# Discrete HMM for Visualizing Domiciliary Human Activity Perception and Comprehension
## 1 Introduction  
The trend of aging societies has attracted much attention globally, as an increasing elderly population is accompanied with gradually decreasing long-term care and nursing manpower. Advances in autonomous AI have led to the feasibility of developing AI robots for elderly care. To investigate AI-based autonomous robots for elder care, visual human activity recognition by AI machines plays a preliminary role for perceiving a user's mental and physical states as well as their daily life activities, etc. For example, elderly people without mobility may use summing gestures to summon a robot for a drink of water, follow-me gestures to monitor their activities, or stop gestures to control a robot's movements. To reach such a goal, this work proposed discrete hidden Markov models (D-HMMs) for visual human activity recognition of eleven daily home activities, using a binocular camera with a Kinect v2 RGB-D sensor to extract embedded skeleton information and to further recognize human sequential poses to understand the implications for specific human activities. Human activity recognition [1] has generally been categorized into two approaches, i.e., vision based [2; 3; 4] and sensor based [5; 6; 7]. The vision-based approach to human activity recognition utilizes computer vision methodology to reach a compromise between privacy consideration and light dependency and to report initial approaches for human activityrecognition [5]. The sensor-based approach to human activity recognition has also been categorized into optical and non-optical methods [8; 9]. The optical method applies a binocular camera with an RGB-D sensor with active or passive markers to sense a person, whereas the non-optical method uses inertial measurement units (IMUs) or a magnetic system, for more complex environments [10]. For feature extraction, frame-based vision systems process frames or sequences using visual sensors in two individual steps, where the outcome is highly dependent on the quality of the captured frame [8]. Conventional computer vision algorithms process each informational frame individually, regardless of the noisy frame chip for performance efficiency, merely keeping the change rate in the scene similar to the frame rate, wherein practical applications are sometimes without any movement or in moments of fast or noisy motions. In addition, [11] reported that the performance of human activity recognition was also affected by several sources of variation, including, perspective, anthropometry, execution rate, personal style, etc. HMMs are numerical methods that focus on representing and learning the sequential and temporal characteristics in activity sequences for human activity recognition. Such dynamic models provide simple and efficient models for learning; however, performance decreases if activities become complex for the Markov assumption [12; 13; 14; 15]. To overcome this shortcoming, explicit duration HMMs [16], segmental HMMs [17], and layered HMMs [18; 19] have been investigated to extend HMMs and to enhance the capability of distinguishing among classes. In this work, discrete HMMs [20; 21; 22] are used for human activity recognition of eleven proposed daily activities in a home scenario. An RGB-D camera is used to capture a total of 25 skeletal joints along the entire human body skeleton, in which a set of feature points can be extracted for classification of the different poses; however, in this work, only ten skeleton joints are required for pose comprehension. Secondly, the relative positions of the ten selected skeletal joints are transformed from a Cartesian coordinate system into a spherical coordinate system for robustness on position invariance. Thirdly, the features are quantized into vectors, such that the sequential observations can be treated as a type of pose in terms of an observation sequence.