## 1 Introduction  
With the development of aerospace techniques, an increasing number of very high-resolution (VHR) satellites have been launched in recent years, such as Ikonos, QuickBird, Pleiades, GeoEye, RapidEye, Skysat-1, WorldView-2, WorldView-3, Jilin-1, and Kompsat [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]. The VHR multispectral remote sensing images captured by these satellites can depict more details of typical land cover, including buildings, vegetation and roads. Along with the improvement in the optical spatial resolution, shadow interference in these multispectral remote sensing images has become more serious. Obviously, shadow analysis is more important than ever before for these VHR multispectral remote sensing image applications. Shadow occurs when ground objects are illuminated by the sun or other light sources. Additional clues can be obtained through analyzing the related shadows,which provide information about the position of the light source as well as the shape and the structure of ground objects. Since shadows in VHR multispectral remote sensing images indicate additional information about ground objects, shadows may supply useful information for applications such as buildings reconstruction and height evaluation [11; 12]. Notably, shadows always result in loss and distortion of land cover within shadow regions, because shadow regions always present low radiance and different spectral reflectivity properties from nonshadow areas [3; 13; 14; 15; 16; 17]. However, objects in shadow regions may contain significant information, especially in VHR multispectral remote sensing images. Given this situation, detecting shadows effectively plays a role in the analysis of VHR multispectral remote sensing images. Besides, though a wide range of research has explored shadow detection, shadow pixels are still more or less omitted and wrongly confused with vegetation pixels in some cases, and these traditional shadow detection methods are usually aimed at detecting shadows in middle resolution remote sensing images rather than in VHR multispectral remote sensing images [11; 12; 13; 14; 18; 19; 20]. Therefore, well-performed shadow detection approaches for VHR multispectral remote sensing images are necessary for effectively detecting shadows especially targeted at further managing problems of shadow omission and vegetation misclassification. During recent decades, an increasing number of shadow detection approaches have been developed for analyzing remote sensing images. In general, the related works on shadow detection are usually categorized into either model-based or property-based methods. The model-based methods require prior knowledge about the scene, the sun, and sensors, such as the geometry of the scene, solar elevation and azimuth, the altitude and acquisition parameters of sensors, etc. [21; 22; 23; 24]. Though the model-based technique usually presents desirable performance in shadow detection in specific applications, it is limited by the unavailability of some required prior information. The shortcomings of the model-based methods mentioned above are effectively overcome with the latter method. The property-based methods identify shadows with shadow characteristics, such as spectral features and geometrical information. Due to its accuracy and simplicity, the property-based methods are being widely explored in the literature [11; 18; 19; 24; 25; 26; 27; 28; 29]. In the property-based group, a certain shadow index image is first generated--in most related works--which usually exploits functions of multispectral bands either directly or indirectly based on the analysis of multispectral remote sensing images. Then, the index image is thresholded by some automatic threshold methods, after which the resulting shadow image is presented. Many researchers at home and abroad have made efforts in these two aspects, attempting to either develop new shadow image indexes, or modify or present improved thresholding methods for better detecting shadows in multispectral remote sensing images.