**Xiaoqun Yu and Shuping Xiong \***

Department of Industrial and Systems Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Korea

**\*** Correspondence: shupingx@kaist.ac.kr; Tel.: +82-42-350-3132

Received: 9 May 2019; Accepted: 24 June 2019; Published: 28 June 2019

**Abstract:** Older people face difficulty engaging in conventional rehabilitation exercises for improving physical functions over a long time period due to the passive nature of the conventional exercise, inconvenience, and cost. This study aims to develop and validate a dynamic time warping (DTW) based algorithm for assessing Kinect-enabled home-based physical rehabilitation exercises, in order to support auto-coaching in a virtual gaming environment. A DTW-based algorithm was first applied to compute motion similarity between two time series from an individual user and a virtual coach. We chose eight bone vectors of the human skeleton and body orientation as the input features and proposed a simple but innovative method to further convert the DTW distance to a meaningful performance score in terms of the percentage (0–100%), without training data and experience of experts. The effectiveness of the proposed algorithm was validated through a follow-up experiment with 21 subjects when playing a Tai Chi exergame. Results showed that the algorithm scores had a strong positive linear relationship (r = 0.86) with experts' ratings and the calibrated algorithm scores were comparable to the gold standard. These findings suggested that the DTW-based algorithm could be effectively used for automatic performance evaluation of an individual when performing home-based rehabilitation exercises.

**Keywords:** aging; physical function; rehabilitation exercise; Kinect; dynamic time warping; automatic coaching; exergame
