Image Matting Using Linear Optimization

Shifeng Chen, Ming Liu, Wei Zhang, and Jianzhuang Liu


An image can be assumed to be a composite of the foreground and the background. The foreground and the background of each pixel are linearly combined in terms of this pixel’s foreground opacity (called alpha). Image matting is the process of estimating the foreground, the background and the alpha for each pixel. In this paper, we transform the ill-posed image matting problem into two over-determined linear optimization problems by introducing two medium variables and imposing smoothness constraints. Closed form solutions can be obtained from the two problems. Extensive experimental results indicate that our algorithm can generate high-quality matting results.



Figure 1. Some comparative results by the five algorithms. The first column includes two input images and two zoomed-in regions bounded by the white boxes in the input images. The results for the two images are the alpha mattes. The results for the zoomed-in parts include the alpha mattes and the composed images with blue background.



Figure 2. Quantitative evaluation of the algorithms. (a) Simulated alpha. (b) Composed image of a fire foreground, the simulated alpha, and blue background. (c) Composed image with a background taken from (e). (d) Trimap. (e) Large image to generate the background. (f) Total errors by the five algorithms.



Figure 3. Some results of alpha matte obtained by our algorithm and new composed images. From left to right: the input images, the alpha mattes, and the composed images with new background images.




Ÿ  References:

ü S. Chen, Z. Li, J. Liu, and X. Tang, “Image Matting Using Linear Optimization,” Proc. ACM Int. Conf. Multimedia (ACM MM), 2007. [pdf]