# Advanced Statistical Analysis of 3D Kinect Data: A Comparison of the Classification Methods
## 1 Introduction  
Image analysis in medicine has been a popular topic in recent decades, and it is still evolving and finding further applications. Imaging techniques such as X-rays, computed tomography, and magnetic resonance imaging have been known and used for many years. However, new imaging methods have recently been developed (e.g., depth maps, 3D reconstructions, etc.) and their use in modern medicine is breathtaking.  
Thus, a new area of image analysis in medicine is beginning, which is expected to be useful for diagnosis, rehabilitation, or validation of the results. This area does not aim to replace clinicians (this would not even be possible), but it does aim to save their time and help to interpret the results. A number of specific applications for biomedical image analysis can be found in the literature; for example, image analysis can be used to diagnosea large number of neurological diseases [1; 2] or sleep apnea [3; 4]. Furthermore, movement analysis has been used in rehabilitation [5].  
It is possible to find a number of innovative diagnostic procedures based on image analysis. A research group based in Oklahoma University introduced a radiomics-based machine learning model to predict peritoneal metastasis in gastric cancer patients using a small and imbalanced computed tomography (CT) image dataset [6]. Meanwhile, 3D reconstruction also plays an important role in precise once-surgery [7].  
This paper is focused on 3D reconstruction and statistical analysis of mimetic muscle rehabilitation after head and neck surgery has caused facial paresis. The muscles of the face include all mimetic muscles innervated by the cranial nerve VII (facial nerve). Within the parotid gland, the facial nerve terminates by bifurcating into five motor branches. These innervate the muscles: temporal branch--innervates the frontalis, orbicularis oculi, and corrugator supercili; zygomatic branch--innervates the orbicularis oculi; buccal branch--inervates the orbicularis oris, buccinator and zygomaticus muscles; marginal mandibular branch--inervates the mentalis muscle; cervical branch--inervates the platysma. Two masticatory muscles (maseter, temporalis) that are supplied by the motoric portion of the cranial nerve V3 (mandibular nerve) also contribute to the contour of the face [8].  
In our analysis, we treat the measurements (i.e., trajectories of selected points on a face) as functional data. Functional data analysis has been applied in many diverse areas, including (bio)medical data. Let us recall the earlier review paper [9] and a more recent paper [10], to name just a few. Besides the parametric model, we also applied a non-parametric approach that is based on (ordinal) random forests. A very recent application of random forests for clinical risk prediction based on complex data can be found in [11].  
Clinicians require an objective, reliable, and valid clinical tool to accurately describe a patient's facial function, to monitor status over time, and to assess the course of recovery and the effects of treatment. For a grading system to have clinical usefulness, it must be easy to administer, require little time or equipment, and be sensitive enough to detect clinically important changes [12].  
This work builds on previous publications and the work of several research groups dealing with similar topics [13].