## 4 Discussion  
This study examined whether an HMM trained using different types of coordinates derived from the same movement is able to detect significant variations in shoulder, elbow and load positional sequence, and therefore changes in movement pattern of the biceps-curl exercise. As demonstrated in Table 2, linear topology HMM, trained with Cartesian coordinates [47; 61] and corrected using environmental measurements, was able to detect significant adjustments in movement patterns in the sagittal plane, and this was confirmed by ANOVA. Therefore, the findings evidenced the confidence in HMM for detecting undesired joint positional adjustments when comparing the standard reference of simple human lift movement (e.g., single-joint action with no load) to the lift attempts with heavy loads. For the ANOVA test, maximal displacement values with the three different loads were provided, and the HMMs were trained with three executions for each load (0% or 25%) for comparison. With HMMs, the use of a small number of training models provides a more rigorous analysis and yields results that are in better agreement with the reference model [62]. In this study, we searched for the limits, aiming at no recognition of the pattern of the reference model. In other words, we searched for instances in which the movement pattern was altered. In this way, a minimum number of states were found to draw attention to the changes in movement pattern executed by each subject, and these states indicated movements that were inadequate for lifting the specific load. To dispense with the need for measurements of the environment and/or subject, HMM modeling was completed using only image coordinates. The positional sequence of coordinates provided by the markers while the subjects performed an upward movement with the barbell were obtained through HMM training and testing. Table 2 presents the results of these methods (nonmetric); they differ little from the results obtained using the environmental data. Of 36 cases shown to have significant variation in movements indicated by the environmental measurements, 31 were also identified by the method that uses only image coordinates, an agreement of approximately 86% between the methods. It is noteworthy that the analysis of the movement described in this work evaluates the adequacy of the movement by comparing the results with a reference that already presents great similarity to the analyzed movement. Wearable sensors that are used to identify movements that are made during different actions, such as movements in a badminton game for example, can provide accuracies of up to 97% in recognizing the type of movement [63]. The authors of the cited study also sought to discriminate the skill levels of professional and amateur badminton athletes, obtaining satisfactory accuracy values ranging from 83.3% to 90%, which is leveled with the percentage of recognition obtained by applying HMM in our research. Current studies in which wearable sensors are used to recognize daily activities such as walking, going up or down stairs, sitting, standing and lying down, achieve an accuracy of 93.77% in the recognition of these activities [64] in the absence of information about the skills or evolution of the practitioner. Hence, the accuracy in recognizing movement patterns from methods using image with no information on the metric of the environment has attaining ~90%, which is an average close to that observed for HMM. As in the work of [PERSON] et al. [65], to conduct an adequate comparison between methods, Bland-Altman agreement tests were used to compare the data load acquired with the image coordinates (CI) and the environmental data (CA). Figure 4 shows Bland-Altman plot comparisons of different methods of HMM modeling for all the loads tested. The plots show that the mean difference between methods is close to zero and that most of the obtained values are within the agreement limits. For the elbow, all values found are within the confidence interval.