## 3 Results  
In this section, we describe the experiment conditions and test images used for comparative experiments to demonstrate the performance of our developed shadow detection approach, as well as other comparable shadow detection approaches for different test images, and state the corresponding shadow detection results. These comparative experiments were implemented in MATLAB 2017a under the Microsoft Windows 7 operation system on a DELL personal computer (3.20 GHz CPU and 4 GB RAM). In these comparative experiments, we tested many multispectral remote sensing images selected from the multispectral WorldView-3 remote sensing image of Rio de Janeiro, Brazil. Given the limitation of paper size, three typical test images (named test image A, B, and C) were selected to validate our MPSI-based shadow detection approach in detecting shadows and correctly distinguishing shadows from vegetation cover of nonshadow areas, as shown in Figure 4. Particularly, four bands in these test images were employed: band-2 (blue), band-3 (green), band-5 (red), and band-7 (near infrared-1). Specifically, test image A in Figure 5a is a 601 \(\times\) 601 pixel image covering a typical forest scene where various kinds of vegetation are found. Test image B in Figure 6a is a 501 \(\times\) 501 pixel image with high vegetation coverage and a smaller fraction of buildings. Test image C in Figure 7a is a 481 \(\times\) 481-pixel image including various land cover types (mainly including vegetation, buildings, roads, and lawns). Figure 3: Flow chart of the proposed mixed property-based shadow detection approach. Furthermore, to assess our MPSI-based shadow detection approach both subjectively and objectively, we applied our developed shadow detection approach and five comparable methods to test images A, B and C. Results were achieved for these three test images A, B, and C, as shown in Figures 5c-h, 6c-h and 7c-h, respectively, and the accuracy data of the different methods for these three test images were summarized in Tables 1-3, respectively. Additionally, interpretations were carried out manually to generate reference images for these three test images, A, B, and C, as shown in Figures 5b, 6b and 7b, based on these corresponding panchromatic images, respectively. Based on these reference images, several related assessments were carried out both subjectively and objectively to evaluate the performance of our MPSI-based shadow detection approach, which is described in the following section in detail. Figure 4: Test images. (**a**) The multispectral WorldView-3 remote sensing image of Rio de Janeiro, Brazil. (**b**) The test image A. (**c**) The test image B. (**d**) The test image C.  
Figure 5: _Cont._  
Figure 5: Test image A. (**a**) The original image. (**b**) The reference shadow image. (**c**) Shadow image by the spectral ratio index (SRI)-based algorithm [11]. (**d**) Shadow image by the normalized saturation value difference index (NSVDI)-based algorithm [18]. (**e**) Shadow image by the modified C3 (MC3)-based algorithm [20]. (**f**) Shadow image by the shadow intensity (SI)-based algorithm [14]. (**g**) Shadow image by the shadow detector index (SDI)-based algorithm [19]. (**h**) Shadow image by the developed mixed property-based shadow index (MPSI)-based approach. Figure 6: _Cont._  
Figure 6: Test image B. (**a**) The original image. (**b**) The reference shadow image. (**c**) Shadow image by the SRI-based algorithm [11]. (**d**) Shadow image by the NSVDI-based algorithm [18]. (**e**) Shadow image by the MC3-based algorithm [20]. (**f**) Shadow image by the SI-based algorithm [14]. (**g**) Shadow image by the SDI-based algorithm [19]. (**h**) Shadow image by the developed MPSI-based approach. Figure 7: _Cont._