Tannaka-Krein duality for finite 2-groups

Let $\mathcal{G}$ be a finite 2-group. We show that the 2-category $2\mathrm{Rep}(\mathcal{G})$ of finite semisimple 2-representations is a symmetric fusion 2-category. We also relate the auto-equivalence 2-group of the symmetric monoidal forgetful 2-functor $\omega : 2\mathrm{Rep}(\mathcal{G}) \to 2\mathrm{Vec}$ to the auto-equivalence 2-group of the regular algebra and show that they are equivalent to $\mathcal{G}$. This result categorifies the usual Tannaka-Krein duality for finite groups.Comment: 15 pages. Comments are welcom

Faithful completion of images of scenic landmarks using internet images

Abstract—Previous works on image completion typically aim to produce visually plausible results rather than factually correct ones. In this paper, we propose an approach to faithfully complete the missing regions of an image. We assume that the input image is taken at a well-known landmark, so similar images taken at the same location can be easily found on the Internet. We first download thousands of images from the Internet using a text label provided by the user. Next, we apply two-step filtering to reduce them to a small set of candidate images for use as source images for completion. For each candidate image, a co-matching algorithm is used to find correspondences of both points and lines between the candidate image and the input image. These are used to find an optimal warp relating the two images. A completion result is obtained by blending the warped candidate image into the missing region of the input image. The completion results are ranked according to combination score, which considers both warping and blending energy, and the highest ranked ones are shown to the user. Experiments and results demonstrate that our method can faithfully complete images

Efficient, edge-aware, combined color quantization and dithering

Abstract—In this paper we present a novel algorithm to simultaneously accomplish color quantization and dithering of images. This is achieved by minimizing a perception-based cost function which considers pixel-wise differences between filtered versions of the quantized image and the input image. We use edge aware filters in defining the cost function to avoid mixing colors on opposite sides of an edge. The importance of each pixel is weighted according to its saliency. To rapidly minimize the cost function, we use a modified multi-scale iterative conditional mode (ICM) algorithm which updates one pixel a time while keeping other pixels unchanged. As ICM is a local method, careful initialization is required to prevent termination at a local minimum far from the global one. To address this problem, we initialize ICM with a palette generated by a modified median-cut method. Compared to previous approaches, our method can produce high quality results with fewer visual artifacts but also requires significantly less computational effort. Index Terms—Color quantization, dithering, optimization-based image processing. I