The monitoring of respiratory rate is a relevant factor in medical applications and day-to-day activities. Contact sensors have been used mostly as a direct solution and they have shown their effectiveness, but with some disadvantages for example in vulnerable skins such as burns patients. For this reason, contactless monitoring systems are gaining increasing attention for respiratory detection. In this paper, we present a new non-contact strategy to estimate respiratory rate based on Eulerian motion video magnification technique using Hermite transform and a system based on a Convolutional Neural Network (CNN). The system tracks chest movements of the subject using two strategies: using a manually selected ROI and without the selection of a ROI in the image frame. The system is based on the classifications of the frames as an inhalation or exhalation using CNN. Our proposal has been tested on 10 healthy subjects in different positions. To compare performance of methods to detect respiratory rate the mean average error and a Bland and Altman analysis is used to investigate the agreement of the methods. The mean average error for the automatic strategy is 3.28 ± 3.33% with and agreement with respect of the reference of ≈98%.