# Parallel Image Completion with Edge and Color Map
## 1 Introduction  
Image completion (a.k.a. image inpainting or image hole-filling) aims at synthesizing alternative structures and textures that visually realistic contents in the missing or damaged regions of an image. It is essential in many image editing tasks and has aroused wide interest in the computer vision and graphic community as it can be used for repairing damaged photographs or filling in holes left after removing the distracting objects from an image. It can also be extended to problems such as digital effect (e.g., object removal), image restoration (e.g., scratch or text removal in photograph), image coding and transmission (e.g., recovery of the missing blocks), rotation, stitching, retargeting, recomposition, super-resolution and many others. Therefore, the generated contents should either be as accurate as the original image, or simply fit well within the context such that the modification appears to be visually natural, photorealistic and semantically correct. In general, image completion can be divided into two categories: generic scene image completion and specific image completion (e.g., human faces). Due to the well-known compositionality and reusability of visual patterns, missing regions in the former usually have a high chance of finding similar patterns in either the surrounding context of the same image or images in an external dataset subject to the context. However, the latter cases are more specific, especially when a large essential portion of an image is missing. The objective of image completion should be not only photorealistic but also semantically consistent withthe surrounding image context at different scales. First, structural features should remain connected inside the missing region or across its boundary. Second, colorization should be plausible and spatially coherent that could potentially fool a human observer. Third, textures filled within the missing region should contain high-frequency details. In addition, missing object parts need to be recovered correctly, which is challenging and requires capturing high-level semantics. The core challenge of image completion problems lies in the inherent ambiguity of this ill-posed inverse problem and synthesizing content with reasonable details for the missing regions that are often not coherent with the surrounding areas. The main reason is that modeling the pixel distribution is difficult and the trained models easily introduce blurry components and artifacts when the dimensionality becomes very high. Therefore, sufficient prior information is required to achieve meaningful and visually believable results. There have been a number of studies attempting to solve this problem. These studies fall into two groups: data similarity driven methods with low-level features and data distribution based generative ones. Broadly speaking, methods in the first group can be classified into two categories: diffusion-based methods [1; 2; 3; 4; 5] and patch-based methods [6; 7; 8; 9; 10; 11; 12; 13; 14]. Diffusion-based methods solve Partial Differential Equations (PDE) [1] or similar diffusion systems, so as to diffuse the information from the known region into the missing region at the pixel level. They have achieved convincingly excellent results for filling narrow or small holes. However, they tend to introduce smooth effects in the textured region or larger missing region. Patch-based methods are capable of recovering large missing regions by copying suitable textures in the known contexts and then pasting them into the missing region from low-resolution to high-resolution at patch level. They can synthesize plausible stationary textures and perform particularly well in background completion tasks (e.g., grass, sky and mountain), and are widely deployed in practical applications [11].