## 1 Introduction  
COVID-19 has posed great challenges to the public globally since the first case of unknown pneumonia detected in humans in December, 2019. On 30 January 2020, the World Health Organization (WHO) announced that the epidemic of COVID-19 was listed as a public health emergency of international concern (PHEIC). In March 2020, the World Health Organization further announced that the outbreak of COVID-19 constituted a global pandemic. By 10 July 2022, 561 million cases of COVID-19 had been confirmed, including over 6 million deaths, according to WHO's report [1]. During the continuous outbreak of the COVID-19 epidemic, various mutants such as Delta and Omicron emerged, which led to an explosive increase in the confirmed cases, requiring effective epidemic prevention and control measures. With the rise of new and more transmissible sub-variants of BA.4 and BA.5 [2], it seems the COVID-19 pandemic is far from over yet. Wearing face masks is an important measure to prevent the transmission of diseases among people. Hence, face mask wearing in public places is still encouraged or even mandatory [3]. To ensure the effectiveness of face masks, according to the guidelines of WHO, one should wear face masks correctly (i.e., making sure the nose, mouth and chin are all covered). Therefore, some countries in the epidemic established monitoring systems to guide people to put on face masks properly in public places, such as public transportation, shopping malls, hospitals, etc. Meanwhile, many researchers have worked on effective face mask detection methods and hardware systems. With the large amount of papers dealing with face-mask detection methods and hardware systems, it is natural to take stock to effectively review these papers for the adoption of those more efficient face-mask detection methods and hardware systems in practical use. While several review papers on this topic have been published in the past years [4; 5; 6; 7], a common limitation of these review papers is that they all mainly concentrate on reviewing the methodologies and software developed, i.e., without reviewing face-mask detection hardware systems properly and systematically. Moreover, while incorrect mask-wearing has been touched upon by some of the review papers [4; 5], no in-depth review is available as of yet. With this background, in this paper, we review face-mask detection methods by singling out both the two-class and three-class cases, where two-class refers to wearing a mask and without mask and three-class has an extra class of incorrect mask-wearing. The main gap between the two cases is analyzed. Moreover, we reviewed papers on face-mask detection hardware systems specifically. In addition, a new framework is introduced to handle the incorrect mask-wearing detection task in the absence of training data of the third class. The main contributions of the study are as follows:  
* We present an up-to-date review of recent face-mask detection methodologies in both two-class and three-class cases and investigate the gap in techniques between them. * We provide an additional review and analysis on mask-face detection hardware systems. Various techniques of implementing mask-face detection models into portable systems are also considered. * We develop a new Out-of-distribution-Mask (OOD-Mask) detection framework, which can perform three-class mask-face detection with only two-class data of wearing a mask and without mask. The outline of the remainder of this paper is as follows: We first explain our review strategy in Section 2. Then, we make a brief summary in Section 3 of commonly used evaluation criteria and previous review papers on mask-face detection methodology in recent years. Following that, we provide a review of face-mask detection methodologies in terms of both two-class and three-class features in Section 4, as well as a review of face-mask detection hardware systems in Section 5. In Section 6, we introduce the new OOD-Mask detection framework, including its implementations and experiments.