Probabilistic Modeling of Motion Blur for Time-of-Flight Sensors

Synthetically creating motion blur in two-dimensional (2D) images is a well-understood process and has been used in image processing for developing deblurring systems. There are no well-established techniques for synthetically generating arbitrary motion blur within three-dimensional (3D) images, such as depth maps and point clouds since their behavior is not as well understood. As a prerequisite, we have previously developed a method for generating synthetic motion blur in a plane that is parallel to the sensor detector plane. In this work, as a major extension, we generalize our previously developed framework for synthetically generating linear and radial motion blur along planes that are at arbitrary angles with respect to the sensor detector plane. Our framework accurately captures the behavior of the real motion blur that is encountered using a Time-of-Flight (ToF) sensor. This work uses a probabilistic model that predicts the location of invalid pixels that are typically present within depth maps that contain real motion blur. More specifically, the probabilistic model considers different angles of motion paths and the velocity of an object with respect to the image plane of a ToF sensor. Extensive experimental results are shown that demonstrate how our framework can be applied to synthetically create radial, linear, and combined radial-linear motion blur. We quantify the accuracy of the synthetic generation method by comparing the resulting synthetic depth map to the experimentally captured depth map with motion. Our results indicate that our framework achieves an average Boundary F1 (BF) score of 0.7192 for invalid pixels for synthetic radial motion blur, an average BF score of 0.8778 for synthetic linear motion blur, and an average BF score of 0.62 for synthetic combined radial-linear motion blur.