Constant Velocity 3D Convolution

We propose a novel three-dimensional (3D)-convolution method, cv3dconv, for detecting spatiotemporal features from videos. It reduces the number of sum-of-products of 3D convolution by thousands of times by assuming the constant moving velocity of the camera. We observed that a specific class of video sequences, such as those captured by an in-vehicle camera, can be well approximated with piece-wise linear movements of 2D features in the temporal dimension. Our principal finding is that the 3D kernel, represented by the constant-velocity, can be decomposed into a convolution of a 2D kernel representing the shapes and a 3D kernel representing the velocity. We derived the efficient recursive algorithm for this class of 3D convolution which is exceptionally suited for sparse data, and this parameterized decomposed representation imposes a structured regularization along the temporal direction. We experimentally verified the validity of our approximation using a controlled damsel, and we also showed the effectiveness of cv3dconv for the visual odometry estimation task using real event camera data captured in urban road scene.