Measuring 3D Vibrations Amplitude with a Single Camera and a Model of the Vibrating Structure

We propose a method to measure the vibrations amplitude of normal modes of a 3D mechanical structure with only one camera. Our method requires only a video sequence taken by a single camera and a collection of admissible 3D deflection shapes. The deflection shapes are projected in the image frame of the camera. This is done thanks to a linearization of the perspective projection model. Comparing the motion of targets seen by the camera and the motion of 2D deflection shapes at the same location gives the time evolution of modes amplitude. Finally, the motion of the model is reconstructed in 2D in the image frame and in 3D in the world frame. By following this procedure, vibration amplitude can be magnified applying a scale factor on a modal basis covering a large frequency bandwidth.