Velocity Estimation From a Single Linear Motion Blurred Image Using Discrete Cosine Transform

There is a growing trend to use a digital camera as an instrument to measure velocity instead of a regular sensor approach. This paper introduces a new proposal for estimating kinematic quantities, namely, the angle and the relative speed, from a single motion blur image using the discrete cosine transform (DCT). Motion blur is a common phenomenon present in images due to the relative movement between the camera and the objects, during sensor exposure to light. Today, this source of kinematic data is mostly dismissed. The introduced technique focuses on cases where the camera moves at a constant linear velocity while the background remains unchanged. 2250 motion blur pictures were shot for the angle experiments and 500 for the speed estimation experiments, in a light and distance controlled environment, using a belt motor slider driven at angles between 0° and 90° and 10 preset speeds. The DCT Hough and DCT Radon results were compared to discrete Fourier transform (DFT) Hough and DFT Radon algorithms for angle estimation. The mean absolute error of the DCT Radon method for direction estimation was 4.66°. In addition, the mean relative error for speed estimation of the DCT Pseudocepstrum was 5.15%. The innovative DCT frequency analysis proposals were more accurate than all competitors evaluated for the reconstruction of the point spread function that enables calculation of relative velocity and motion direction. These results demonstrate that cameras as an instrument can be used to measure velocity even using a single linear motion blur degraded image.