## 4 Results and Discussion  
### Performance of the Proposed System  
The dataset used in the present study included 100 images with shaded areas gathered from LabelMe [42]. Given an image under analysis, boundary pixels were selected through Canny method [45] and for each pixel 36 features were evaluated through the proposed ADT filter (Section 3). An overall of 389856 36-dimensional feature vectors were taken into account (194928 belonging to the shadow pixel class and 194928 to the non-shadow pixel class) and used as input to the developed MLP, AE, 1D-CNN, SVM classifiers to perform the 2-way pixel-based classification task: shadow vs. non-shadow. Standard metrics (i.e., Accuracy (A), Recall (R), Precision (P), F-measure (FM)) were employed to assess the effectiveness of the proposed classifiers:  
\[A=\frac{TP+TN}{(TP+FP+TN+FN)} \tag{14}\]  
\[R=\frac{TP}{(TP+FN)} \tag{15}\]  
\[P=\frac{TP}{(TP+FP)} \tag{16}\]  
\[FM=2\times\frac{P\times R}{(P+R)} \tag{17}\]  
where TP, FP, TN, FN represent the true positive, false positive, true negative and false negative, respectively. Furthermore, the \(k\)-fold cross validation (with \(k=7\)) procedure was also applied for quantifying the discrimination performance. In particular, for each class, train set consisted of 70% of instances and test set of remaining 30%. Hence, all evaluation performance are reported as average value \(\pm\) standard deviation. It is worth noting that the proposed MLP/SVM/CNN are supervised learning approaches and use the class label information in the training procedure. In contrast, AE is trained with unsupervised learning, hence the label was not used during the training phase. The extracted features from unlabeled data were the input to a softmax layer for classification purposes. The whole network is then fine-tuned to enhance performance. Table 1 reports the pixel detection performance (evaluated on test sets) in terms of averaged precision, recall, F-measure, accuracy for the MLP, AE, 1D-CNN and SVM classifier. In relation to MLP classifiers, MLP\({}_{1}\) outperformed MLP\({}_{2}\) and MLP\({}_{3}\), achieving F-measure and accuracy values of 85.05 \(\pm\) 0.57% and 84.63 \(\pm\) 0.63% respectively. However, it is to be noted that high performance were observed also with MLP\({}_{2}\) (F-measure of 82.39 \(\pm\) 0.69%, accuracy of 81.71 \(\pm\) 0.77%) and MLP  
Figure 9: Architecture of 1D-CNN composed of 1D-convolutional layer (+RelU), 1D-max pooling layer and 2-hidden layer NN with softmax output layer for classification purpose. (F-measure of 84.55 \(\pm\) 0.53%, accuracy of 84.19 \(\pm\) 0.56%). In relation to AE classifiers, the model with two hidden layer denoted as AE\({}_{3}\), produced F-measure and accuracy rates up to 78.84 \(\pm\) 0.66% and 77.91 \(\pm\) 0.72%, respectively. Very good results were achieved also by AE\({}_{1}\) and AE\({}_{2}\). In particular, the average accuracies were of 76.51 \(\pm\) 1.04% and 77.51 \(\pm\) 1.89%, respectively. As regards the proposed 1D-CNN (Figure 9) the following average performance were achieved: accuracy of 75.8 \(\pm\) 1.2%, precision of 73.5 \(\pm\) 1.91%, recall of 81.0 \(\pm\) 2.3% and F-measure of 76.9 \(\pm\) 1%. Finally, as regards SVM classifier, lower average performance were achieved: precision of 62.5 \(\pm\) 3.88%, recall of 58.6 \(\pm\) 9.64%, F-measure 59.93 \(\pm\) 3.85%, accuracy of 61.27 \(\pm\) 2.18%. Hence, comparative simulation results showed that the proposed MLP\({}_{1}\) classifier achieved the highest pixel-based detection performance (accuracy of 84.63 \(\pm\) 0.63%) as compared to MLP\({}_{2}\), MLP\({}_{3}\), AE\({}_{1}\), AE\({}_{2}\), AE\({}_{3}\), SVM classifiers. In support of this result, the Area Under the Curve (AUC) of the Receiver Operating Characteristic (ROC) was estimated. Specifically, Figure 10 shows the average values of AUC and related ROC curves, evaluated for the developed MLP, AE, 1D-CNN, SVM classifiers. As can be seen, MLP\({}_{1}\) outperformed all the other approaches reporting an AUC = 92 \(\pm\) 0.53%.