Find Outliers of Image Edge Consistency by Weighted Local Linear Regression with Equality Constraints

In this paper, we propose a general method to detect outliers from contaminated estimates of various image estimation applications. The method does not require any prior knowledge about the purpose, theory or hardware of the application but simply relies on the law of edge consistency between sources and estimates. The method is termed as ALRe (anchored linear residual) because it is based on the residual of weighted local linear regression with an equality constraint exerted on the measured pixel. Given a pair of source and contaminated estimate, ALRe offers per-pixel outlier likelihoods, which can be used to compose the data weights of post-refinement algorithms, improving the quality of refined estimate. ALRe has the features of asymmetry, no false positive and linear complexity. Its effectiveness is verified on four applications, four post-refinement algorithms and three datasets. It demonstrates that, with the help of ALRe, refined estimates are better in the aspects of both quality and edge consistency. The results are even comparable to model-based and hardware-based methods. Accuracy comparison on synthetic images shows that ALRe could detect outliers reliably. It is as effective as the mainstream weighted median filter at spike detection and is significantly better at bad region detection.