## 4 Results and Discussion
### Comparison of Shadow Detection Models  
The proposed ADT filter based machine learning shadow boundary detection system was also compared with other approaches reported in the literature. In particular, here [PERSON]'s [9] and [PERSON]'s [11] approaches were taken into account. In [9] [PERSON] et al. proposed a physical model of shadow able to compute the width, shape, color of the penumbra and extract some visual features such as shadow sharpness, dark to bright slope, dark to bright ratio and dark to bright gradient used as input to a RBF-based SVM classifier to perform shadow detection task. In [11] [PERSON] et al. proposed a decision tree classifier for pixel shadow detection. Specifically, they used a CRF-based optimization to concatenate the shadow pixels to produce a more coherent shadow contour and remove the high unlikely shadow boundaries and isolate weak edges. In contrast, in this study, we propose an ADT filter able to extract HOS and optical features only along the direction of boundary (in simple and complex real scenes) avoiding redundant information [67]. The estimated parameters are then used as input to a very simple and computationally not expensive MLP architecture to perform the 2-way  
Figure 12: Training plot of the proposed MLP\({}_{1}\) classifier. classification task: shadow vs. non-shadow. Furthermore, since [PERSON]'s and [PERSON]'s approaches are fully publicly available, for fair comparison we decided also to apply such methods on the same images dataset used in the present study. Comparative experimental results are reported in Table 2. As can be seen, accuracies of 84.63 \(\pm\) 0.63%, 62.52 \(\pm\) 5.54% and 52.67 \(\pm\) 0.1% were achieved by our proposed detection system (i.e. MLP\({}_{1}\)), [PERSON]'s and [PERSON]'s approaches, respectively. Hence, our proposed MLP\({}_{1}\) classifier reported the highest performance. Similar result was observed also by evaluating the AUC as reported in Figure 13. As an example, Figure 14 shows the shadow detection results achieved by MLP, AE, 1D-CNN, SVM, [PERSON]'s and [PERSON]'s approaches of a realistic scene. Note that only the best MLP and AE classifiers are reported (i.e., MLP\({}_{1}\), AE\({}_{3}\)). As can be seen MLP\({}_{1}\) is able to detect shadow boundaries better than other approaches; indeed, 1D-CNN, SVM and [PERSON]'s classifiers detect also buildings and other profiles of the scene that do not belong to a shadow, whereas [PERSON]'s is deficient to identify shaded areas. Finally, as previously mentioned, AE\({}_{3}\) shows considerable discrimination capability. However, the proposed shadow detection system (i.e., MLP\({}_{1}\)) has some drawbacks. Features of object boundaries may be similar to those features of shadow boundaries, causing a misclassification of the pixel under analysis. Furthermore, the extracted features are based on physical characteristics, hence, when the intensity of light is weak or when the shadows lie on some special material surface that can cause a significant change of physical properties, the shaded boundary is very difficult to identify. Last limitation is that our proposed system (i.e., MLP\({}_{1}\)) may include also the object profile in the detection process, as shown in Figure 14b. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **Precision** & **Recall** & **F-Measure** & **Accuracy** \\ \hline MLP\({}_{1}\) & 82.72 \(\pm\) 0.77\% & 87.52 \(\pm\) 0.4\% & 85.05 \(\pm\) 0.57\% & 84.63 \(\pm\) 0.63\% \\ [PERSON] & 60 \(\pm\) 4.91\% & 77.17 \(\pm\) 5.50\% & 67.37 \(\pm\) 4.10\% & 62.52 \(\pm\) 5.54\% \\ [PERSON] & 74.03 \(\pm\) 0.75\% & 8.19 \(\pm\) 0.12\% & 14.74 \(\pm\) 0.21\% & 52.67 \(\pm\) 0.1\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparative results of our proposed shadow detection system (i.e., MLP\({}_{1}\)), [PERSON]’s and [PERSON]’s methods evaluated on the test sets. All the outcomes are reported as mean value \(\pm\) standard deviation.