High Dimensional Convolution Acceleration via Tensor Decomposition

Abstract

The high-dimensional convolution, in either linear or nonlinear form, has been employed in a wide range of computer vision solutions due to its beneficial smoothing property. However, its full-kernel implementation is extremely slow. We do need a fast algorithm for this important operation. To solve this problem, we propose an acceleration pipeline assembled by three steps: [Formula: see text]-D nonlinear convolution [Formula: see text] [Formula: see text]-D linear convolution [Formula: see text] 1-D dimensional convolution [Formula: see text] 1-D recursive box filter. Thanks to the low computational complexity of box filtering, we speed up the computation significantly. Roughly speaking, our contribution is two-fold: (1) establishing the connection between the high-dimensional convolution acceleration algorithm and tensor decomposition; (2) propose total four acceleration technologies including demultiplexing–blurring–multiplexing framework, convolution decomposition, periodic tensorization and recursively box filtering to compose our acceleration pipeline under the line of the above connection. The effectiveness of these techniques is demonstrated in various comparisons and experiments. The running times of various applications are largely shortened from several minutes to fewer seconds or less.