Digital Visual Effect

Final Project

A Global Sampling Method for Alpha Matting

Wei Sheng, Lai

R01942068

2013.06.26

(a) (b)
Figure 1. (a) Input image with foreground/background sample set. (b) Result alpha matte.

1. Project Description

In this project, we do an overall servey to recent image matting research, and implement the robust matting [1] and the global sampling matting [2]. The global sampling method consider all samples on the trimap boundary to avoid missing good samples. This method adopt a randomized algorithm "PatchMatch"[3] to efficiently produce high quality results. For alpha matte refinement, we use closed-form matting [4] and guided image filter [5]. We also evaluate our results on the alpha matting evaluation website.

2. Algorithm

2.1. Sampling Criterion

How to choose a good foregroundand background pairs is an important issue in sampling-based image matting methods. Instead of collect sampling nearby unknown pixels, the global sampling method use all samples on the trimap boundary.
(a) (b) (c)
Figure 2. Different sampling criterion. (a) Sample from nearest neighbors in image space. (b) Sample from trimap boundary locally [1]. (c) Global sampling [2].
However, a brute-force implementation will result in $O(N \cdot n_F \cdot n_B)$ time complexity (where $N$ is the number of unknown pixels, $n_F$ is the number of foreground samples, and $n_B$ is the number of background pixels), which is inefficiency to solve. Global sampling method adopt the "PatchMatch" algorithm to find a fast approximate solution in $O(N \log(n_F \cdot n_B))$ time. We briefly describe this algorithm in the follow.

The algorithm first sort all the foreground samples $F$ and background samples $B$ by intensity respectively. The two ordered set span a 2-D $FB$ search space, as illustrated in Figure 3. Each point on this 2-D space represents a sample pair $(F^i, B^j)$, and corresponds to a cost defined in Eqn (5) in [2]. The algorithm alternated between two steps: propogation and random search. For each iteration, it will update the sample pair $(F^i, B^j)$ if the new cost is lower than current cost. The random search step is visualized in Figure 3. For more detail of this algorithm, please refer to the paper [2].


Figure 3. Visualization of the random search process.

2.2. Refinement

After selecting sample pairs and estimating an initial alpha matte, we can apply a smoothing post-process to further refine the alpha matte. One of the method is to solve a global optimization problem whose smooth term is the matting Laplacian defined in closed-form matting [4]. However, this method is very slow if image size become large. Another method is to adopted the guided image filter [5], which has been proven to be a good approximation of solving the matting Laplacian and can be evaluated very fast. Since the initial alpha matte from global sampling method is often visually acceptable, applying a local filter can produce even high quality result as global optimization.

3. Result

We compare between a simple local nearest neighbor sampling method, sparse sampling of the robust matting and the global sampling method. For post-processing, we use the same parameters and the same method to build the data term and smooth term of the matting Laplacian.

(a) Input image (b) Trimap
Figure 4.
(a) Initial (b) Refine by closed-form matting (c) Refine by guided image filter
Figure 5. Results of the local nearest neighbors sampling in image space.
(a) Initial (b) Refine by closed-form matting (c) Refine by guided image filter
Figure 6. Results of the robust matting.
(a) Initial (b) Refine by closed-form matting (c) Refine by guided image filter
Figure 7. Result of the global sampling method.


We also submit our results to the alpha matting evaluation website to compare the quality between three sampling criterion we have implemented.

Table 1. Evaluation result of MSE ranking.
Table 2. Evaluation result of SAD ranking.
Table 3. Evaluation result of gradient ranking.
Table 4. Evaluation result of connectivity ranking.


We can see that the global sampling method can obtain overall better quality than other sampling methods. For more results from the dataset on the alpha matting evaluation website, please see our result page.

Reference

[1] Wang, Jue, and Michael F. Cohen. "Optimized color sampling for robust matting." Computer Vision and Pattern Recognition, 2007. IEEE Conference on. (CVPR 2007).
[2] He, Kaiming, et al. "A global sampling method for alpha matting." Computer Vision and Pattern Recognition, 2011 IEEE Conference on. (CVPR 2011)
[3] Barnes, Connelly, et al. "PatchMatch: a randomized correspondence algorithm for structural image editing." ACM Transactions on Graphics, 2009. (TOG 2009)
[4] Levin, Anat, Dani Lischinski, and Yair Weiss. "A closed-form solution to natural image matting."  IEEE Transactions on Pattern Analysis and Machine Intelligence, 2008. (TPAMI 2008)
[5] He, Kaiming, Jian Sun, and Xiaoou Tang. "Guided image filtering." Computer Vision–ECCV 2010. Springer Berlin Heidelberg, 2010. (ECCV 2010)
[6] Chuang, Yung-Yu, et al. "A bayesian approach to digital matting." Computer Vision and Pattern Recognition, 2001. IEEE Conference on. (CVPR 2001). (ECCV 2010)


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