Computational Efficiency Improvements for Image

We propose an efficient algorithm for colorization of greyscale images. As in prior work, colorization is posed as an optimization problem: a user specifies the color for a few scribbles drawn on the greyscale image and the color image is obtained by propagating color information from the scribbles to surrounding regions, while maximizing the local smoothness of colors. In this formulation, colorization is obtained by solving a large sparse linear system, which normally requires substantial computation and memory resources. Our algorithm improves the computational performance through three innovations over prior colorization implementations. First, the linear system is solved iteratively without explicitly constructing the sparse matrix, which significantly reduces the required memory. Second, we formulate each iteration in terms of integral images obtained by dynamic programming, reducing repetitive computation. Third, we use a coarse-to-fine framework, where a lower resolution subsampled image is first colorized and this low resolution color image is upsampled to initialize the colorization process for the fine level. The improvements we develop provide significant speed-up and memory savings compared to the conventional approach of solving the linear system directly using off-the-shelf sparse solvers, and allow us to colorize images with typical sizes encountered in realistic applications on typical commodity computing platforms. 1