Vorticity Transport Equation‐Based Shadow Removal Approach for Image Inpainting

ABSTRACT Shadows are common in many types of images, causing information loss or disturbance. Shadow removal can help improve the quality of the digital image. If there is no effective information available to restore the original image in the shaded area, the interpolation‐based inpainting technique can be used to remove the shadow from the digital image. This image inpainting technique typically involves establishing and solving partial differential equations (PDEs), an iterative solving process that is very time‐consuming. To solve the time‐consuming problem, a method that introduces the fast marching method (FMM) into the vorticity transport equation (VTE) is demonstrated. VTE is a type of partial differential equation describing two‐dimensional fluids. FMM is a numerical scheme for tracking the evolution of monotonically advancing interfaces via finite difference solution of the eikonal equation. The proposed method contains three main steps: (a) by investigating the relationship between VTE and the traditional PDE‐based image inpainting method, a new image inpainting model using VTE is developed;(b) the area to be inpainted is divided into boundaries that shrink in layers from the outside inwards using FMM; and (c) the VTE image inpainting model is converted into a weighted average form to coordinate with FMM. The visual and quantitative evaluation of the experimental results of shadow removal shows that the proposed method outperforms PDE‐based and state‐of‐the‐art methods in terms of shadow‐removal effect and running time. The results also show that our method excels at inpainting images with near‐smooth textures and simple geometric structures and where the pixels to be inpainted are continuous with neighbouring pixels.