The presence of urban shadows in optical satellite images with high spatial resolution limits the application of remote sensing technology in urban areas. These shadows can misrepresent image information

thereby generating potential errors in the derivation of surface parameters such as surface reflectance and reflectance-based indices. Thus

these shadows must be corrected and their radiance information restored to improve the effectiveness of remote sensing images. Many shadow correction methods have been developed according to the complex statistical relationships between shadowed and sunlit areas because the former maintains weak spectral radiance information. In addition

another physical relationship has often been detected between shadowed and sunlit areas

namely

the reflectance equality relationship（ RER）. This relationship can be regarded as the reflectance of the fact that similar-type features can be identical in both a shadowed area and its nearby sunlit area under the Lambertian surface condition.RER is generally independent of shadow detection processing; nonetheless

this relationship has not been fully considered in the development of shadow restoration algorithms. In this study

an RER-based（ RERB） method were derived to correct the shadowed areas in optical multispectral satellite imageries of urban areas according to the principles of radiance transfer processes. This approach reduces the number of parameters; thus

it can lower the risk of errors propagated by the uncertainties of additional parameters. The new RERB method is tested via Geo Eye-1 and Quick Bird multispectral imageries with high spatial resolution in two different urban areas（ Beijing and Enschede） that exhibit many urban building shadows. As per a comparison of this method with the widely used mean and variance transformation method

the former can restore the colors

texture

tone

and brightness of the shadowed areas in the image to a visually satisfactory level. Quantitative analysis results suggest that the RERB method can help restore the reflectance of shadowed asphalt roads accurately

with a mean error of 7%. This method can also be used to effectively restore the spectral shape information on shadowed features; this information is particularly important when the RERB method is applied to restore multispectral imagery for classifying an image based on spectral information and band indices. Another RERB shadow correction strategy that restores shadow surface reflectance instead of apparent radiance is discussed as well; nonetheless

this strategy requires further study because much auxiliary data is needed.