In this paper, a Hidden Semi-Markov Model (HSMM) based approach is proposed to evaluate and monitor body motion during a rehabilitation training program. The approach extracts clinically relevant motion features from skeleton joint trajectories, acquired by the RGB-D camera, and provides a score for the subject’s performance. The approach combines different aspects of rule and template based methods. The features have been defined by clinicians as exercise descriptors and are then assessed by a HSMM, trained upon an exemplar motion sequence. The reliability of the proposed approach is studied by evaluating its correlation with both a clinical assessment and a Dynamic Time Warping (DTW) algorithm, while healthy and neurological disabled people performed physical exercises. With respect to the discrimination between healthy and pathological conditions, the HSMM based method correlates better with the physician’s score than DTW. The study supports the use of HSMMs to assess motor performance providing a quantitative feedback to physiotherapist and patients. This result is particularly appropriate and useful for a remote assessment in the home.

Introduction
The aging of the population is rapidly becoming a global phenomenon and the incidence of chronic diseases is influencing the public budget allocation [1]. The treatment and prevention of motor disabilities can be efficiently faced through a task-oriented, continuous and context interactive rehabilitation program [2], [3]. In this scenario, telerehabilitation is a solution for delivering services at home, supporting patients and clinicians by minimizing the barriers of distance, time and cost. Although telerehabilitation platforms, based on vision and wearable sensors, are widely spread [4], [5], [6], continuous monitoring of body motion and an accurate evaluation of rehabilitation therapy remain a challenge.

In literature, human motion assessment approaches can be divided into two main categories [7]: rule and template based. In the rule based approach, experts (e.g., medical staff) identify some motion descriptors, a set of rules (e.g., angles, joints position, relative distance, velocity), which define the “motion sample”. In the template based approach, a motion sequence is recorded a priori and then used as an exemplar to be compared with the observations, through action similarity approaches or using a trained probabilistic model.

The main advantage of the template based approach is the automatic assessment process that can be easily generalized to different types of exercise. On the other hand, the rule based method is less computationally expensive and provides a motion assessment with specific functional feedback (e.g., “Is the primary objective of the exercise reached?”), particularly useful in the rehabilitation context. In addition, the medical staff defines the rules of each movement according to the motor-functional scope and postural constraints of the exercise. These rules satisfy the invariance property of the movement and normalization or scaling is not needed. Nevertheless, drawbacks of the rule based approach are the lack of generalization and reusability for different exercises. This leads to a large rule data set, difficult to synthesize within a telerehabilitation framework. Moreover, when the complexity of the movement increases, it may be difficult to precisely map the rule and to obtain an accurate movement assessment.

The goal of this study is to test the feasibility and reliability of a Hidden Semi-Markov Model (HSMM) based approach to rehabilitation assessment. The novelty, introduced in this work, lies in combining aspects of the rule and template based methods, in order to overcome their drawbacks.

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