985 Abstract Shadows, the common phenomena in most outdoor scenes, are illuminated by diffuse skylight whereas shaded from direct sunlight. Generally shadows take place in sunny weather when the spectral power distributions (SPD) of sunlight, skylight, and daylight show strong regularity: they principally vary with sun angles. In this paper, we first deduce that the pixel values of a surface illuminated by skylight (in shadow region) and by daylight (in non-shadow region) have a linear relationship, and the linearity is independent of surface reflectance and holds in each color channel. We then use six simulated images that contain 1995 surfaces and two real captured images to test the linearity. The results validate the linearity. Based on the deduced linear relationship, we develop three shadow processing applications include intrinsic image deriving, shadow verification, and shadow removal. The results of the applications demonstrate that the linear relationship have practical values. 1. Introduction Shadows are physical phenomena observed in most natural scenes. They often bring some undesirable problems in many computer vision and image analysis tasks such as edge detection, segmentation, target recognition, and tracking. Shadow processing is of great practical significance and has attracted a lot of attentions. The research on shadows may be generally categorized into the following three scopes. ĉ) Intrinsic image: Intrinsic image here is referred to an image insensitive to shadows. The simplest intrinsic image may be the chromaticity image. For example, in [1], the authors detect shadows by assuming hue component change within a certain limit in HSV space. Normalized RGB [2] and 1 2 3 ccc [3] are also simple features used to derive intrinsic images. Tian et al. [4] proposed a simple transformation to get intrinsic images based on detected shadows. Finlayson et al. [5] create an intrinsic image from a single image by finding the special direction in a 2D chromaticity feature space. In this paper, we deduce that the pixel values of a surface illuminated by skylight (in shadow region) and by daylight (in non-shadow region) have a linear relationship in each channel. Based on the linearity, we propose a new method which uses a RGB image to generate a grayscale intrinsic image. Ċ) Shadow detection: The most straightforward feature of a shadow is that it darkens the surface it casts on. This feature is adopted by some methods directly [6, 7] or indirectly [8, 9]. An intrinsic image is also useful for shadow detection, since shadows can be located by comparing the intrinsic image and the original one [3, 10]. In the moving shadow detections, the frame difference feature can be employed to locate moving objects and their moving shadows. Then the problem of shadow detection becomes differentiating the moving shadows from moving objects. To adapt to the changes of the background, learning approaches have proven useful [11-14]. Prati et al. [15] present a good review for moving shadow detection methods. Shadow detection in a single outdoor image is difficult but has wide applications. In [16], the authors use the Fisher distribution to model shadows with 3D geometry information as priori knowledge. Lalonde et al. [17] obtain impressive shadow detection results by using a learning method. ċ) Shadow removal: Shadow removal is often required in some computer vision applications. Many methods have been presented to do this work. A classical approach for shadow removal in a single image is to differentiate the image, set derivatives at shadow boundaries to zero, and then reintegrate the image to obtain a shadow free image [18]. This approach can produce good results on non-textured surfaces. The methods in [19] and [20] can effectively remove shadows while preserve image textures. Linearity of Each Channel Pixel Values from a Surface in and out of Shadows and Its Applications Jiandong Tian [1] State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang, P. R. China. [2] Graduate School of the Chinese Academy of Sciences, Beijing, P. R. China. tianjd@sia.cn Yandong Tang State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang, P. R. China. ytang@sia.cn