## 1 Introduction  
More complex details of land covers (e.g., buildings, towers, vegetation, farms and roads) are obtained easily from high spatial resolution (HSR) multispectral satellite remote sensing images which are captured by the recently launched HSR satellites (like IKONOS, GeoEye-1, QuickBird, WorldView-2, WorldView-3 and Jilin-1) [1; 2; 3; 4; 5; 6; 7]. However, shadow inevitably formed by land objects and clouds affects more seriously for these HSR image applications, such as change detection, object recognition and image classification. Additional cues are obtained from the HSR images with the palpable shadow, such as the general shape and structure of cast objects, the illumination direction and the position of the sun, as well as parameters of the satellite sensor. These cues are also helpful in numerous applications, like building detection, height estimation, 3D reconstruction, change surveillance, scene interpretation and position estimation of the sun and satellites [4; 5; 8; 9; 10; 11; 12]. On the other hand, shadow in HSR images may cause serious shape distortion of cast objects, false color tone and loss of feature information, which may result in negative effects in subsequent image applications [13]. Given either the useful or troublesome influence of shadow in HSR multispectral satellite remote sensing images, in order to improve the utilization of HSR multispectral satellite remote sensing images, shadow detection is an important scientific issue for HSR multispectral remote sensing images, which is usually the first step followed by shadow compensation and image utilization [9; 12; 14]. Much research has been developed on shadow detection for both color aerial images and multispectral satellite remote sensing images in recent decades. [PERSON] et al. [15] proposed a shadow detection method through developing an imaging model indicating the increased amount of hue values in shadow regions compared with the corresponding nonshadow ones. A certain threshold was employed to obtain shadow candidate in accordance with the increased hue values in shadow regions, and two other thresholds were subsequently used with respect to blue (B) and green (G) components to refine the shadow candidate by eliminating greenish and bluish nonshadow objects. [PERSON] et al. developed a useful imaging model and the deduced shadow detection algorithm was firstly dedicated to resolving the bluish and greenish nonshadow object misclassification problem in color aerial images, even though thresholds were selected manually. Moreover, [PERSON] et al. [16] proposed a C3 shadow detection method by studying the shadow identification results of both IKONOS and QuickBird multispectral images through C1, C2 and C3 components in the color space C1C2C3, respectively. The C3-based algorithm could identify the broad outline of large shadow regions. However, most greenish nonshadow objects were misclassified. Similarly, [PERSON] et al. [17] presented a semi-automatic shadow detection algorithm built on the C3 component of C1C2C3 color space and a region-growing procedure for HSR pan-sharpening satellite remote sensing images. Comparative experiments revealed that the presented shadow detection approach achieved higher accuracies and better robustness against the RGB-based algorithm by [PERSON] et al. [15] and the C3-based algorithm by [PERSON] et al. [16] Considering all available bands of the multispectral image, [PERSON] et al. [18] proposed a modified C3 (MC3) index through developing an improved C1C2C3 invariant color space by employing the near-infrared (_NIR_) band information in addition to visible bands (i.e., red (R), green and blue bands) in the original C1C2C3 invariant color space. Then, the shadow was segmented with a bimodal histogram threshold. The MC3 method delivered an improved performance by picking up the _NIR_ component into consideration in contrast to the C3 method by [PERSON] et al. [16] and [PERSON] et al. [17].