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The Point-In-Polyhedron problem is to check whether a point is inside or outside of a given polyhedron. When a degenerate case is detected, the traditional ray-crossing algorithms avoid the case by selecting a different ray or erase the case by perturbing input data. This paper introduces a Threshold-Based Ray-Crossing (TBRC) algorithm for solving the Point-In-Polyhedron problem. The TBRC algorithm copes directly with degenerate cases by checking whether to count the face intersecting with the ray.It is worth mentioning that the TBRC algorithm can handle all degeneracies without extra computation and storage. Moreover, we analyze the basic algorithm and examine how to accelerate it. The experimental results show that TBRC algorithm is highly efficient and robust for the Point-In-Polyhedron problem, compared to a classical tetrahedron-based algorithm without pre-processing.

Face Restoration (FR) aims to restore High-Quality (HQ) faces from Low-Quality (LQ) input images, which is a domain-specific image restoration problem in the low-level computer vision area. The early face restoration methods mainly use statistic priors and degradation models, which are difficult to meet the requirements of real-world applications in practice. In recent years, face restoration has witnessed great progress after stepping into the deep learning era. However, there are few works to study deep learning-based face restoration methods systematically. Thus, this paper comprehensively surveys recent advances in deep learning techniques for face restoration. Specifically, we first summarize different problem formulations and analyze the characteristic of the face image. Second, we discuss the challenges of face restoration. Concerning these challenges, we present a comprehensive review of existing FR methods, including prior based methods and deep learning-based methods. Then, we explore developed techniques in the task of FR covering network architectures, loss functions, and benchmark datasets. We also conduct a systematic benchmark evaluation on representative methods. Finally, we discuss future directions, including network designs, metrics, benchmark datasets, applications, etc. We also provide an open-source repository for all the discussed methods, which is available at https://github.com/TaoWangzj/Awesome-Face-Restoration.

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