## 1 Introduction
Additionally, based on the [PERSON]'s imaging model [15] and the [PERSON] illumination model [19], [PERSON] [20] presented an automatic property-based shadow detection approach utilizing the ratio of hue value over intensity value, called the spectral ratio index (SRI) shadow detection method. Subsequently, the Otsu thresholding method [21] was used to determine an optimal threshold automatically. The SRI algorithm was tested with comparative studies in various invariant color spaces (HIS, HSV, HCV, YIQ and YCbCr) for color aerial images. The comparative results showed that the SRI shadow detection approach drew higher shadow detection accuracies in HIS, YIQ and YCbCr color spaces, though some greenish grass in nonshadow regions was still misclassified more or less. Subsequently, [PERSON] et al. [22] further enhanced the shadow detection results of the SRI algorithm by [PERSON] [20] particularly in the YIQ invariant color space by using a series of post-processing methods (e.g., histogram equalization and box filter). Comparative experiments in color aerial images against the original SRI images of [PERSON] showed that the enhanced shadow detection method improved the shadow omission problem in the visual aspect. On the foundation of [PERSON]'s efficient shadow detection algorithm, [PERSON] et al. [23] proposed a modified ratio map by applying an exponential function to the SRI by [PERSON], and presented a successive thresholding scheme (STS) rather than only using a global threshold [20]. Experiments in color aerial images revealed that the proposed algorithm by [PERSON] et al. [23] showed an improved performance in detecting shadow in images containing low brightness objects. Inspired by the STS procedure by [PERSON] et al. [23]. [PERSON] et al. [24] extended the SRI method by [PERSON] [20] specifically in the CIELCh color space by applying a natural logarithm function to the original ratio map to compress the original values, resulting in the logarithmic spectral ratio index (LSRI) algorithm. Then, the ratio map was segmented by applying multilevel thresholding. This modified ratio method performed better in color aerial images by accurately detecting shadow and avoiding misclassifying dark areas compared with the original ratio method by [PERSON] [20] and the STS method by [PERSON] et al. [23]. In addition, [PERSON] et al. [25] presented a similar shadow detection method based on the normalized saturation-value index (NSVDI) in the HSV color space. A rough shadow index image was formed at first with the NSVDI method. Then the rough shadow index image was segmented to obtain the final shadow image with a certain threshold. This NSVDI method performed well in detecting large shadow in IKONOS multispectral images despite omitting some small shadow. [PERSON] et al. [26] also presented a shadow detector index (SDI) for shadow detection in HSR multispectral satellite remote sensing images. The SDI algorithm was developed by first analyzing the difference between shadow and typical nonshadow, particularly for vegetation, in terms of green and blue components, and subsequently applying the neighborhood valley-emphasis method (NVEM) to binarize the SDI index image for obtaining the shadow image [27]. The SDI approach performed well in classifying shadow from vegetation, and acquired high shadow detection accuracies, except for the shortcomings of some small shadow omission and misclassification of some dull red roof. Though an increasing number of shadow detection algorithms have been put forward for detecting shadow in HSR multispectral satellite remote sensing images and color aerial images in recent years, shadow detection problems still need a further settlement, mainly including high small shadow omission and typical nonshadow misclassification (like bluish and greenish dark nonshadow misclassification, as well as large dark nonshadow misclassification). Therefore, shadow detection is still challenging for HSR multispectral satellite remote sensing images.