## 1 Introduction
[PERSON] and [PERSON] [30] present a remote respiratory monitoring system to magnify motion using the Wavelet decomposition obtaining smaller errors in RR estimation than with use of traditional Laplacian decomposition. Other works [27; 32] show that the magnification Hermite approach allows a better reconstruction and a better robustness to the noise than traditional Laplacian decomposition used in [22]. The camera distance to the subject is an important parameter; in general, systems use short distances but as shown by [PERSON] et al. [23], magnification techniques allow usage of long ranges for monitoring vital signs. Another important characteristic is the possibility of processing after magnification using other techniques as optical flow [24]. Major research using motion-detection techniques to estimate RR is reviewed and summarized in Table 1. Most studies listed in Table 1 were limited to use of motion magnification method from a single subject and for short distances. In this Table 1, the characteristics of each method to extract RR is summarized: choice of ROI (manually [20; 29; 30], automatically [18; 24; 25], or not ROI [26] ), the kind of signal extracted to estimate RR (raw respiratory signal [18; 20; 24; 25] or binary signal corresponding to inhalations and exhalations [26; 29; 30]), the method to obtain motion (amplitude magnification [24; 29; 30], phase magnification [25; 26], frame subtraction [18]), the obtaining of the reference used to validate the method (visually using magnified video directly [24; 26; 29; 30], using an electronic device [20; 25; 26]) and the number of subjects used in the work to validate the method. All works in this review use their own database. In the last column in Table 1 the metric error to measure the assessment of each method is shown. Most methods use Mean Absolute Error (MAE) defined as the absolute value of the difference between the reference value and the estimated value with units of breaths per minute (bpm), or its version in percentage, normalizing the error by reference value. Other works [25] use Root Mean Squared Error (RMSE) between estimated RR and the reference one. Bland-Altman (BA) analysis [33] was used to obtain the Mean of the Differences (MOD) between the reference value and the estimated value and the limits of Agreements (LOAs) values that are typically reported in other studies and very useful for comparing our results to relevant scientific literature [20, 30]. In addition, correlation coefficients as Spearman coefficients (SCC) and Pearson coefficients (PCC) are also reported in some works [30]. In this paper, we present a combined strategy using motion magnified video and a Convolutional Neural Network (CNN) to classify inhalations and exhalations frames to estimate respiratory rate. First, a Eulerian magnification technique based on Hermite transform is carried out. Then, the CNN is trained using tagged frames of reconstructed magnified motion component images. Two strategies are used as input to the CNN. In the first case, a region of interest (ROI) is selected manually on the image frame (CNN-ROI approach) and in the second case, the whole image frame is selected (CNN-Whole-Image proposal). The CNN-Whole-Image proposal includes three approaches: using as input the original video, the magnified video, and the magnified components of the sequence. Finally, RR is estimated from the classified tagged frames. The CNN-ROI proposal is tested on five subjects lying face down and it is compared to a procedure using different image processing methods (IPM) presented in [29, 30] to tag the frames as inhalation or exhalation, while the final CNN-Whole-Image proposal is tested on ten subjects in four different positions (lying face down, lying face up, seat and lying fetal). We compared the different approaches computing a percentage error regarding a visual reference of the RR.