## 1 Introduction  
Human motion analysis is particularly relevant nowadays both for clinical purposes and for biomechanics research. For instance, loading conditions in human joints can be investigated through musculoskeletal analyses, to evaluate the effects of a therapeutic or surgical treatment, or to guide the clinician in the diagnosis of postural irregularities. Although different systems are available today to perform the acquisition of the human movement, such as inertial measurement units whose applications can be increasingly observed in the recent literature [1], most of the analyses are still conducted, especially at clinical level, through motion capture (stereo-photogrammetry) systems [2]. These systems typically involve passive reflective markers that are fixed on the surface of body segments (such as the trunk or a limb) and that are tracked by multiple cameras in a controlled environment. The number and the positioning of the markers selected for each body segment have an impact on the quality of the measurement and on the following analyses [3, 4]. In particular, the marker reference positions are often used to implement biomechanical models that enable the estimation of the kinematics and dynamics related to a single segment or, most likely, to a group of segments up to the whole body. Although commercial motion capture systems can already implement the most accepted and widely recognized marker positioning protocols and related biomechanical modeling [5, 6, 7, 8], there is still interest in the development of new techniques and models for the investigation of human motion, especially when subject-specific analyses are required. Among the several aspects that can be investigated by full dynamic analyses of human motion, or through a gait analysis, joint biomechanics still represents one of the most relevant to focus on, since an improved understanding of the mechanisms behind the functionality of a human joint enables more sophisticated clinical analyses to be developed, in addition to a more detailed knowledge of the degrees of freedom (DoFs) of the motion allowed by an articulation. In particular, such knowledge can be critical when a device that directly interacts with a human joint is designed [9; 10; 11; 12; 13]. In those situations, the kinematic or dynamic models already developed and implemented in commercial motion analysis systems could not be sufficient to describe the joint behavior with such a detailed approach. Since the actual anatomical segments are not rigid, nor is the fixation of the markers on each segment due to skin sliding and soft tissue artifacts [14], the definition of traditional biomechanical models, based on rigid body motion, is subjected to several sources of errors that, in most cases, cannot be estimated and prevented appropriately. These errors indirectly affect the estimation of joint centers and axes that are necessary for the related kinematic and dynamic analyses [15; 16]. For this reason, several techniques proposed in the literature have tried to tackle those issues, which are certainly evident during in vivo analyses [17; 18; 19]. Functional methodologies for joint kinematics estimation do not rely on regression equations and on specific marker positioning protocols, unlike predictive techniques [20]. In such approaches, it is still necessary to track the motion of each segment, e.g., by fixing a certain amount of markers on the body of the subject; however, the outcome of the analysis mainly depends on the ability of the methodology to estimate the relative motion between each couple of segments under investigation. Thanks to their formulations, functional methods can enable the analysis of kinematic abnormalities and non-standard subjects with deformities. Of course, any alteration to the positioning of each marker relative to the underlying bone due to skin sliding still affects the quality and the accuracy of the results [16].