Saerom Ha(1), Sojin Oh(1), Jonghee Back(1), Sung-Eui Yoon(2), Bochang Moon(1)
1GIST, South Korea 2KAIST, South Korea

We present a new outlier removal technique（离群值去除技术？） for a gradient-domain path tracing（梯度域路径跟踪？） (G-PT) that computes image gradients as well as colors. Our approach rejects gradient outliers whose estimated errors are much higher than those of the other gradients for improving reconstruction quality for the G-PT. We formulate our outlier removal problem as a least trimmed squares optimization（最小二乘优化）, which employs only a subset of gradients so that a final image can be reconstructed without including the gradient outliers（仅使用梯度的子集，这样重建的最终图像不会包含梯度异常的像素）. In addition, we design this outlier removal process so that the chosen subset of gradients maintains connectivity through gradients between pixels, preventing pixels from being isolated（选择的梯度子集在像素间保持梯度连接性，这样可以防止像素被孤立）. Lastly, the optimal number of inlier gradients is estimated to minimize our reconstruction error（估计inlier 梯度的最优数目进而最小化重建误差）. We have demonstrated that our reconstruction with robustly rejecting gradient outliers produces visually and numerically improved results, compared to the previous screened Poisson reconstruction that uses all the gradients.

Our technical contributions to remove the outliers are summarized as the following:
1. We formulate our robust reconstruction using a least trimmed squares (LTS) so that the screened Poisson reconstruction can be performed with only a subset of gradients, instead of all gradients.
2. We propose to predict gradient outliers within LTS based on an actual error that is independent from a particular reconstruction, accelerating our outlier detection process.
3. We further improve reconstruction quality by preserving the connectivity, i.e., information flow, through gradients between pixels, while minimizing reconstruction errors during our outlier trimming process. This is achieved efficiently by utilizing a minimum spanning tree.
4. An optimal trimming parameter that controls how many gradients are used in the LTS is estimated.

In this paper, we have proposed a novel technique that rejects gradient outliers to minimize visual artifacts generated by erroneous gradients for the gradient-domain path tracing [KMA15]. Removing outliers in a reconstruction stage has been a well-known problem in rendering, but the previous outlier removal techniques focused on only color outliers. Our technique can be considered a new technical attempt to reject gradient outliers, which introduces an additional technical challenge (e.g., consideration of connectivity between pixels). Our approach that removes gradient outliers is formulated with a least trimmed squares (LTS) and the LTS is efficiently performed based on estimated actual errors instead of residual errors. In addition, we add a novel constraint formed by MST into the LTS, in order to resolve the connectivity issue. We have demonstrated that robustly handling gradient outliers in a reconstruction stage can be a new route to improve performance of the gradient-domain rendering.