## 3 Experiments and Performance Assessment
### Quantitative Evaluation  
Different from the qualitative visual sense comparison mentioned above, a quantitative assessment is also performed by calculating the confusion matrix for shadow detection results of both test images Tripoli-1 and Tripoli-2. Particularly, several shadow detection accuracy measurements utilized in the objective assessment are specifically calculated with the confusion matrix [26; 38; 39; 40]. These corresponding measurements are computed at the pixel level with Equations (34)-(38) [9; 14; 20], including the producer's accuracy (\(\rho_{\text{s}}\) and \(\rho_{\text{n}}\)), the user's accuracy (\(\mu_{\text{s}}\) and \(\mu_{\text{n}}\)), the committed error (\(e_{\text{c}}\)), the omitted error (\(e_{\text{o}}\)), and the overall accuracy (\(\tau\)):  
\[\left\{ \begin{array}{l}\rho_{\text{s}}=\frac{TP}{TP+FN}\times 100\%\\ \rho_{\text{n}}=\frac{TN}{TN+FP}\times 100\%\end{array} \right. \tag{34}\]  
\[\left\{ \begin{array}{l}\mu_{\text{s}}=\frac{TP}{TP+FP}\times 100\%\\ \mu_{\text{n}}=\frac{TN}{TN+FN}\times 100\%\end{array} \right. \tag{35}\]  
\[e_{\text{c}}=\frac{FP}{TN+FP}\times 100\% \tag{36}\]\[e_{0}=\frac{FN}{TP+FN}\times 100\% \tag{37}\]  
\[\tau=\frac{TP+TN}{TP+TN+FP+FN}\times 100\% \tag{38}\]  
where _TP_ (true positive) indicates the total number of true shadow pixels correctly identified, _TN_ (true negative) refers to the number of true nonshadow pixels correctly classified, _FP_ (false positive) is the number of true nonshadow pixels wrongly identified as shadow ones, _FN_ (false negative) reveals the number of true shadow pixels wrongly classified as nonshadow ones, _TP_ + _FN_ and _TN_ + _FP_ respectively denote the number of true shadow pixels and true nonshadow pixels in the original image, _TP_ + _FP_ and _TN_ + _FN_ respectively indicate the number of shadow pixels and nonshadow pixels in the classified resulting image, and _TP_ + _TN_ + _FP_ + _FN_ is the total number of the whole image. Ideal shadow detection methods usually own high values of the producer's accuracy, the user's accuracy and the overall accuracy, as well as low values of the committed error and the omitted error. In particular, the overall accuracy is the most important measurement among these shadow detection accuracy measurements described above, which states the overall shadow detection ability of a certain shadow detection algorithm. Accordingly, these shadow detection accuracy measurements are mainly employed for evaluating the performance of the proposed _LSI_ shadow detection approach in comparative experiments. Additionally, these shadow detection accuracy measurements are respectively presented in Tables 1 and 2 for shadow detection results by the _LSI_ algorithm in five invariant color spaces (i.e., HIS, HSV, CIELCh, YCbCr and YIQ) and five comparative algorithms (i.e., MC3 [18], NSVDI [25], LSRI [24], SDI [26] and SRI [20]) in comparative experiments with test images Tripoli-1 and Tripoli-2. As shown in Table 1, high values are achieved for shadow detection results by the _LSI_ algorithm in various invariant color spaces (i.e., HIS, HSV, CIELCh, YCbCr and YIQ) for the test image Tripoli-1 in