# Image Shadow Removal Using End-To-End Deep Convolutional Neural Networks
## 1 Introduction  
Today's world is an era of rapid information development. With the continuous upgrading of multimedia technology and electronic products, human beings are exposed to more multimedia information such as text, images, and audio in their daily life. Most of this multimedia information is obtained through people's visual systems. We define the multimedia information obtained through this channel as an image. However, when the image is acquired, it is susceptible to various conditions that generally degrade the quality of image. Shadows are one of them. Shadows are a phenomenon of quality degradation caused by imaging conditions. These conditions lead to missing or interfered information reflected by the target; therefore, the interpretation accuracy of the image is sharply reduced, and it affects various quantitative analyses and applications of the image. Shadow detection and removal [1; 2; 3; 4] is one of the most basic and challenging problems in computer graphics and computer vision. The removal of shadow images are important pre-processing stages in computer vision and image enhancement. The existence of shadow not only affects the visual interpretation of the image, but also affects the analysis of the image and the subsequent processing results. For instance, a darker area (caused by shadows) introduces incorrect segments in imagesegmentation [5; 6]; radiation changes (caused by shadows) reduce the performance of the target recognition [7] system; and the presence of shadows reduces the performance of the target tracking [8] system. Therefore, it is necessary to perform shadow detection and analysis on the image in order to reduce or eliminate the influence of the image shadow, it also increases the visual authenticity and physical authenticity of the image through editing and processing. Shadows are generated by different illumination conditions, and the shadow image \(I_{s}\) is represented by the multiple of the shadow-free image \(I_{sf}\) and the shadow ratio \(\alpha\) (pixel level \(\otimes\)) according to [9; 10; 11], as shown in (1). \[I_{s}=\alpha\otimes I_{sf}. \tag{1}\]  
Shadows can be divided into two categories according to different causes [12]: one type is self-shadow, which is produced by the occluded object itself not being illuminated by the light source; the other type is projection (cast shadow), which is caused by an object blocking the light source while producing shadows on the surface of other object. The projection is further divided into an umbra zone and penumbra zone, wherein the umbra zone is formed by completely direct ray-blocking, and the penumbra zone is partially blocked by light. Given a single shadow image, shadow removal aims to generate a high-quality, shadow-free image with the original shadow image area restored to the shadow-free image in texture, color, and other features. Existing methods of removing shadow regions typically involve two steps: shadow detection and shadow removal. Firstly, shadow detection is used to locate the shadow area [13; 14] or the user manually marks the shadow area [9; 15; 16], then the model is constructed to rebuild both and to remove shadows. However, shadow detection is an extremely challenging task. Traditional physics-based methods can only be applied to high-quality images, while statistical learning-based methods rely on features that users have to manually label [15; 17]. With the development of neural networks, convolutional neural networks (CNNs) [14; 18; 19] are used to learn the features of shadow detection. CNNs overcome the shortcomings of traditional methods that require high-quality images and manual annotation features. However, they still limited to small network architectures, owing to the shortage of training data. Similarly, even if the shadow area is known, it is still a challenge to remove it. At the same time, it can be clearly understood that the effect of shadow detection will seriously affect the result of shadow removal.