## 1 Introduction
The SI-based method presents good shadow detection performance for high-resolution multispectral remote sensing images, especially for the WorldView-2 multispectral images, except for wrongly identifying vegetation pixels as shadow ones in some cases. In the next year, [PERSON] et al. [24] presented a novel method that joined model and observation cues: pixels values, chromaticity, and luminance. A shadow mask in an image was first outlined with an improved bright channel prior (BCP), which was developed based on the original BCP. Then, the shadow mask was refined by combining the shadow mask with observation cues. This method is suitable not only for remote sensing images but also natural images. In 2017, [PERSON] et al. [19] proposed a new shadow detector index (SDI) for detecting shadows in high-resolution multispectral remote sensing images, especially aimed at accurately classifying shadow pixels from vegetation pixels. This SDI-based method was developed by analyzing the difference in shadow pixels and vegetation pixels in nonsmadows in terms of green and blue bands, as well as low red values in shadow pixels. An SDI index image was first obtained. Then a shadow image was generated by applying an optimal threshold over the rough index image, in which the optimal threshold was automatically achieved from the SDI histogram with the modified neighborhood valley-emphasis threshold method (NVETM) [33]. This SDI-based approach performs well in classifying shadow pixels from vegetation pixels, and achieves high shadow detection accuracies, except for the shortcomings of omitting some small shadow areas and misclassifying some dull red roof pixels as shadow pixels. [PERSON] et al. [23] proposed a simple and automatic shadow detection method. In this method, a shadow mask was achieved by delineating shadow and nonshadow regions in the VHR image with a geometric model of the scene and the solar position. Then, the shadow mask was refined by applying a matting method to the image. This method performed well for detecting fine shadows and shadows within water regions. However, some small shadow areas were ignored in the detecting shadow process. Besides, the geometrical information for the scene and the solar position is usually unavailable, and two-step shadow detection is time-consuming. For efficiency and simplicity, the reviewed shadow detection algorithms [11; 14; 18; 19; 20] are selected for comparing algorithm performance with that of our proposed shadow detection approach. In this paper, a mixed property-based shadow index (MPSI) is developed for detecting shadows in VHR multispectral remote sensing images, especially to further address the problem where true shadow areas are more or less omitted and vegetation cover types in nonshadow areas are usually wrongly classified as shadows to somewhat. This developed approach employs the difference in properties between shadows and nonshadows with respect to the chromaticity (specifically for the hue component) and the luminance (namely, the intensity component) in HSV invariant color space, and the reflectivity difference properties between shadow regions and vegetation cover in nonshadows in terms of multispectral bands (visible bands and near infrared band). Based on these properties, rough shadow images are first obtained. Then, final shadow images are generated with an optimal threshold on the rough shadow images. The rest of the paper proceeds as follows. Property analysis and the proposed shadow detection approach are described in Section 2. Section 3 presents the experimental conditions and comparative experiment results on three test images of the multispectral WorldView-3 remote sensing images of Rio de Janeiro, Brazil in comparison with five standard shadow detection algorithms [11; 14; 18; 19; 20]. After that, these comparative experiment results are discussed in Section 4. Finally, conclusions are drawn in Section 5.