*}{**Two illumination sources**} & \multirow{2}{*}{Measured} & Elevation & 46.3\({}^{\circ}\) & 40.3\({}^{\circ}\) & - \\  & & Azimuth & 148.0\({}^{\circ}\) & 349.0\({}^{\circ}\) & - \\ \cline{2-6}  & & Proposed & Elevation & 49.1\({}^{\circ}\) & 39.8\({}^{\circ}\) & 1.65\({}^{\circ}\) \\  & & method & Azimuth & 146.5\({}^{\circ}\) & 350.5\({}^{\circ}\) & 1.50\({}^{\circ}\) \\ \cline{2-6}  & & Previous & Elevation & 50.0\({}^{\circ}\) & 40.0\({}^{\circ}\) & 2.00\({}^{\circ}\) \\  & & method & Azimuth & 145.0\({}^{\circ}\) & 350.0\({}^{\circ}\) & 2.00\({}^{\circ}\) \\ \cline{2-6}  & & \multirow{2}{*}{Measured} & Elevation & 63.1\({}^{\circ}\) & 57.3\({}^{\circ}\) & - \\  & & Azimuth & 81.0\({}^{\circ}\) & 316.0\({}^{\circ}\) & - \\ \cline{2-6}  & & Proposed & Elevation & 64.0\({}^{\circ}\) & 58.6\({}^{\circ}\) & 1.10\({}^{\circ}\) \\  & & method & Azimuth & 81.0\({}^{\circ}\) & 320.7\({}^{\circ}\) & 2.35\({}^{\circ}\) \\ \cline{2-6}  & & Previous & Elevation & 60.0\({}^{\circ}\) & 55.0\({}^{\circ}\) & 2.70\({}^{\circ}\) \\  & & method & Azimuth & 75.0\({}^{\circ}\) & 320.0\({}^{\circ}\) & 5.00\({}^{\circ}\) \\ \hline \multirow{8}{*}{**Three illumination sources**} & \multirow{2}{*}{Measured} & Elevation & 39.4\({}^{\circ}\) & 40.3\({}^{\circ}\) & 41.2\({}^{\circ}\) & - \\  & & Azimuth & 206.0\({}^{\circ}\) & 154.0\({}^{\circ}\) & 26.0\({}^{\circ}\) & - \\ \cline{2-6}  & & Proposed & Elevation & 41.2\({}^{\circ}\) & 40.5\({}^{\circ}\) & 41.6\({}^{\circ}\) & 0.80\({}^{\circ}\) \\ \cline{2-6}  & & method & Azimuth & 206.2\({}^{\circ}\) & 154.3\({}^{\circ}\) & 26.1\({}^{\circ}\) & 0.20\({}^{\circ}\) \\ \cline{2-6}  & & Previous & Elevation & 40.0\({}^{\circ}\) & 35.0\({}^{\circ}\) & 55.0\({}^{\circ}\) & 6.57\({}^{\circ}\) \\  & & method & Azimuth & 210.0\({}^{\circ}\) & 155.0\({}^{\circ}\) & 35.0\({}^{\circ}\) & 4.67\({}^{\circ}\) \\ \cline{2-6}  & & \multirow{2}{*}{Measured} & Elevation & 41.3\({}^{\circ}\) & 38.4\({}^{\circ}\) & 45.6\({}^{\circ}\) & - \\  & & Azimuth & 35.0\({}^{\circ}\) & 154.0\({}^{\circ}\) & 340.0\({}^{\circ}\) & - \\ \cline{2-6}  & & Proposed & Elevation & 43.6\({}^{\circ}\) & 40.9\({}^{\circ}\) & 46.3\({}^{\circ}\) & 1.83\({}^{\circ}\) \\  & & method & Azimuth & 36.4\({}^{\circ}\) & 149.0\({}^{\circ}\) & 341.2\({}^{\circ}\) & 2.53\({}^{\circ}\) \\ \cline{2-6}  & & Previous & Elevation & 40.0\({}^{\circ}\) & 50.0\({}^{\circ}\) & 45.0\({}^{\circ}\) & 4.50\({}^{\circ}\) \\  & & method & Azimuth & 35.0\({}^{\circ}\) & 140.0\({}^{\circ}\) & 335.0\({}^{\circ}\) & 6.33\({}^{\circ}\) \\ \hline \multirow{8}{*}{**Three illumination sources**} & \multirow{2}{*}{Measured} & Elevation & 33.9\({}^{\circ}\) & 30.0\({}^{\circ}\) & 37.0\({}^{\circ}\) & - \\  & & Azimuth & 20.0\({}^{\circ}\) & 140.0\({}^{\circ}\) & 200.0\({}^{\circ}\) & - \\ \cline{2-6}  & & Proposed & Elevation & 35.0\({}^{\circ}\) & 32.0\({}^{\circ}\) & 38.6\({}^{\circ}\) & 1.57\({}^{\circ}\) \\ \cline{1-1}  & & method & Azimuth & 18.5\({}^{\circ}\) & 143.6\({}^{\circ}\) & 193.8\({}^{\circ}\) & 3.77\({}^{\circ}\) \\ \cline{1-1} \cline{2-6}  & & Previous & Elevation & 60.0\({}^{\circ}\) & 30.0\({}^{\circ}\) & 35.0\({}^{\circ}\) & 9.37\({}^{\circ}\) \\ \cline{1-1} \cline{2-6}  & & Previously & Azimuth & 30.0\({}^{\circ}\) & 145.0\({}^{\circ}\) & 195.0\({}^{\circ}\) & 6.67\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of the measured and estimated light directions. Table 2 shows the modular computation performance. Initially, the AR marker was recognized and candidate shadow maps were generated. The image gradient-based matching procedure including color converting, Gaussian smoothing, and Sobel operations (gradient and magnitude computation) was performed. The gradient-based matching procedure, consisting of line fitting and junction point evaluation, took almost half the total calculation time.